TSTP Solution File: SYN548+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN548+1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:56:22 EDT 2022
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN548+1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 05:36:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(reachable_type, type, (
% 0.20/0.42 reachable: ( $i * $i ) > $o)).
% 0.20/0.42 tff(tptp_fun_V_2_type, type, (
% 0.20/0.42 tptp_fun_V_2: $i > $i)).
% 0.20/0.42 tff(tptp_fun_W_3_type, type, (
% 0.20/0.42 tptp_fun_W_3: $i > $i)).
% 0.20/0.42 tff(initial_world_type, type, (
% 0.20/0.42 initial_world: $i)).
% 0.20/0.42 tff(tptp_fun_Y_0_type, type, (
% 0.20/0.42 tptp_fun_Y_0: $i > $i)).
% 0.20/0.42 tff(tptp_fun_Z_1_type, type, (
% 0.20/0.42 tptp_fun_Z_1: $i > $i)).
% 0.20/0.42 tff(q_type, type, (
% 0.20/0.42 q: $i > $o)).
% 0.20/0.42 tff(p_type, type, (
% 0.20/0.42 p: $i > $o)).
% 0.20/0.42 tff(tptp_fun_W_4_type, type, (
% 0.20/0.42 tptp_fun_W_4: $i > $i)).
% 0.20/0.42 tff(1,plain,
% 0.20/0.42 (^[X: $i] : refl(reachable(X, X) <=> reachable(X, X))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (![X: $i] : reachable(X, X) <=> ![X: $i] : reachable(X, X)),
% 0.20/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (![X: $i] : reachable(X, X) <=> ![X: $i] : reachable(X, X)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(4,axiom,(![X: $i] : reachable(X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity_of_reachable')).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (![X: $i] : reachable(X, X)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.42 tff(6,plain,(
% 0.20/0.42 ![X: $i] : reachable(X, X)),
% 0.20/0.42 inference(skolemize,[status(sab)],[5])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (![X: $i] : reachable(X, X)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 ((~![X: $i] : reachable(X, X)) | reachable(initial_world, initial_world)),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (reachable(initial_world, initial_world)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (^[X: $i] : rewrite(((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))))))) <=> ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))))))) <=> ![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (^[X: $i] : refl(((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))))))) <=> ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))))))) <=> ![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (^[X: $i] : rewrite(((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))))))) <=> ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))))))) <=> ![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))))))) <=> ![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[15, 13])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (^[X: $i] : rewrite(((~reachable(initial_world, X)) | (reachable(X, tptp_fun_Y_0(X)) & (![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W)))) & (((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))) | ((~p(tptp_fun_Z_1(X))) & reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))))) <=> ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (![X: $i] : ((~reachable(initial_world, X)) | (reachable(X, tptp_fun_Y_0(X)) & (![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W)))) & (((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))) | ((~p(tptp_fun_Z_1(X))) & reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))))) <=> ![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (^[X: $i] : rewrite(((~reachable(initial_world, X)) | ((~(~reachable(X, tptp_fun_Y_0(X)))) & ((![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) & (((~p(tptp_fun_Z_1(X))) & (~(~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)))) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))) | ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))))))) <=> ((~reachable(initial_world, X)) | (reachable(X, tptp_fun_Y_0(X)) & (![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W)))) & (((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))) | ((~p(tptp_fun_Z_1(X))) & reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (![X: $i] : ((~reachable(initial_world, X)) | ((~(~reachable(X, tptp_fun_Y_0(X)))) & ((![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) & (((~p(tptp_fun_Z_1(X))) & (~(~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)))) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))) | ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))))))) <=> ![X: $i] : ((~reachable(initial_world, X)) | (reachable(X, tptp_fun_Y_0(X)) & (![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W)))) & (((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))) | ((~p(tptp_fun_Z_1(X))) & reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 ((~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W)))))))) <=> (~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 ((~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : (reachable(X, Y) => (![Z: $i] : (reachable(Y, Z) => (p(Z) | ![V: $i] : (reachable(Z, V) => q(V)))) <=> (![W: $i] : (reachable(Y, W) => p(W)) | ![W: $i] : (reachable(Y, W) => q(W))))))) <=> (~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(23,axiom,(~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : (reachable(X, Y) => (![Z: $i] : (reachable(Y, Z) => (p(Z) | ![V: $i] : (reachable(Z, V) => q(V)))) <=> (![W: $i] : (reachable(Y, W) => p(W)) | ![W: $i] : (reachable(Y, W) => q(W))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (^[X: $i] : nnf_neg(refl($oeq((~reachable(initial_world, X)), (~reachable(initial_world, X)))), trans(sk($oeq((~![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W))))))), (~((~reachable(X, tptp_fun_Y_0(X))) | (![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))))), nnf_neg(refl($oeq((~(~reachable(X, tptp_fun_Y_0(X)))), (~(~reachable(X, tptp_fun_Y_0(X)))))), nnf_neg(nnf_pos(proof_bind(^[Z: $i] : monotonicity(refl($oeq(p(Z), p(Z))), refl($oeq((~reachable(tptp_fun_Y_0(X), Z)), (~reachable(tptp_fun_Y_0(X), Z)))), nnf_pos(proof_bind(^[V: $i] : refl($oeq((q(V) | (~reachable(Z, V))), (q(V) | (~reachable(Z, V)))))), $oeq(![V: $i] : (q(V) | (~reachable(Z, V))), ![V: $i] : (q(V) | (~reachable(Z, V))))), $oeq((p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))), (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))))), $oeq(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))), ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))), trans(sk($oeq((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))), (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(X), V))))))), nnf_neg(refl($oeq((~p(tptp_fun_Z_1(X))), (~p(tptp_fun_Z_1(X))))), refl($oeq((~(~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)))), (~(~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)))))), sk($oeq((~![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(X), V)))), (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))), $oeq((~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(X), V))))), ((~p(tptp_fun_Z_1(X))) & (~(~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)))) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))))), $oeq((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))), ((~p(tptp_fun_Z_1(X))) & (~(~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)))) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))))), monotonicity(nnf_pos(proof_bind(^[W: $i] : refl($oeq((p(W) | (~reachable(tptp_fun_Y_0(X), W))), (p(W) | (~reachable(tptp_fun_Y_0(X), W)))))), $oeq(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))), ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))))), nnf_pos(proof_bind(^[W: $i] : refl($oeq((q(W) | (~reachable(tptp_fun_Y_0(X), W))), (q(W) | (~reachable(tptp_fun_Y_0(X), W)))))), $oeq(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))), ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))), $oeq((![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W)))), (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W)))))), nnf_neg(sk($oeq((~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W)))), (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))))), sk($oeq((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W)))), (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))), $oeq((~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))), ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))))), $oeq((~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W)))))), ((![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) & (((~p(tptp_fun_Z_1(X))) & (~(~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)))) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))) | ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))))))), $oeq((~((~reachable(X, tptp_fun_Y_0(X))) | (![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))), ((~(~reachable(X, tptp_fun_Y_0(X)))) & ((![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) & (((~p(tptp_fun_Z_1(X))) & (~(~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)))) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))) | ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))))))), $oeq((~![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W))))))), ((~(~reachable(X, tptp_fun_Y_0(X)))) & ((![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) & (((~p(tptp_fun_Z_1(X))) & (~(~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)))) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))) | ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))))))), $oeq((~(reachable(initial_world, X) & ![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W)))))))), ((~reachable(initial_world, X)) | ((~(~reachable(X, tptp_fun_Y_0(X)))) & ((![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) & (((~p(tptp_fun_Z_1(X))) & (~(~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)))) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))) | ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(32,plain,(
% 0.20/0.43 ![X: $i] : ((~reachable(initial_world, X)) | ((~(~reachable(X, tptp_fun_Y_0(X)))) & ((![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) & (((~p(tptp_fun_Z_1(X))) & (~(~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)))) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))) | ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))))))),
% 0.20/0.43 inference(nnf-neg,[status(sab)],[30, 31])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 (![X: $i] : ((~reachable(initial_world, X)) | (reachable(X, tptp_fun_Y_0(X)) & (![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W)))) & (((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))) | ((~p(tptp_fun_Z_1(X))) & reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[32, 20])).
% 0.20/0.43 tff(34,plain,
% 0.20/0.43 (![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[33, 18])).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 (![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[34, 16])).
% 0.20/0.43 tff(36,plain,
% 0.20/0.43 (![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[35, 11])).
% 0.20/0.43 tff(37,plain,
% 0.20/0.43 (((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))))) | ((~reachable(initial_world, initial_world)) | (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world)))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world)))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))))))))) <=> ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))))) | (~reachable(initial_world, initial_world)) | (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world)))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world)))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 (((~reachable(initial_world, initial_world)) | (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~(p(tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))))) | (~(p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))))))) <=> ((~reachable(initial_world, initial_world)) | (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world)))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world)))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 (((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))))) | ((~reachable(initial_world, initial_world)) | (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~(p(tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))))) | (~(p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))))))))) <=> ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))))) | ((~reachable(initial_world, initial_world)) | (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world)))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world)))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.43 tff(40,plain,
% 0.20/0.43 (((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))))) | ((~reachable(initial_world, initial_world)) | (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~(p(tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))))) | (~(p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))))))))) <=> ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))))) | (~reachable(initial_world, initial_world)) | (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world)))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world)))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[39, 37])).
% 0.20/0.43 tff(41,plain,
% 0.20/0.43 ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))))) | ((~reachable(initial_world, initial_world)) | (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~(p(tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))))) | (~(p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))))) | (~reachable(initial_world, initial_world)) | (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world)))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world)))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world)))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world)))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[42, 36, 9])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 (((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world)))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world)))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))))) | (![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 (![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.20/0.44 tff(46,assumption,(~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))), introduced(assumption)).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 (((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world)))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world)))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))))) | ((~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world)))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world)))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 ((~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world)))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[47, 43])).
% 0.20/0.44 tff(49,assumption,(~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world)))), introduced(assumption)).
% 0.20/0.44 tff(50,plain,
% 0.20/0.44 (((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world))) | reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 (reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 (((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(53,plain,
% 0.20/0.44 (reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[52, 49])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(55,plain,
% 0.20/0.44 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((reachable(X, Y) & reachable(Y, Z)) <=> (~((~reachable(Y, Z)) | (~reachable(X, Y))))), ((~(reachable(X, Y) & reachable(Y, Z))) <=> (~(~((~reachable(Y, Z)) | (~reachable(X, Y))))))), rewrite((~(~((~reachable(Y, Z)) | (~reachable(X, Y))))) <=> ((~reachable(Y, Z)) | (~reachable(X, Y)))), ((~(reachable(X, Y) & reachable(Y, Z))) <=> ((~reachable(Y, Z)) | (~reachable(X, Y))))), (((~(reachable(X, Y) & reachable(Y, Z))) | reachable(X, Z)) <=> (((~reachable(Y, Z)) | (~reachable(X, Y))) | reachable(X, Z)))), rewrite((((~reachable(Y, Z)) | (~reachable(X, Y))) | reachable(X, Z)) <=> (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))), (((~(reachable(X, Y) & reachable(Y, Z))) | reachable(X, Z)) <=> (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : ((~(reachable(X, Y) & reachable(Y, Z))) | reachable(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.44 tff(57,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : ((~(reachable(X, Y) & reachable(Y, Z))) | reachable(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(reachable(X, Y) & reachable(Y, Z))) | reachable(X, Z))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (^[X: $i, Y: $i, Z: $i] : rewrite(((reachable(X, Y) & reachable(Y, Z)) => reachable(X, Z)) <=> ((~(reachable(X, Y) & reachable(Y, Z))) | reachable(X, Z)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : ((reachable(X, Y) & reachable(Y, Z)) => reachable(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(reachable(X, Y) & reachable(Y, Z))) | reachable(X, Z))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.44 tff(60,axiom,(![X: $i, Y: $i, Z: $i] : ((reachable(X, Y) & reachable(Y, Z)) => reachable(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','transitivity_of_reachable')).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : ((~(reachable(X, Y) & reachable(Y, Z))) | reachable(X, Z))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.44 tff(62,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : ((~(reachable(X, Y) & reachable(Y, Z))) | reachable(X, Z))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.20/0.44 tff(63,plain,(
% 0.20/0.44 ![X: $i, Y: $i, Z: $i] : ((~(reachable(X, Y) & reachable(Y, Z))) | reachable(X, Z))),
% 0.20/0.44 inference(skolemize,[status(sab)],[62])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.20/0.44 tff(65,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world)))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(67,plain,
% 0.20/0.44 ((reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world)))) <=> ((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(68,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[67])).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[68, 66])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 (reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[71, 65, 53, 51])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 (((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world))) | (~p(tptp_fun_Z_1(initial_world)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 (~p(tptp_fun_Z_1(initial_world))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[73, 49])).
% 0.20/0.44 tff(75,assumption,(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))), introduced(assumption)).
% 0.20/0.44 tff(76,assumption,(~p(tptp_fun_Z_1(initial_world))), introduced(assumption)).
% 0.20/0.44 tff(77,assumption,(reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))), introduced(assumption)).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 (((~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | (p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))) <=> ((~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 ((~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | (p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 ((~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[80, 77, 76, 75])).
% 0.20/0.44 tff(82,plain,((~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | p(tptp_fun_Z_1(initial_world))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 (~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[82, 53, 74])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 ((~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 (![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[84, 83, 46, 45])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 (((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world))) | (~q(tptp_fun_V_2(initial_world)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 (~q(tptp_fun_V_2(initial_world))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[86, 49])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 (((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | (q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world))))) <=> ((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 ((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | (q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 ((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[90, 87, 85, 72])).
% 0.20/0.44 tff(92,plain,(((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 ((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[92, 46])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 ((~((~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world)))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world)))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[94, 93, 48])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 (((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 (reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.20/0.44 tff(98,plain,
% 0.20/0.44 (((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world))) | (~q(tptp_fun_W_4(initial_world)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 (~q(tptp_fun_W_4(initial_world))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[98, 95])).
% 0.20/0.44 tff(100,assumption,(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))), introduced(assumption)).
% 0.20/0.44 tff(101,assumption,(reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))), introduced(assumption)).
% 0.20/0.44 tff(102,assumption,(~q(tptp_fun_W_4(initial_world))), introduced(assumption)).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 (((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | (q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))))) <=> ((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 ((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | (q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 ((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[105, 102, 101, 100])).
% 0.20/0.44 tff(107,plain,((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 (~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[107, 99, 97])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[84, 108, 46, 45])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 (((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world))) | (~p(tptp_fun_W_3(initial_world)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 (~p(tptp_fun_W_3(initial_world))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[110, 95])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 (((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 (reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[112, 95])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 (((~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | (p(tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))))) <=> ((~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | p(tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(115,plain,
% 0.20/0.45 ((~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | (p(tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(116,plain,
% 0.20/0.45 ((~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | p(tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.45 tff(117,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[116, 113, 111, 109])).
% 0.20/0.45 tff(118,plain,(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(119,plain,
% 0.20/0.45 (((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | (p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V))))) <=> ((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(120,plain,
% 0.20/0.45 ((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | (p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(121,plain,
% 0.20/0.45 ((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.20/0.45 tff(122,plain,
% 0.20/0.45 (![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[121, 53, 74, 118])).
% 0.20/0.45 tff(123,plain,
% 0.20/0.45 (((~![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V)))) | (q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))))) <=> ((~![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V)))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(124,plain,
% 0.20/0.45 ((~![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V)))) | (q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(125,plain,
% 0.20/0.45 ((~![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V)))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.45 tff(126,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[125, 87, 51, 122])).
% 0.20/0.45 tff(127,plain,((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(128,plain,
% 0.20/0.45 ((~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world)))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[94, 48])).
% 0.20/0.45 tff(129,plain,
% 0.20/0.45 (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.20/0.45 tff(130,plain,
% 0.20/0.45 (reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[112, 129])).
% 0.20/0.45 tff(131,plain,
% 0.20/0.45 (((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | p(tptp_fun_W_3(initial_world)))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | p(tptp_fun_Z_1(initial_world)))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))))) | reachable(initial_world, tptp_fun_Y_0(initial_world))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(132,plain,
% 0.20/0.45 (reachable(initial_world, tptp_fun_Y_0(initial_world))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[131, 43])).
% 0.20/0.45 tff(133,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))) | reachable(initial_world, tptp_fun_W_3(initial_world)))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))) | reachable(initial_world, tptp_fun_W_3(initial_world)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(134,plain,
% 0.20/0.45 ((reachable(initial_world, tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world)))) <=> ((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))) | reachable(initial_world, tptp_fun_W_3(initial_world)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(135,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(initial_world, tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))) | reachable(initial_world, tptp_fun_W_3(initial_world))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[134])).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(initial_world, tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))) | reachable(initial_world, tptp_fun_W_3(initial_world)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[135, 133])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(initial_world, tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))) | reachable(initial_world, tptp_fun_W_3(initial_world))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 (reachable(initial_world, tptp_fun_W_3(initial_world))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[138, 65, 132, 130])).
% 0.20/0.45 tff(140,plain,
% 0.20/0.45 (((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))))) | ((~reachable(initial_world, tptp_fun_W_3(initial_world))) | (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) <=> ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))))) | (~reachable(initial_world, tptp_fun_W_3(initial_world))) | (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 (((~reachable(initial_world, tptp_fun_W_3(initial_world))) | (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~(p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W)))))))) <=> ((~reachable(initial_world, tptp_fun_W_3(initial_world))) | (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 (((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))))) | ((~reachable(initial_world, tptp_fun_W_3(initial_world))) | (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~(p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))))))))) <=> ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))))) | ((~reachable(initial_world, tptp_fun_W_3(initial_world))) | (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[141])).
% 0.20/0.45 tff(143,plain,
% 0.20/0.45 (((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))))) | ((~reachable(initial_world, tptp_fun_W_3(initial_world))) | (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~(p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))))))))) <=> ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))))) | (~reachable(initial_world, tptp_fun_W_3(initial_world))) | (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[142, 140])).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))))) | ((~reachable(initial_world, tptp_fun_W_3(initial_world))) | (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~(p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(145,plain,
% 0.20/0.45 ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))) | (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))) | (~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))))) | (~reachable(initial_world, tptp_fun_W_3(initial_world))) | (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[145, 36, 139])).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 (((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))))) | ((~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(148,plain,
% 0.20/0.45 ((~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.20/0.45 tff(149,assumption,(~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))), introduced(assumption)).
% 0.20/0.45 tff(150,plain,
% 0.20/0.45 (((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world))))) | (~q(tptp_fun_W_4(tptp_fun_W_3(initial_world))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(151,plain,
% 0.20/0.45 (~q(tptp_fun_W_4(tptp_fun_W_3(initial_world)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.20/0.45 tff(152,plain,
% 0.20/0.45 (~p(tptp_fun_W_3(initial_world))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[110, 129])).
% 0.20/0.45 tff(153,plain,
% 0.20/0.45 (((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | (p(tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V))))) <=> ((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | p(tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(154,plain,
% 0.20/0.45 ((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | (p(tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(155,plain,
% 0.20/0.45 ((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | p(tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.20/0.45 tff(156,plain,
% 0.20/0.45 (![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[155, 130, 152, 118])).
% 0.20/0.45 tff(157,plain,
% 0.20/0.45 (((~![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))) | (q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))) <=> ((~![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(158,plain,
% 0.20/0.45 ((~![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))) | (q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(159,plain,
% 0.20/0.45 ((~![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.20/0.45 tff(160,plain,
% 0.20/0.45 (~reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[159, 156, 151])).
% 0.20/0.45 tff(161,plain,
% 0.20/0.45 (((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world))))) | reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(162,plain,
% 0.20/0.45 (reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[161, 149])).
% 0.20/0.45 tff(163,plain,
% 0.20/0.45 (((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(164,plain,
% 0.20/0.45 (reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[163, 146])).
% 0.20/0.45 tff(165,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(166,plain,
% 0.20/0.46 ((reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world))))) <=> ((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(167,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[166])).
% 0.20/0.46 tff(168,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[167, 165])).
% 0.20/0.46 tff(169,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(170,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.20/0.46 tff(171,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[170, 65, 164, 162, 160])).
% 0.20/0.46 tff(172,plain,((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(173,plain,
% 0.20/0.46 ((~((~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world)))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(174,plain,
% 0.20/0.46 (~(p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[173, 172, 148])).
% 0.20/0.46 tff(175,plain,
% 0.20/0.46 ((p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(176,plain,
% 0.20/0.46 (reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.20/0.46 tff(177,plain,
% 0.20/0.46 ((p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(178,plain,
% 0.20/0.46 (reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[177, 174])).
% 0.20/0.46 tff(179,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(180,plain,
% 0.20/0.46 ((reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world))))) <=> ((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(181,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[180])).
% 0.20/0.46 tff(182,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[181, 179])).
% 0.20/0.46 tff(183,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(184,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.20/0.46 tff(185,plain,
% 0.20/0.46 (reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[184, 65, 178, 176])).
% 0.20/0.46 tff(186,plain,
% 0.20/0.46 ((p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | (~q(tptp_fun_V_2(tptp_fun_W_3(initial_world))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(187,plain,
% 0.20/0.46 (~q(tptp_fun_V_2(tptp_fun_W_3(initial_world)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[186, 174])).
% 0.20/0.46 tff(188,plain,
% 0.20/0.46 (((~![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))) | (q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world)))))) <=> ((~![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(189,plain,
% 0.20/0.46 ((~![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))) | (q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(190,plain,
% 0.20/0.46 ((~![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.20/0.46 tff(191,plain,
% 0.20/0.46 (~reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[190, 156, 187])).
% 0.20/0.46 tff(192,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(193,plain,
% 0.20/0.46 ((reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world))))) <=> ((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(194,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[193])).
% 0.20/0.46 tff(195,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[194, 192])).
% 0.20/0.46 tff(196,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(197,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.20/0.46 tff(198,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[197, 65, 164, 191, 185])).
% 0.20/0.46 % SZS output end Proof
%------------------------------------------------------------------------------