TSTP Solution File: SEU406+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU406+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 : Tue Sep 20 07:29:22 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU406+1 : TPTP v8.1.0. Released v3.4.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 13:25:10 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.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(k2_xboole_0_type, type, (
% 0.13/0.40 k2_xboole_0: ( $i * $i ) > $i)).
% 0.13/0.40 tff(k4_xboole_0_type, type, (
% 0.13/0.40 k4_xboole_0: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_D_0_type, type, (
% 0.13/0.40 tptp_fun_D_0: $i)).
% 0.13/0.40 tff(tptp_fun_C_1_type, type, (
% 0.13/0.40 tptp_fun_C_1: $i)).
% 0.13/0.40 tff(r2_hidden_type, type, (
% 0.13/0.40 r2_hidden: ( $i * $i ) > $o)).
% 0.13/0.40 tff(tptp_fun_B_2_type, type, (
% 0.13/0.40 tptp_fun_B_2: $i)).
% 0.13/0.40 tff(tptp_fun_D_4_type, type, (
% 0.13/0.40 tptp_fun_D_4: ( $i * $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_A_3_type, type, (
% 0.13/0.40 tptp_fun_A_3: $i)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (^[A: $i, B: $i] : refl((k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B)) <=> (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B)) <=> ![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B)) <=> ![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(4,axiom,(![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t39_xboole_1')).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.40 tff(6,plain,(
% 0.13/0.40 ![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B))),
% 0.13/0.40 inference(skolemize,[status(sab)],[5])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B))) | (k2_xboole_0(D!0, k4_xboole_0(C!1, D!0)) = k2_xboole_0(D!0, C!1))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (k2_xboole_0(D!0, k4_xboole_0(C!1, D!0)) = k2_xboole_0(D!0, C!1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0))),
% 0.13/0.40 inference(symmetry,[status(thm)],[9])).
% 0.13/0.40 tff(11,assumption,((~((~(k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0)))) | (r2_hidden(B!2, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(B!2, k4_xboole_0(C!1, D!0)) | r2_hidden(B!2, D!0))))) | (~((k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0))) | ((~r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), k2_xboole_0(D!0, C!1))) <=> (r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), k4_xboole_0(C!1, D!0)) | r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), D!0)))))), introduced(assumption)).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))))) <=> (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))))),
% 0.13/0.40 inference(pull_quant,[status(thm)],[])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A)))) <=> ![D: $i] : ((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))), ((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) <=> (~![D: $i] : ((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))))), pull_quant((~![D: $i] : ((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) <=> ?[D: $i] : (~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A)))))), ((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) <=> ?[D: $i] : (~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))))), (((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))) <=> (?[D: $i] : (~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))))), pull_quant((?[D: $i] : (~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))) <=> ?[D: $i] : ((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))))), (((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))) <=> ?[D: $i] : ((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))))), ((~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))))) <=> (~?[D: $i] : ((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))))))), pull_quant((~?[D: $i] : ((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))))) <=> ![D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))))), ((~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))))) <=> ![D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[16, 14])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[17, 13])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))))) <=> (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[20, 18])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A)))) <=> ((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))), ((((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A)))) & ((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))) <=> (((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A)))) & ((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))))), rewrite((((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A)))) & ((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))) <=> (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))))), ((((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A)))) & ((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))) <=> (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : (((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A)))) & ((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A)))) & ((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_4(C, B, A), C) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))) <=> (((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A)))) & ((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : (((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A)))) & ((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_4(C, B, A), C) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A)))) & ((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[24])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 (![A: $i, B: $i, C: $i] : ((C = k2_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A)))) <=> ![A: $i, B: $i, C: $i] : ((C = k2_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 (^[A: $i, B: $i, C: $i] : rewrite(((C = k2_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B)))) <=> ((C = k2_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(28,plain,
% 0.13/0.41 (![A: $i, B: $i, C: $i] : ((C = k2_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = k2_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.13/0.41 tff(29,axiom,(![A: $i, B: $i, C: $i] : ((C = k2_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_xboole_0')).
% 0.13/0.41 tff(30,plain,
% 0.13/0.41 (![A: $i, B: $i, C: $i] : ((C = k2_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.13/0.41 tff(31,plain,
% 0.13/0.41 (![A: $i, B: $i, C: $i] : ((C = k2_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.13/0.41 tff(32,plain,(
% 0.13/0.41 ![A: $i, B: $i, C: $i] : (((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A)))) & ((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_4(C, B, A), C) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A))))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[31])).
% 0.13/0.41 tff(33,plain,
% 0.13/0.41 (![A: $i, B: $i, C: $i] : (((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A)))) & ((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.13/0.41 tff(34,plain,
% 0.13/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[33, 23])).
% 0.13/0.41 tff(35,plain,
% 0.13/0.41 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[34, 21])).
% 0.13/0.41 tff(36,plain,
% 0.13/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))))) | (~((~((~(k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0)))) | (r2_hidden(B!2, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(B!2, k4_xboole_0(C!1, D!0)) | r2_hidden(B!2, D!0))))) | (~((k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0))) | ((~r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), k2_xboole_0(D!0, C!1))) <=> (r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), k4_xboole_0(C!1, D!0)) | r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), D!0)))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(37,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[36, 35, 11])).
% 0.13/0.41 tff(38,plain,(~((~((~(k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0)))) | (r2_hidden(B!2, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(B!2, k4_xboole_0(C!1, D!0)) | r2_hidden(B!2, D!0))))) | (~((k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0))) | ((~r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), k2_xboole_0(D!0, C!1))) <=> (r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), k4_xboole_0(C!1, D!0)) | r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), D!0))))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(39,plain,
% 0.13/0.41 (((~((~(k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0)))) | (r2_hidden(B!2, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(B!2, k4_xboole_0(C!1, D!0)) | r2_hidden(B!2, D!0))))) | (~((k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0))) | ((~r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), k2_xboole_0(D!0, C!1))) <=> (r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), k4_xboole_0(C!1, D!0)) | r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), D!0)))))) | ((~(k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0)))) | (r2_hidden(B!2, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(B!2, k4_xboole_0(C!1, D!0)) | r2_hidden(B!2, D!0))))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(40,plain,
% 0.13/0.41 ((~(k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0)))) | (r2_hidden(B!2, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(B!2, k4_xboole_0(C!1, D!0)) | r2_hidden(B!2, D!0)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.13/0.41 tff(41,plain,
% 0.13/0.41 ((~((~(k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0)))) | (r2_hidden(B!2, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(B!2, k4_xboole_0(C!1, D!0)) | r2_hidden(B!2, D!0))))) | (~(k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0)))) | (r2_hidden(B!2, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(B!2, k4_xboole_0(C!1, D!0)) | r2_hidden(B!2, D!0)))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(42,plain,
% 0.13/0.41 (r2_hidden(B!2, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(B!2, k4_xboole_0(C!1, D!0)) | r2_hidden(B!2, D!0))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[41, 10, 40])).
% 0.13/0.41 tff(43,plain,
% 0.13/0.41 (^[A: $i, B: $i] : refl((k2_xboole_0(A, B) = k2_xboole_0(B, A)) <=> (k2_xboole_0(A, B) = k2_xboole_0(B, A)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(44,plain,
% 0.13/0.41 (![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[43])).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 (![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(46,axiom,(![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 (![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.13/0.41 tff(48,plain,(
% 0.13/0.41 ![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A))),
% 0.13/0.41 inference(skolemize,[status(sab)],[47])).
% 0.13/0.41 tff(49,plain,
% 0.13/0.41 (![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 ((~![A: $i, B: $i] : (k2_xboole_0(A, B) = k2_xboole_0(B, A))) | (k2_xboole_0(C!1, D!0) = k2_xboole_0(D!0, C!1))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(51,plain,
% 0.13/0.41 (k2_xboole_0(C!1, D!0) = k2_xboole_0(D!0, C!1)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 (k2_xboole_0(D!0, C!1) = k2_xboole_0(C!1, D!0)),
% 0.13/0.41 inference(symmetry,[status(thm)],[51])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 (r2_hidden(B!2, k2_xboole_0(D!0, C!1)) <=> r2_hidden(B!2, k2_xboole_0(C!1, D!0))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[52])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 (r2_hidden(B!2, k2_xboole_0(C!1, D!0)) <=> r2_hidden(B!2, k2_xboole_0(D!0, C!1))),
% 0.13/0.41 inference(symmetry,[status(thm)],[53])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 ((~(~(r2_hidden(A!3, k2_xboole_0(C!1, D!0)) & r2_hidden(B!2, k2_xboole_0(C!1, D!0)) & (~(r2_hidden(A!3, k4_xboole_0(C!1, D!0)) & r2_hidden(B!2, k4_xboole_0(C!1, D!0)))) & (~(r2_hidden(A!3, D!0) & r2_hidden(B!2, D!0))) & (~(r2_hidden(A!3, k4_xboole_0(C!1, D!0)) & r2_hidden(B!2, D!0))) & (~(r2_hidden(A!3, D!0) & r2_hidden(B!2, k4_xboole_0(C!1, D!0))))))) <=> (r2_hidden(A!3, k2_xboole_0(C!1, D!0)) & r2_hidden(B!2, k2_xboole_0(C!1, D!0)) & (~(r2_hidden(A!3, k4_xboole_0(C!1, D!0)) & r2_hidden(B!2, k4_xboole_0(C!1, D!0)))) & (~(r2_hidden(A!3, D!0) & r2_hidden(B!2, D!0))) & (~(r2_hidden(A!3, k4_xboole_0(C!1, D!0)) & r2_hidden(B!2, D!0))) & (~(r2_hidden(A!3, D!0) & r2_hidden(B!2, k4_xboole_0(C!1, D!0)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(56,plain,
% 0.13/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~(r2_hidden(A, k2_xboole_0(C, D)) & r2_hidden(B, k2_xboole_0(C, D)) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, k4_xboole_0(C, D)))) & (~(r2_hidden(A, D) & r2_hidden(B, D))) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, D))) & (~(r2_hidden(A, D) & r2_hidden(B, k4_xboole_0(C, D))))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (~(r2_hidden(A, k2_xboole_0(C, D)) & r2_hidden(B, k2_xboole_0(C, D)) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, k4_xboole_0(C, D)))) & (~(r2_hidden(A, D) & r2_hidden(B, D))) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, D))) & (~(r2_hidden(A, D) & r2_hidden(B, k4_xboole_0(C, D)))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(57,plain,
% 0.13/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((((r2_hidden(A, k2_xboole_0(C, D)) & r2_hidden(B, k2_xboole_0(C, D))) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, k4_xboole_0(C, D))))) & (~(r2_hidden(A, D) & r2_hidden(B, D)))) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, D)))) & (~(r2_hidden(A, D) & r2_hidden(B, k4_xboole_0(C, D))))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (~(r2_hidden(A, k2_xboole_0(C, D)) & r2_hidden(B, k2_xboole_0(C, D)) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, k4_xboole_0(C, D)))) & (~(r2_hidden(A, D) & r2_hidden(B, D))) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, D))) & (~(r2_hidden(A, D) & r2_hidden(B, k4_xboole_0(C, D)))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(58,axiom,(~![A: $i, B: $i, C: $i, D: $i] : (~(((((r2_hidden(A, k2_xboole_0(C, D)) & r2_hidden(B, k2_xboole_0(C, D))) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, k4_xboole_0(C, D))))) & (~(r2_hidden(A, D) & r2_hidden(B, D)))) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, D)))) & (~(r2_hidden(A, D) & r2_hidden(B, k4_xboole_0(C, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_latsum_1')).
% 0.13/0.41 tff(59,plain,
% 0.13/0.41 (~![A: $i, B: $i, C: $i, D: $i] : (~(r2_hidden(A, k2_xboole_0(C, D)) & r2_hidden(B, k2_xboole_0(C, D)) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, k4_xboole_0(C, D)))) & (~(r2_hidden(A, D) & r2_hidden(B, D))) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, D))) & (~(r2_hidden(A, D) & r2_hidden(B, k4_xboole_0(C, D))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.13/0.41 tff(60,plain,
% 0.13/0.41 (~![A: $i, B: $i, C: $i, D: $i] : (~(r2_hidden(A, k2_xboole_0(C, D)) & r2_hidden(B, k2_xboole_0(C, D)) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, k4_xboole_0(C, D)))) & (~(r2_hidden(A, D) & r2_hidden(B, D))) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, D))) & (~(r2_hidden(A, D) & r2_hidden(B, k4_xboole_0(C, D))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[59, 56])).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 (~![A: $i, B: $i, C: $i, D: $i] : (~(r2_hidden(A, k2_xboole_0(C, D)) & r2_hidden(B, k2_xboole_0(C, D)) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, k4_xboole_0(C, D)))) & (~(r2_hidden(A, D) & r2_hidden(B, D))) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, D))) & (~(r2_hidden(A, D) & r2_hidden(B, k4_xboole_0(C, D))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 (~![A: $i, B: $i, C: $i, D: $i] : (~(r2_hidden(A, k2_xboole_0(C, D)) & r2_hidden(B, k2_xboole_0(C, D)) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, k4_xboole_0(C, D)))) & (~(r2_hidden(A, D) & r2_hidden(B, D))) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, D))) & (~(r2_hidden(A, D) & r2_hidden(B, k4_xboole_0(C, D))))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[61, 56])).
% 0.13/0.42 tff(63,plain,
% 0.13/0.42 (~![A: $i, B: $i, C: $i, D: $i] : (~(r2_hidden(A, k2_xboole_0(C, D)) & r2_hidden(B, k2_xboole_0(C, D)) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, k4_xboole_0(C, D)))) & (~(r2_hidden(A, D) & r2_hidden(B, D))) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, D))) & (~(r2_hidden(A, D) & r2_hidden(B, k4_xboole_0(C, D))))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[62, 56])).
% 0.13/0.42 tff(64,plain,
% 0.13/0.42 (~![A: $i, B: $i, C: $i, D: $i] : (~(r2_hidden(A, k2_xboole_0(C, D)) & r2_hidden(B, k2_xboole_0(C, D)) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, k4_xboole_0(C, D)))) & (~(r2_hidden(A, D) & r2_hidden(B, D))) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, D))) & (~(r2_hidden(A, D) & r2_hidden(B, k4_xboole_0(C, D))))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.13/0.42 tff(65,plain,
% 0.13/0.42 (~![A: $i, B: $i, C: $i, D: $i] : (~(r2_hidden(A, k2_xboole_0(C, D)) & r2_hidden(B, k2_xboole_0(C, D)) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, k4_xboole_0(C, D)))) & (~(r2_hidden(A, D) & r2_hidden(B, D))) & (~(r2_hidden(A, k4_xboole_0(C, D)) & r2_hidden(B, D))) & (~(r2_hidden(A, D) & r2_hidden(B, k4_xboole_0(C, D))))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[64, 56])).
% 0.13/0.42 tff(66,plain,(
% 0.13/0.42 ~(~(r2_hidden(A!3, k2_xboole_0(C!1, D!0)) & r2_hidden(B!2, k2_xboole_0(C!1, D!0)) & (~(r2_hidden(A!3, k4_xboole_0(C!1, D!0)) & r2_hidden(B!2, k4_xboole_0(C!1, D!0)))) & (~(r2_hidden(A!3, D!0) & r2_hidden(B!2, D!0))) & (~(r2_hidden(A!3, k4_xboole_0(C!1, D!0)) & r2_hidden(B!2, D!0))) & (~(r2_hidden(A!3, D!0) & r2_hidden(B!2, k4_xboole_0(C!1, D!0))))))),
% 0.13/0.42 inference(skolemize,[status(sab)],[65])).
% 0.13/0.42 tff(67,plain,
% 0.13/0.42 (r2_hidden(A!3, k2_xboole_0(C!1, D!0)) & r2_hidden(B!2, k2_xboole_0(C!1, D!0)) & (~(r2_hidden(A!3, k4_xboole_0(C!1, D!0)) & r2_hidden(B!2, k4_xboole_0(C!1, D!0)))) & (~(r2_hidden(A!3, D!0) & r2_hidden(B!2, D!0))) & (~(r2_hidden(A!3, k4_xboole_0(C!1, D!0)) & r2_hidden(B!2, D!0))) & (~(r2_hidden(A!3, D!0) & r2_hidden(B!2, k4_xboole_0(C!1, D!0))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[66, 55])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (r2_hidden(B!2, k2_xboole_0(C!1, D!0))),
% 0.20/0.42 inference(and_elim,[status(thm)],[67])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (r2_hidden(B!2, k2_xboole_0(D!0, C!1))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[68, 54])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 ((~(r2_hidden(B!2, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(B!2, k4_xboole_0(C!1, D!0)) | r2_hidden(B!2, D!0)))) | (~r2_hidden(B!2, k2_xboole_0(D!0, C!1))) | (r2_hidden(B!2, k4_xboole_0(C!1, D!0)) | r2_hidden(B!2, D!0))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 ((~(r2_hidden(B!2, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(B!2, k4_xboole_0(C!1, D!0)) | r2_hidden(B!2, D!0)))) | (r2_hidden(B!2, k4_xboole_0(C!1, D!0)) | r2_hidden(B!2, D!0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 (r2_hidden(B!2, k4_xboole_0(C!1, D!0)) | r2_hidden(B!2, D!0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[71, 42])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, B) | r2_hidden(D, A))))) | (~((C = k2_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_4(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_4(C, B, A), B) | r2_hidden(tptp_fun_D_4(C, B, A), A)))))))) | (~((~((~(k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0)))) | (r2_hidden(A!3, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(A!3, k4_xboole_0(C!1, D!0)) | r2_hidden(A!3, D!0))))) | (~((k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0))) | ((~r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), k2_xboole_0(D!0, C!1))) <=> (r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), k4_xboole_0(C!1, D!0)) | r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), D!0)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (~((~((~(k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0)))) | (r2_hidden(A!3, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(A!3, k4_xboole_0(C!1, D!0)) | r2_hidden(A!3, D!0))))) | (~((k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0))) | ((~r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), k2_xboole_0(D!0, C!1))) <=> (r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), k4_xboole_0(C!1, D!0)) | r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), D!0))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[73, 35])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 (((~((~(k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0)))) | (r2_hidden(A!3, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(A!3, k4_xboole_0(C!1, D!0)) | r2_hidden(A!3, D!0))))) | (~((k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0))) | ((~r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), k2_xboole_0(D!0, C!1))) <=> (r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), k4_xboole_0(C!1, D!0)) | r2_hidden(tptp_fun_D_4(k2_xboole_0(D!0, C!1), k4_xboole_0(C!1, D!0), D!0), D!0)))))) | ((~(k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0)))) | (r2_hidden(A!3, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(A!3, k4_xboole_0(C!1, D!0)) | r2_hidden(A!3, D!0))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 ((~(k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0)))) | (r2_hidden(A!3, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(A!3, k4_xboole_0(C!1, D!0)) | r2_hidden(A!3, D!0)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 ((~((~(k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0)))) | (r2_hidden(A!3, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(A!3, k4_xboole_0(C!1, D!0)) | r2_hidden(A!3, D!0))))) | (~(k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0)))) | (r2_hidden(A!3, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(A!3, k4_xboole_0(C!1, D!0)) | r2_hidden(A!3, D!0)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 ((~((~(k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0)))) | (r2_hidden(A!3, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(A!3, k4_xboole_0(C!1, D!0)) | r2_hidden(A!3, D!0))))) | (r2_hidden(A!3, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(A!3, k4_xboole_0(C!1, D!0)) | r2_hidden(A!3, D!0)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[77, 10])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 (r2_hidden(A!3, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(A!3, k4_xboole_0(C!1, D!0)) | r2_hidden(A!3, D!0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[78, 76])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (r2_hidden(A!3, k2_xboole_0(D!0, C!1)) <=> r2_hidden(A!3, k2_xboole_0(C!1, D!0))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[52])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 (r2_hidden(A!3, k2_xboole_0(C!1, D!0)) <=> r2_hidden(A!3, k2_xboole_0(D!0, C!1))),
% 0.20/0.42 inference(symmetry,[status(thm)],[80])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 (r2_hidden(A!3, k2_xboole_0(C!1, D!0))),
% 0.20/0.42 inference(and_elim,[status(thm)],[67])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (r2_hidden(A!3, k2_xboole_0(D!0, C!1))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 ((~(r2_hidden(A!3, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(A!3, k4_xboole_0(C!1, D!0)) | r2_hidden(A!3, D!0)))) | (~r2_hidden(A!3, k2_xboole_0(D!0, C!1))) | (r2_hidden(A!3, k4_xboole_0(C!1, D!0)) | r2_hidden(A!3, D!0))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 ((~(r2_hidden(A!3, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(A!3, k4_xboole_0(C!1, D!0)) | r2_hidden(A!3, D!0)))) | (r2_hidden(A!3, k4_xboole_0(C!1, D!0)) | r2_hidden(A!3, D!0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (r2_hidden(A!3, k4_xboole_0(C!1, D!0)) | r2_hidden(A!3, D!0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[85, 79])).
% 0.20/0.42 tff(87,assumption,(~r2_hidden(A!3, k4_xboole_0(C!1, D!0))), introduced(assumption)).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 ((~(r2_hidden(A!3, k4_xboole_0(C!1, D!0)) | r2_hidden(A!3, D!0))) | r2_hidden(A!3, k4_xboole_0(C!1, D!0)) | r2_hidden(A!3, D!0)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 ((~(r2_hidden(A!3, k4_xboole_0(C!1, D!0)) | r2_hidden(A!3, D!0))) | r2_hidden(A!3, D!0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (r2_hidden(A!3, D!0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[89, 86])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 ((~(~((~r2_hidden(A!3, D!0)) | (~r2_hidden(B!2, D!0))))) <=> ((~r2_hidden(A!3, D!0)) | (~r2_hidden(B!2, D!0)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 ((r2_hidden(A!3, D!0) & r2_hidden(B!2, D!0)) <=> (~((~r2_hidden(A!3, D!0)) | (~r2_hidden(B!2, D!0))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 ((~(r2_hidden(A!3, D!0) & r2_hidden(B!2, D!0))) <=> (~(~((~r2_hidden(A!3, D!0)) | (~r2_hidden(B!2, D!0)))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[92])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 ((~(r2_hidden(A!3, D!0) & r2_hidden(B!2, D!0))) <=> ((~r2_hidden(A!3, D!0)) | (~r2_hidden(B!2, D!0)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[93, 91])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (~(r2_hidden(A!3, D!0) & r2_hidden(B!2, D!0))),
% 0.20/0.42 inference(and_elim,[status(thm)],[67])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 ((~r2_hidden(A!3, D!0)) | (~r2_hidden(B!2, D!0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 (~r2_hidden(B!2, D!0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[96, 90])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 ((~(~((~r2_hidden(A!3, D!0)) | (~r2_hidden(B!2, k4_xboole_0(C!1, D!0)))))) <=> ((~r2_hidden(A!3, D!0)) | (~r2_hidden(B!2, k4_xboole_0(C!1, D!0))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 ((r2_hidden(A!3, D!0) & r2_hidden(B!2, k4_xboole_0(C!1, D!0))) <=> (~((~r2_hidden(A!3, D!0)) | (~r2_hidden(B!2, k4_xboole_0(C!1, D!0)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 ((~(r2_hidden(A!3, D!0) & r2_hidden(B!2, k4_xboole_0(C!1, D!0)))) <=> (~(~((~r2_hidden(A!3, D!0)) | (~r2_hidden(B!2, k4_xboole_0(C!1, D!0))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[99])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 ((~(r2_hidden(A!3, D!0) & r2_hidden(B!2, k4_xboole_0(C!1, D!0)))) <=> ((~r2_hidden(A!3, D!0)) | (~r2_hidden(B!2, k4_xboole_0(C!1, D!0))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[100, 98])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 (~(r2_hidden(A!3, D!0) & r2_hidden(B!2, k4_xboole_0(C!1, D!0)))),
% 0.20/0.42 inference(and_elim,[status(thm)],[67])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 ((~r2_hidden(A!3, D!0)) | (~r2_hidden(B!2, k4_xboole_0(C!1, D!0)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 (~r2_hidden(B!2, k4_xboole_0(C!1, D!0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[103, 90])).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 ((~(r2_hidden(B!2, k4_xboole_0(C!1, D!0)) | r2_hidden(B!2, D!0))) | r2_hidden(B!2, k4_xboole_0(C!1, D!0)) | r2_hidden(B!2, D!0)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[105, 104, 97, 72])).
% 0.20/0.42 tff(107,plain,(r2_hidden(A!3, k4_xboole_0(C!1, D!0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 ((~(~((~r2_hidden(A!3, k4_xboole_0(C!1, D!0))) | (~r2_hidden(B!2, k4_xboole_0(C!1, D!0)))))) <=> ((~r2_hidden(A!3, k4_xboole_0(C!1, D!0))) | (~r2_hidden(B!2, k4_xboole_0(C!1, D!0))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 ((r2_hidden(A!3, k4_xboole_0(C!1, D!0)) & r2_hidden(B!2, k4_xboole_0(C!1, D!0))) <=> (~((~r2_hidden(A!3, k4_xboole_0(C!1, D!0))) | (~r2_hidden(B!2, k4_xboole_0(C!1, D!0)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 ((~(r2_hidden(A!3, k4_xboole_0(C!1, D!0)) & r2_hidden(B!2, k4_xboole_0(C!1, D!0)))) <=> (~(~((~r2_hidden(A!3, k4_xboole_0(C!1, D!0))) | (~r2_hidden(B!2, k4_xboole_0(C!1, D!0))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[109])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 ((~(r2_hidden(A!3, k4_xboole_0(C!1, D!0)) & r2_hidden(B!2, k4_xboole_0(C!1, D!0)))) <=> ((~r2_hidden(A!3, k4_xboole_0(C!1, D!0))) | (~r2_hidden(B!2, k4_xboole_0(C!1, D!0))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[110, 108])).
% 0.20/0.42 tff(112,plain,
% 0.20/0.42 (~(r2_hidden(A!3, k4_xboole_0(C!1, D!0)) & r2_hidden(B!2, k4_xboole_0(C!1, D!0)))),
% 0.20/0.42 inference(and_elim,[status(thm)],[67])).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 ((~r2_hidden(A!3, k4_xboole_0(C!1, D!0))) | (~r2_hidden(B!2, k4_xboole_0(C!1, D!0)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 (~r2_hidden(B!2, k4_xboole_0(C!1, D!0))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[113, 107])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 ((~(~((~r2_hidden(A!3, k4_xboole_0(C!1, D!0))) | (~r2_hidden(B!2, D!0))))) <=> ((~r2_hidden(A!3, k4_xboole_0(C!1, D!0))) | (~r2_hidden(B!2, D!0)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 ((r2_hidden(A!3, k4_xboole_0(C!1, D!0)) & r2_hidden(B!2, D!0)) <=> (~((~r2_hidden(A!3, k4_xboole_0(C!1, D!0))) | (~r2_hidden(B!2, D!0))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 ((~(r2_hidden(A!3, k4_xboole_0(C!1, D!0)) & r2_hidden(B!2, D!0))) <=> (~(~((~r2_hidden(A!3, k4_xboole_0(C!1, D!0))) | (~r2_hidden(B!2, D!0)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[116])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 ((~(r2_hidden(A!3, k4_xboole_0(C!1, D!0)) & r2_hidden(B!2, D!0))) <=> ((~r2_hidden(A!3, k4_xboole_0(C!1, D!0))) | (~r2_hidden(B!2, D!0)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[117, 115])).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 (~(r2_hidden(A!3, k4_xboole_0(C!1, D!0)) & r2_hidden(B!2, D!0))),
% 0.20/0.43 inference(and_elim,[status(thm)],[67])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 ((~r2_hidden(A!3, k4_xboole_0(C!1, D!0))) | (~r2_hidden(B!2, D!0))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 (~r2_hidden(B!2, D!0)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[120, 107])).
% 0.20/0.43 tff(122,plain,
% 0.20/0.43 (~(r2_hidden(B!2, k4_xboole_0(C!1, D!0)) | r2_hidden(B!2, D!0))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[105, 121, 114])).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 (~(r2_hidden(B!2, k2_xboole_0(D!0, C!1)) <=> (r2_hidden(B!2, k4_xboole_0(C!1, D!0)) | r2_hidden(B!2, D!0)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[71, 122])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 (~(k2_xboole_0(D!0, C!1) = k2_xboole_0(D!0, k4_xboole_0(C!1, D!0)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[41, 123, 40])).
% 0.20/0.43 tff(125,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[124, 10])).
% 0.20/0.43 % SZS output end Proof
%------------------------------------------------------------------------------