TSTP Solution File: DAT099_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT099_1 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 : Fri Sep 16 14:36:44 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : DAT099_1 : TPTP v8.1.0. Released v6.1.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n005.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 : Wed Aug 31 01:51:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(inRange_type, type, (
% 0.20/0.40 inRange: ( $int * list ) > $o)).
% 0.20/0.40 tff(nil_type, type, (
% 0.20/0.40 nil: list)).
% 0.20/0.40 tff(tptp_fun_N_2_type, type, (
% 0.20/0.40 tptp_fun_N_2: $int)).
% 0.20/0.40 tff(cons_type, type, (
% 0.20/0.40 cons: ( $int * list ) > list)).
% 0.20/0.40 tff(tptp_fun_T_0_type, type, (
% 0.20/0.40 tptp_fun_T_0: ( list * $int ) > list)).
% 0.20/0.40 tff(tptp_fun_K_1_type, type, (
% 0.20/0.40 tptp_fun_K_1: ( list * $int ) > $int)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[N: $int, L: list] : refl((~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))))) <=> (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))))) <=> ![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (^[N: $int, L: list] : rewrite((~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))))) <=> (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))))) <=> ![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))))) <=> ![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (^[N: $int, L: list] : trans(monotonicity(trans(monotonicity(rewrite(((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0)) & inRange(N, tptp_fun_T_0(L, N))) <=> (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N)))))), (((L = nil) | (~inRange(N, L)) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0)) & inRange(N, tptp_fun_T_0(L, N)))) <=> ((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N)))))))), rewrite(((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N)))))) <=> ((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))), (((L = nil) | (~inRange(N, L)) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0)) & inRange(N, tptp_fun_T_0(L, N)))) <=> ((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N)))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[K: $int, T: list] : trans(monotonicity(rewrite(((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T)) <=> (~($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))), ((~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T))) <=> (~(~($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))), rewrite((~(~($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))) <=> ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))), ((~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T))) <=> ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))), (![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T))) <=> ![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))), (((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T)))) <=> ((~(L = nil)) & ![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))), rewrite(((~(L = nil)) & ![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))) <=> (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))), (((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T)))) <=> (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))), ((inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T))))) <=> (inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))), rewrite((inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))) <=> (inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))), ((inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T))))) <=> (inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))), ((((L = nil) | (~inRange(N, L)) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0)) & inRange(N, tptp_fun_T_0(L, N)))) & (inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T)))))) <=> (((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N)))))) & (inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))))), rewrite((((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N)))))) & (inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))) <=> (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))), ((((L = nil) | (~inRange(N, L)) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0)) & inRange(N, tptp_fun_T_0(L, N)))) & (inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T)))))) <=> (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![N: $int, L: list] : (((L = nil) | (~inRange(N, L)) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0)) & inRange(N, tptp_fun_T_0(L, N)))) & (inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T)))))) <=> ![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (^[N: $int, L: list] : rewrite((((~inRange(N, L)) | ((L = nil) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$greatereq($sum(tptp_fun_K_1(L, N), $product(-1, N)), 0)) & inRange(N, tptp_fun_T_0(L, N))))) & (inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T)))))) <=> (((L = nil) | (~inRange(N, L)) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0)) & inRange(N, tptp_fun_T_0(L, N)))) & (inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (![N: $int, L: list] : (((~inRange(N, L)) | ((L = nil) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$greatereq($sum(tptp_fun_K_1(L, N), $product(-1, N)), 0)) & inRange(N, tptp_fun_T_0(L, N))))) & (inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T)))))) <=> ![N: $int, L: list] : (((L = nil) | (~inRange(N, L)) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0)) & inRange(N, tptp_fun_T_0(L, N)))) & (inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (^[N: $int, L: list] : rewrite((inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $greatereq(K, 0) & (~$lesseq($sum(N, $product(-1, K)), 0)) & inRange(N, T)))) <=> (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $greatereq(K, 0) & (~$lesseq($sum(N, $product(-1, K)), 0)) & inRange(N, T)))) <=> ![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (^[N: $int, L: list] : rewrite((inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $lesseq(0, K) & (~$lesseq(N, K)) & inRange(N, T)))) <=> (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $greatereq(K, 0) & (~$lesseq($sum(N, $product(-1, K)), 0)) & inRange(N, T)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $lesseq(0, K) & (~$lesseq(N, K)) & inRange(N, T)))) <=> ![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $greatereq(K, 0) & (~$lesseq($sum(N, $product(-1, K)), 0)) & inRange(N, T))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $lesseq(0, K) & (~$lesseq(N, K)) & inRange(N, T)))) <=> ![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $lesseq(0, K) & (~$lesseq(N, K)) & inRange(N, T))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (^[N: $int, L: list] : rewrite((inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((((L = cons(K, T)) & $lesseq(0, K)) & $less(K, N)) & inRange(N, T)))) <=> (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $lesseq(0, K) & (~$lesseq(N, K)) & inRange(N, T)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((((L = cons(K, T)) & $lesseq(0, K)) & $less(K, N)) & inRange(N, T)))) <=> ![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $lesseq(0, K) & (~$lesseq(N, K)) & inRange(N, T))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.40 tff(17,axiom,(![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((((L = cons(K, T)) & $lesseq(0, K)) & $less(K, N)) & inRange(N, T))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','inRange')).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $lesseq(0, K) & (~$lesseq(N, K)) & inRange(N, T))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $lesseq(0, K) & (~$lesseq(N, K)) & inRange(N, T))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $greatereq(K, 0) & (~$lesseq($sum(N, $product(-1, K)), 0)) & inRange(N, T))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[20, 11])).
% 0.20/0.40 tff(22,plain,(
% 0.20/0.40 ![N: $int, L: list] : (((~inRange(N, L)) | ((L = nil) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$greatereq($sum(tptp_fun_K_1(L, N), $product(-1, N)), 0)) & inRange(N, tptp_fun_T_0(L, N))))) & (inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T))))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[21])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (![N: $int, L: list] : (((L = nil) | (~inRange(N, L)) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0)) & inRange(N, tptp_fun_T_0(L, N)))) & (inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[22, 9])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[23, 7])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[24, 5])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(2, nil) = nil) | (~inRange(N!2, cons(2, nil))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(2, nil), N!2))), 0) | (~(cons(2, nil) = cons(tptp_fun_K_1(cons(2, nil), N!2), tptp_fun_T_0(cons(2, nil), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(2, nil), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(2, nil), N!2))))))) | (~(inRange(N!2, cons(2, nil)) | (~((cons(2, nil) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T)))))))))))) <=> ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(2, nil) = nil) | (~inRange(N!2, cons(2, nil))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(2, nil), N!2))), 0) | (~(cons(2, nil) = cons(tptp_fun_K_1(cons(2, nil), N!2), tptp_fun_T_0(cons(2, nil), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(2, nil), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(2, nil), N!2))))))) | (~(inRange(N!2, cons(2, nil)) | (~((cons(2, nil) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T))))))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 ((~((~((cons(2, nil) = nil) | (~inRange(N!2, cons(2, nil))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(2, nil), N!2))), 0) | (~(cons(2, nil) = cons(tptp_fun_K_1(cons(2, nil), N!2), tptp_fun_T_0(cons(2, nil), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(2, nil), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(2, nil), N!2))))))) | (~(inRange(N!2, cons(2, nil)) | (~((cons(2, nil) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(2, nil) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T)))))))))) <=> (~((~((cons(2, nil) = nil) | (~inRange(N!2, cons(2, nil))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(2, nil), N!2))), 0) | (~(cons(2, nil) = cons(tptp_fun_K_1(cons(2, nil), N!2), tptp_fun_T_0(cons(2, nil), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(2, nil), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(2, nil), N!2))))))) | (~(inRange(N!2, cons(2, nil)) | (~((cons(2, nil) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T)))))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(2, nil) = nil) | (~inRange(N!2, cons(2, nil))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(2, nil), N!2))), 0) | (~(cons(2, nil) = cons(tptp_fun_K_1(cons(2, nil), N!2), tptp_fun_T_0(cons(2, nil), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(2, nil), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(2, nil), N!2))))))) | (~(inRange(N!2, cons(2, nil)) | (~((cons(2, nil) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(2, nil) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T))))))))))) <=> ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(2, nil) = nil) | (~inRange(N!2, cons(2, nil))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(2, nil), N!2))), 0) | (~(cons(2, nil) = cons(tptp_fun_K_1(cons(2, nil), N!2), tptp_fun_T_0(cons(2, nil), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(2, nil), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(2, nil), N!2))))))) | (~(inRange(N!2, cons(2, nil)) | (~((cons(2, nil) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T))))))))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[27])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(2, nil) = nil) | (~inRange(N!2, cons(2, nil))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(2, nil), N!2))), 0) | (~(cons(2, nil) = cons(tptp_fun_K_1(cons(2, nil), N!2), tptp_fun_T_0(cons(2, nil), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(2, nil), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(2, nil), N!2))))))) | (~(inRange(N!2, cons(2, nil)) | (~((cons(2, nil) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(2, nil) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T))))))))))) <=> ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(2, nil) = nil) | (~inRange(N!2, cons(2, nil))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(2, nil), N!2))), 0) | (~(cons(2, nil) = cons(tptp_fun_K_1(cons(2, nil), N!2), tptp_fun_T_0(cons(2, nil), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(2, nil), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(2, nil), N!2))))))) | (~(inRange(N!2, cons(2, nil)) | (~((cons(2, nil) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T))))))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[28, 26])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(2, nil) = nil) | (~inRange(N!2, cons(2, nil))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(2, nil), N!2))), 0) | (~(cons(2, nil) = cons(tptp_fun_K_1(cons(2, nil), N!2), tptp_fun_T_0(cons(2, nil), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(2, nil), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(2, nil), N!2))))))) | (~(inRange(N!2, cons(2, nil)) | (~((cons(2, nil) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(2, nil) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T))))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(2, nil) = nil) | (~inRange(N!2, cons(2, nil))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(2, nil), N!2))), 0) | (~(cons(2, nil) = cons(tptp_fun_K_1(cons(2, nil), N!2), tptp_fun_T_0(cons(2, nil), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(2, nil), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(2, nil), N!2))))))) | (~(inRange(N!2, cons(2, nil)) | (~((cons(2, nil) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T)))))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (~((~((cons(2, nil) = nil) | (~inRange(N!2, cons(2, nil))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(2, nil), N!2))), 0) | (~(cons(2, nil) = cons(tptp_fun_K_1(cons(2, nil), N!2), tptp_fun_T_0(cons(2, nil), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(2, nil), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(2, nil), N!2))))))) | (~(inRange(N!2, cons(2, nil)) | (~((cons(2, nil) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T))))))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[31, 25])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (((~((cons(2, nil) = nil) | (~inRange(N!2, cons(2, nil))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(2, nil), N!2))), 0) | (~(cons(2, nil) = cons(tptp_fun_K_1(cons(2, nil), N!2), tptp_fun_T_0(cons(2, nil), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(2, nil), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(2, nil), N!2))))))) | (~(inRange(N!2, cons(2, nil)) | (~((cons(2, nil) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T)))))))))) | (inRange(N!2, cons(2, nil)) | (~((cons(2, nil) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T))))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (inRange(N!2, cons(2, nil)) | (~((cons(2, nil) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T)))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(3, cons(2, nil)) = nil) | (~inRange(N!2, cons(3, cons(2, nil)))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(3, cons(2, nil)), N!2))), 0) | (~(cons(3, cons(2, nil)) = cons(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), tptp_fun_T_0(cons(3, cons(2, nil)), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(3, cons(2, nil)), N!2))))))) | (~(inRange(N!2, cons(3, cons(2, nil))) | (~((cons(3, cons(2, nil)) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T)))))))))))) <=> ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(3, cons(2, nil)) = nil) | (~inRange(N!2, cons(3, cons(2, nil)))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(3, cons(2, nil)), N!2))), 0) | (~(cons(3, cons(2, nil)) = cons(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), tptp_fun_T_0(cons(3, cons(2, nil)), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(3, cons(2, nil)), N!2))))))) | (~(inRange(N!2, cons(3, cons(2, nil))) | (~((cons(3, cons(2, nil)) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T))))))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 ((~((~((cons(3, cons(2, nil)) = nil) | (~inRange(N!2, cons(3, cons(2, nil)))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(3, cons(2, nil)), N!2))), 0) | (~(cons(3, cons(2, nil)) = cons(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), tptp_fun_T_0(cons(3, cons(2, nil)), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(3, cons(2, nil)), N!2))))))) | (~(inRange(N!2, cons(3, cons(2, nil))) | (~((cons(3, cons(2, nil)) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(3, cons(2, nil)) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T)))))))))) <=> (~((~((cons(3, cons(2, nil)) = nil) | (~inRange(N!2, cons(3, cons(2, nil)))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(3, cons(2, nil)), N!2))), 0) | (~(cons(3, cons(2, nil)) = cons(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), tptp_fun_T_0(cons(3, cons(2, nil)), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(3, cons(2, nil)), N!2))))))) | (~(inRange(N!2, cons(3, cons(2, nil))) | (~((cons(3, cons(2, nil)) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T)))))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(3, cons(2, nil)) = nil) | (~inRange(N!2, cons(3, cons(2, nil)))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(3, cons(2, nil)), N!2))), 0) | (~(cons(3, cons(2, nil)) = cons(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), tptp_fun_T_0(cons(3, cons(2, nil)), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(3, cons(2, nil)), N!2))))))) | (~(inRange(N!2, cons(3, cons(2, nil))) | (~((cons(3, cons(2, nil)) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(3, cons(2, nil)) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T))))))))))) <=> ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(3, cons(2, nil)) = nil) | (~inRange(N!2, cons(3, cons(2, nil)))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(3, cons(2, nil)), N!2))), 0) | (~(cons(3, cons(2, nil)) = cons(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), tptp_fun_T_0(cons(3, cons(2, nil)), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(3, cons(2, nil)), N!2))))))) | (~(inRange(N!2, cons(3, cons(2, nil))) | (~((cons(3, cons(2, nil)) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T))))))))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[36])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(3, cons(2, nil)) = nil) | (~inRange(N!2, cons(3, cons(2, nil)))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(3, cons(2, nil)), N!2))), 0) | (~(cons(3, cons(2, nil)) = cons(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), tptp_fun_T_0(cons(3, cons(2, nil)), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(3, cons(2, nil)), N!2))))))) | (~(inRange(N!2, cons(3, cons(2, nil))) | (~((cons(3, cons(2, nil)) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(3, cons(2, nil)) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T))))))))))) <=> ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(3, cons(2, nil)) = nil) | (~inRange(N!2, cons(3, cons(2, nil)))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(3, cons(2, nil)), N!2))), 0) | (~(cons(3, cons(2, nil)) = cons(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), tptp_fun_T_0(cons(3, cons(2, nil)), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(3, cons(2, nil)), N!2))))))) | (~(inRange(N!2, cons(3, cons(2, nil))) | (~((cons(3, cons(2, nil)) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T))))))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[37, 35])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(3, cons(2, nil)) = nil) | (~inRange(N!2, cons(3, cons(2, nil)))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(3, cons(2, nil)), N!2))), 0) | (~(cons(3, cons(2, nil)) = cons(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), tptp_fun_T_0(cons(3, cons(2, nil)), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(3, cons(2, nil)), N!2))))))) | (~(inRange(N!2, cons(3, cons(2, nil))) | (~((cons(3, cons(2, nil)) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(3, cons(2, nil)) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T))))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(3, cons(2, nil)) = nil) | (~inRange(N!2, cons(3, cons(2, nil)))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(3, cons(2, nil)), N!2))), 0) | (~(cons(3, cons(2, nil)) = cons(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), tptp_fun_T_0(cons(3, cons(2, nil)), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(3, cons(2, nil)), N!2))))))) | (~(inRange(N!2, cons(3, cons(2, nil))) | (~((cons(3, cons(2, nil)) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T)))))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (~((~((cons(3, cons(2, nil)) = nil) | (~inRange(N!2, cons(3, cons(2, nil)))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(3, cons(2, nil)), N!2))), 0) | (~(cons(3, cons(2, nil)) = cons(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), tptp_fun_T_0(cons(3, cons(2, nil)), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(3, cons(2, nil)), N!2))))))) | (~(inRange(N!2, cons(3, cons(2, nil))) | (~((cons(3, cons(2, nil)) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T))))))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[40, 25])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (((~((cons(3, cons(2, nil)) = nil) | (~inRange(N!2, cons(3, cons(2, nil)))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(3, cons(2, nil)), N!2))), 0) | (~(cons(3, cons(2, nil)) = cons(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), tptp_fun_T_0(cons(3, cons(2, nil)), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(3, cons(2, nil)), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(3, cons(2, nil)), N!2))))))) | (~(inRange(N!2, cons(3, cons(2, nil))) | (~((cons(3, cons(2, nil)) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T)))))))))) | (inRange(N!2, cons(3, cons(2, nil))) | (~((cons(3, cons(2, nil)) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T))))))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (inRange(N!2, cons(3, cons(2, nil))) | (~((cons(3, cons(2, nil)) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T)))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 ((~![N: $int] : ((~$greatereq(N, 4)) | inRange(N, cons(1, cons(3, cons(2, nil)))))) <=> (~![N: $int] : ((~$greatereq(N, 4)) | inRange(N, cons(1, cons(3, cons(2, nil))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 ((~![N: $int] : ($greatereq(N, 4) => inRange(N, cons(1, cons(3, cons(2, nil)))))) <=> (~![N: $int] : ((~$greatereq(N, 4)) | inRange(N, cons(1, cons(3, cons(2, nil))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(46,axiom,(~![N: $int] : ($greatereq(N, 4) => inRange(N, cons(1, cons(3, cons(2, nil)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c')).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (~![N: $int] : ((~$greatereq(N, 4)) | inRange(N, cons(1, cons(3, cons(2, nil)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (~![N: $int] : ((~$greatereq(N, 4)) | inRange(N, cons(1, cons(3, cons(2, nil)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[47, 44])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (~![N: $int] : ((~$greatereq(N, 4)) | inRange(N, cons(1, cons(3, cons(2, nil)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (~![N: $int] : ((~$greatereq(N, 4)) | inRange(N, cons(1, cons(3, cons(2, nil)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[49, 44])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (~![N: $int] : ((~$greatereq(N, 4)) | inRange(N, cons(1, cons(3, cons(2, nil)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[50, 44])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (~![N: $int] : ((~$greatereq(N, 4)) | inRange(N, cons(1, cons(3, cons(2, nil)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (~![N: $int] : ((~$greatereq(N, 4)) | inRange(N, cons(1, cons(3, cons(2, nil)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[52, 44])).
% 0.20/0.42 tff(54,plain,(
% 0.20/0.42 ~((~$greatereq(N!2, 4)) | inRange(N!2, cons(1, cons(3, cons(2, nil)))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[53])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 ($greatereq(N!2, 4)),
% 0.20/0.42 inference(or_elim,[status(thm)],[54])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 ((~$lesseq(N!2, 1)) | (~$greatereq(N!2, 4))),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (~$lesseq(N!2, 1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((~inRange(N!2, cons(1, cons(3, cons(2, nil))))) | (cons(1, cons(3, cons(2, nil))) = nil) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2))), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2))))))) | (~(inRange(N!2, cons(1, cons(3, cons(2, nil)))) | (~((cons(1, cons(3, cons(2, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T))))))))))) <=> ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((~inRange(N!2, cons(1, cons(3, cons(2, nil))))) | (cons(1, cons(3, cons(2, nil))) = nil) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2))), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2))))))) | (~(inRange(N!2, cons(1, cons(3, cons(2, nil)))) | (~((cons(1, cons(3, cons(2, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T)))))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 ((~((~((cons(1, cons(3, cons(2, nil))) = nil) | (~inRange(N!2, cons(1, cons(3, cons(2, nil))))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2))), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2))))))) | (~(inRange(N!2, cons(1, cons(3, cons(2, nil)))) | (~((cons(1, cons(3, cons(2, nil))) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T)))))))))) <=> (~((~((~inRange(N!2, cons(1, cons(3, cons(2, nil))))) | (cons(1, cons(3, cons(2, nil))) = nil) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2))), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2))))))) | (~(inRange(N!2, cons(1, cons(3, cons(2, nil)))) | (~((cons(1, cons(3, cons(2, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T))))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(1, cons(3, cons(2, nil))) = nil) | (~inRange(N!2, cons(1, cons(3, cons(2, nil))))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2))), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2))))))) | (~(inRange(N!2, cons(1, cons(3, cons(2, nil)))) | (~((cons(1, cons(3, cons(2, nil))) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T))))))))))) <=> ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((~inRange(N!2, cons(1, cons(3, cons(2, nil))))) | (cons(1, cons(3, cons(2, nil))) = nil) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2))), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2))))))) | (~(inRange(N!2, cons(1, cons(3, cons(2, nil)))) | (~((cons(1, cons(3, cons(2, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T)))))))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[59])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 (((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(1, cons(3, cons(2, nil))) = nil) | (~inRange(N!2, cons(1, cons(3, cons(2, nil))))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2))), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2))))))) | (~(inRange(N!2, cons(1, cons(3, cons(2, nil)))) | (~((cons(1, cons(3, cons(2, nil))) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T))))))))))) <=> ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((~inRange(N!2, cons(1, cons(3, cons(2, nil))))) | (cons(1, cons(3, cons(2, nil))) = nil) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2))), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2))))))) | (~(inRange(N!2, cons(1, cons(3, cons(2, nil)))) | (~((cons(1, cons(3, cons(2, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T)))))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[60, 58])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(1, cons(3, cons(2, nil))) = nil) | (~inRange(N!2, cons(1, cons(3, cons(2, nil))))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2))), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2))))))) | (~(inRange(N!2, cons(1, cons(3, cons(2, nil)))) | (~((cons(1, cons(3, cons(2, nil))) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T))))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((~inRange(N!2, cons(1, cons(3, cons(2, nil))))) | (cons(1, cons(3, cons(2, nil))) = nil) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2))), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2))))))) | (~(inRange(N!2, cons(1, cons(3, cons(2, nil)))) | (~((cons(1, cons(3, cons(2, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 (~((~((~inRange(N!2, cons(1, cons(3, cons(2, nil))))) | (cons(1, cons(3, cons(2, nil))) = nil) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2))), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2))))))) | (~(inRange(N!2, cons(1, cons(3, cons(2, nil)))) | (~((cons(1, cons(3, cons(2, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T)))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[63, 25])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (((~((~inRange(N!2, cons(1, cons(3, cons(2, nil))))) | (cons(1, cons(3, cons(2, nil))) = nil) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2))), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2)))) | (~$greatereq(tptp_fun_K_1(cons(1, cons(3, cons(2, nil))), N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(cons(1, cons(3, cons(2, nil))), N!2))))))) | (~(inRange(N!2, cons(1, cons(3, cons(2, nil)))) | (~((cons(1, cons(3, cons(2, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T))))))))) | (inRange(N!2, cons(1, cons(3, cons(2, nil)))) | (~((cons(1, cons(3, cons(2, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T)))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (inRange(N!2, cons(1, cons(3, cons(2, nil)))) | (~((cons(1, cons(3, cons(2, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (~inRange(N!2, cons(1, cons(3, cons(2, nil))))),
% 0.20/0.43 inference(or_elim,[status(thm)],[54])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 ((~(inRange(N!2, cons(1, cons(3, cons(2, nil)))) | (~((cons(1, cons(3, cons(2, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T)))))))) | inRange(N!2, cons(1, cons(3, cons(2, nil)))) | (~((cons(1, cons(3, cons(2, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 ((~(inRange(N!2, cons(1, cons(3, cons(2, nil)))) | (~((cons(1, cons(3, cons(2, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T)))))))) | (~((cons(1, cons(3, cons(2, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (~((cons(1, cons(3, cons(2, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[69, 66])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 (((cons(1, cons(3, cons(2, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T))))) | ![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 (![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 (((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T)))) | ((~inRange(N!2, cons(3, cons(2, nil)))) | $lesseq(N!2, 1))) <=> ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T)))) | (~inRange(N!2, cons(3, cons(2, nil)))) | $lesseq(N!2, 1))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 (($false | $lesseq(N!2, 1) | $false | (~inRange(N!2, cons(3, cons(2, nil))))) <=> ((~inRange(N!2, cons(3, cons(2, nil)))) | $lesseq(N!2, 1))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 ((~$true) <=> $false),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 ((cons(1, cons(3, cons(2, nil))) = cons(1, cons(3, cons(2, nil)))) <=> $true),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 ((~(cons(1, cons(3, cons(2, nil))) = cons(1, cons(3, cons(2, nil))))) <=> (~$true)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[76])).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 ((~(cons(1, cons(3, cons(2, nil))) = cons(1, cons(3, cons(2, nil))))) <=> $false),
% 0.20/0.44 inference(transitivity,[status(thm)],[77, 75])).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 ($greatereq($sum(1, $product(-1, N!2)), 0) <=> $lesseq(N!2, 1)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 ($greatereq(1, 0) <=> $true),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 ((~$greatereq(1, 0)) <=> (~$true)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[80])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 ((~$greatereq(1, 0)) <=> $false),
% 0.20/0.44 inference(transitivity,[status(thm)],[81, 75])).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 (((~$greatereq(1, 0)) | $greatereq($sum(1, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(1, cons(3, cons(2, nil))))) | (~inRange(N!2, cons(3, cons(2, nil))))) <=> ($false | $lesseq(N!2, 1) | $false | (~inRange(N!2, cons(3, cons(2, nil)))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[82, 79, 78])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 (((~$greatereq(1, 0)) | $greatereq($sum(1, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(1, cons(3, cons(2, nil))))) | (~inRange(N!2, cons(3, cons(2, nil))))) <=> ((~inRange(N!2, cons(3, cons(2, nil)))) | $lesseq(N!2, 1))),
% 0.20/0.44 inference(transitivity,[status(thm)],[83, 74])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 (((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T)))) | ((~$greatereq(1, 0)) | $greatereq($sum(1, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(1, cons(3, cons(2, nil))))) | (~inRange(N!2, cons(3, cons(2, nil)))))) <=> ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T)))) | ((~inRange(N!2, cons(3, cons(2, nil)))) | $lesseq(N!2, 1)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[84])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 (((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T)))) | ((~$greatereq(1, 0)) | $greatereq($sum(1, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(1, cons(3, cons(2, nil))))) | (~inRange(N!2, cons(3, cons(2, nil)))))) <=> ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T)))) | (~inRange(N!2, cons(3, cons(2, nil)))) | $lesseq(N!2, 1))),
% 0.20/0.44 inference(transitivity,[status(thm)],[85, 73])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T)))) | ((~$greatereq(1, 0)) | $greatereq($sum(1, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(1, cons(3, cons(2, nil))))) | (~inRange(N!2, cons(3, cons(2, nil)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(cons(1, cons(3, cons(2, nil))) = cons(K, T))) | (~inRange(N!2, T)))) | (~inRange(N!2, cons(3, cons(2, nil)))) | $lesseq(N!2, 1)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 (~inRange(N!2, cons(3, cons(2, nil)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[88, 72, 57])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 ((~(inRange(N!2, cons(3, cons(2, nil))) | (~((cons(3, cons(2, nil)) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T))))))))) | inRange(N!2, cons(3, cons(2, nil))) | (~((cons(3, cons(2, nil)) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T)))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 ((~(inRange(N!2, cons(3, cons(2, nil))) | (~((cons(3, cons(2, nil)) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T))))))))) | (~((cons(3, cons(2, nil)) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T)))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 (~((cons(3, cons(2, nil)) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[91, 43])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 (((cons(3, cons(2, nil)) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T)))))) | ![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 (![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 ((~$lesseq(N!2, 3)) | (~$greatereq(N!2, 4))),
% 0.20/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 (~$lesseq(N!2, 3)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[95, 55])).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 (((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T))))) | ((~inRange(N!2, cons(2, nil))) | $lesseq(N!2, 3))) <=> ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T))))) | (~inRange(N!2, cons(2, nil))) | $lesseq(N!2, 3))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(98,plain,
% 0.20/0.44 (($false | $lesseq(N!2, 3) | (~inRange(N!2, cons(2, nil))) | $false) <=> ((~inRange(N!2, cons(2, nil))) | $lesseq(N!2, 3))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 ((cons(3, cons(2, nil)) = cons(3, cons(2, nil))) <=> $true),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(100,plain,
% 0.20/0.44 ((~(cons(3, cons(2, nil)) = cons(3, cons(2, nil)))) <=> (~$true)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[99])).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 ((~(cons(3, cons(2, nil)) = cons(3, cons(2, nil)))) <=> $false),
% 0.20/0.44 inference(transitivity,[status(thm)],[100, 75])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 ($greatereq($sum(3, $product(-1, N!2)), 0) <=> $lesseq(N!2, 3)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 ($greatereq(3, 0) <=> $true),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 ((~$greatereq(3, 0)) <=> (~$true)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[103])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 ((~$greatereq(3, 0)) <=> $false),
% 0.20/0.44 inference(transitivity,[status(thm)],[104, 75])).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 (((~$greatereq(3, 0)) | $greatereq($sum(3, $product(-1, N!2)), 0) | (~inRange(N!2, cons(2, nil))) | (~(cons(3, cons(2, nil)) = cons(3, cons(2, nil))))) <=> ($false | $lesseq(N!2, 3) | (~inRange(N!2, cons(2, nil))) | $false)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[105, 102, 101])).
% 0.20/0.44 tff(107,plain,
% 0.20/0.44 (((~$greatereq(3, 0)) | $greatereq($sum(3, $product(-1, N!2)), 0) | (~inRange(N!2, cons(2, nil))) | (~(cons(3, cons(2, nil)) = cons(3, cons(2, nil))))) <=> ((~inRange(N!2, cons(2, nil))) | $lesseq(N!2, 3))),
% 0.20/0.44 inference(transitivity,[status(thm)],[106, 98])).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 (((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T))))) | ((~$greatereq(3, 0)) | $greatereq($sum(3, $product(-1, N!2)), 0) | (~inRange(N!2, cons(2, nil))) | (~(cons(3, cons(2, nil)) = cons(3, cons(2, nil)))))) <=> ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T))))) | ((~inRange(N!2, cons(2, nil))) | $lesseq(N!2, 3)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[107])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 (((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T))))) | ((~$greatereq(3, 0)) | $greatereq($sum(3, $product(-1, N!2)), 0) | (~inRange(N!2, cons(2, nil))) | (~(cons(3, cons(2, nil)) = cons(3, cons(2, nil)))))) <=> ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T))))) | (~inRange(N!2, cons(2, nil))) | $lesseq(N!2, 3))),
% 0.20/0.44 inference(transitivity,[status(thm)],[108, 97])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T))))) | ((~$greatereq(3, 0)) | $greatereq($sum(3, $product(-1, N!2)), 0) | (~inRange(N!2, cons(2, nil))) | (~(cons(3, cons(2, nil)) = cons(3, cons(2, nil)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(3, cons(2, nil)) = cons(K, T))))) | (~inRange(N!2, cons(2, nil))) | $lesseq(N!2, 3)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 (~inRange(N!2, cons(2, nil))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[111, 96, 94])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 ((~(inRange(N!2, cons(2, nil)) | (~((cons(2, nil) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T))))))))) | inRange(N!2, cons(2, nil)) | (~((cons(2, nil) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T)))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 ((~(inRange(N!2, cons(2, nil)) | (~((cons(2, nil) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T))))))))) | (~((cons(2, nil) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T)))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 (~((cons(2, nil) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[114, 34])).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 (((cons(2, nil) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T)))))) | ![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 (![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 ((~$lesseq(N!2, 2)) | (~$greatereq(N!2, 4))),
% 0.20/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 (~$lesseq(N!2, 2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[118, 55])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 (((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T))))) | ((~inRange(N!2, nil)) | $lesseq(N!2, 2))) <=> ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T))))) | (~inRange(N!2, nil)) | $lesseq(N!2, 2))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(121,plain,
% 0.20/0.45 (($false | $lesseq(N!2, 2) | (~inRange(N!2, nil)) | $false) <=> ((~inRange(N!2, nil)) | $lesseq(N!2, 2))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(122,plain,
% 0.20/0.45 ((cons(2, nil) = cons(2, nil)) <=> $true),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(123,plain,
% 0.20/0.45 ((~(cons(2, nil) = cons(2, nil))) <=> (~$true)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[122])).
% 0.20/0.45 tff(124,plain,
% 0.20/0.45 ((~(cons(2, nil) = cons(2, nil))) <=> $false),
% 0.20/0.45 inference(transitivity,[status(thm)],[123, 75])).
% 0.20/0.45 tff(125,plain,
% 0.20/0.45 ($greatereq($sum(2, $product(-1, N!2)), 0) <=> $lesseq(N!2, 2)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(126,plain,
% 0.20/0.45 ($greatereq(2, 0) <=> $true),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(127,plain,
% 0.20/0.45 ((~$greatereq(2, 0)) <=> (~$true)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[126])).
% 0.20/0.45 tff(128,plain,
% 0.20/0.45 ((~$greatereq(2, 0)) <=> $false),
% 0.20/0.45 inference(transitivity,[status(thm)],[127, 75])).
% 0.20/0.45 tff(129,plain,
% 0.20/0.45 (((~$greatereq(2, 0)) | $greatereq($sum(2, $product(-1, N!2)), 0) | (~inRange(N!2, nil)) | (~(cons(2, nil) = cons(2, nil)))) <=> ($false | $lesseq(N!2, 2) | (~inRange(N!2, nil)) | $false)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[128, 125, 124])).
% 0.20/0.45 tff(130,plain,
% 0.20/0.45 (((~$greatereq(2, 0)) | $greatereq($sum(2, $product(-1, N!2)), 0) | (~inRange(N!2, nil)) | (~(cons(2, nil) = cons(2, nil)))) <=> ((~inRange(N!2, nil)) | $lesseq(N!2, 2))),
% 0.20/0.45 inference(transitivity,[status(thm)],[129, 121])).
% 0.20/0.45 tff(131,plain,
% 0.20/0.45 (((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T))))) | ((~$greatereq(2, 0)) | $greatereq($sum(2, $product(-1, N!2)), 0) | (~inRange(N!2, nil)) | (~(cons(2, nil) = cons(2, nil))))) <=> ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T))))) | ((~inRange(N!2, nil)) | $lesseq(N!2, 2)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[130])).
% 0.20/0.45 tff(132,plain,
% 0.20/0.45 (((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T))))) | ((~$greatereq(2, 0)) | $greatereq($sum(2, $product(-1, N!2)), 0) | (~inRange(N!2, nil)) | (~(cons(2, nil) = cons(2, nil))))) <=> ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T))))) | (~inRange(N!2, nil)) | $lesseq(N!2, 2))),
% 0.20/0.45 inference(transitivity,[status(thm)],[131, 120])).
% 0.20/0.45 tff(133,plain,
% 0.20/0.45 ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T))))) | ((~$greatereq(2, 0)) | $greatereq($sum(2, $product(-1, N!2)), 0) | (~inRange(N!2, nil)) | (~(cons(2, nil) = cons(2, nil))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(134,plain,
% 0.20/0.45 ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~inRange(N!2, T)) | (~(cons(2, nil) = cons(K, T))))) | (~inRange(N!2, nil)) | $lesseq(N!2, 2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.45 tff(135,plain,
% 0.20/0.45 (~inRange(N!2, nil)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[134, 119, 117])).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 (((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | inRange(N!2, nil)) <=> ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | inRange(N!2, nil))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 ((~(~inRange(N!2, nil))) <=> inRange(N!2, nil)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 (($false | (~inRange(N!2, nil))) <=> (~inRange(N!2, nil))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 ((~(inRange(N!2, nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T)))))))) <=> (~inRange(N!2, nil))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(140,plain,
% 0.20/0.45 (($true | (~inRange(N!2, nil)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(nil, N!2))), 0) | (~(nil = cons(tptp_fun_K_1(nil, N!2), tptp_fun_T_0(nil, N!2)))) | (~$greatereq(tptp_fun_K_1(nil, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(nil, N!2)))))) <=> $true),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 ((~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(nil, N!2))), 0) | (~(nil = cons(tptp_fun_K_1(nil, N!2), tptp_fun_T_0(nil, N!2)))) | (~$greatereq(tptp_fun_K_1(nil, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(nil, N!2))))) <=> (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(nil, N!2))), 0) | (~(nil = cons(tptp_fun_K_1(nil, N!2), tptp_fun_T_0(nil, N!2)))) | (~$greatereq(tptp_fun_K_1(nil, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(nil, N!2)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 ((nil = nil) <=> $true),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(143,plain,
% 0.20/0.45 (((nil = nil) | (~inRange(N!2, nil)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(nil, N!2))), 0) | (~(nil = cons(tptp_fun_K_1(nil, N!2), tptp_fun_T_0(nil, N!2)))) | (~$greatereq(tptp_fun_K_1(nil, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(nil, N!2)))))) <=> ($true | (~inRange(N!2, nil)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(nil, N!2))), 0) | (~(nil = cons(tptp_fun_K_1(nil, N!2), tptp_fun_T_0(nil, N!2)))) | (~$greatereq(tptp_fun_K_1(nil, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(nil, N!2))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[142, 141])).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 (((nil = nil) | (~inRange(N!2, nil)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(nil, N!2))), 0) | (~(nil = cons(tptp_fun_K_1(nil, N!2), tptp_fun_T_0(nil, N!2)))) | (~$greatereq(tptp_fun_K_1(nil, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(nil, N!2)))))) <=> $true),
% 0.20/0.45 inference(transitivity,[status(thm)],[143, 140])).
% 0.20/0.45 tff(145,plain,
% 0.20/0.45 ((~((nil = nil) | (~inRange(N!2, nil)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(nil, N!2))), 0) | (~(nil = cons(tptp_fun_K_1(nil, N!2), tptp_fun_T_0(nil, N!2)))) | (~$greatereq(tptp_fun_K_1(nil, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(nil, N!2))))))) <=> (~$true)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[144])).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 ((~((nil = nil) | (~inRange(N!2, nil)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(nil, N!2))), 0) | (~(nil = cons(tptp_fun_K_1(nil, N!2), tptp_fun_T_0(nil, N!2)))) | (~$greatereq(tptp_fun_K_1(nil, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(nil, N!2))))))) <=> $false),
% 0.20/0.45 inference(transitivity,[status(thm)],[145, 75])).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 (((~((nil = nil) | (~inRange(N!2, nil)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(nil, N!2))), 0) | (~(nil = cons(tptp_fun_K_1(nil, N!2), tptp_fun_T_0(nil, N!2)))) | (~$greatereq(tptp_fun_K_1(nil, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(nil, N!2))))))) | (~(inRange(N!2, nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T))))))))) <=> ($false | (~inRange(N!2, nil)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[146, 139])).
% 0.20/0.45 tff(148,plain,
% 0.20/0.45 (((~((nil = nil) | (~inRange(N!2, nil)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(nil, N!2))), 0) | (~(nil = cons(tptp_fun_K_1(nil, N!2), tptp_fun_T_0(nil, N!2)))) | (~$greatereq(tptp_fun_K_1(nil, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(nil, N!2))))))) | (~(inRange(N!2, nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T))))))))) <=> (~inRange(N!2, nil))),
% 0.20/0.45 inference(transitivity,[status(thm)],[147, 138])).
% 0.20/0.45 tff(149,plain,
% 0.20/0.45 ((~((~((nil = nil) | (~inRange(N!2, nil)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(nil, N!2))), 0) | (~(nil = cons(tptp_fun_K_1(nil, N!2), tptp_fun_T_0(nil, N!2)))) | (~$greatereq(tptp_fun_K_1(nil, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(nil, N!2))))))) | (~(inRange(N!2, nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T)))))))))) <=> (~(~inRange(N!2, nil)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[148])).
% 0.20/0.45 tff(150,plain,
% 0.20/0.45 ((~((~((nil = nil) | (~inRange(N!2, nil)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(nil, N!2))), 0) | (~(nil = cons(tptp_fun_K_1(nil, N!2), tptp_fun_T_0(nil, N!2)))) | (~$greatereq(tptp_fun_K_1(nil, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(nil, N!2))))))) | (~(inRange(N!2, nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T)))))))))) <=> inRange(N!2, nil)),
% 0.20/0.45 inference(transitivity,[status(thm)],[149, 137])).
% 0.20/0.45 tff(151,plain,
% 0.20/0.45 (((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((nil = nil) | (~inRange(N!2, nil)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(nil, N!2))), 0) | (~(nil = cons(tptp_fun_K_1(nil, N!2), tptp_fun_T_0(nil, N!2)))) | (~$greatereq(tptp_fun_K_1(nil, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(nil, N!2))))))) | (~(inRange(N!2, nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T))))))))))) <=> ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | inRange(N!2, nil))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[150])).
% 0.20/0.45 tff(152,plain,
% 0.20/0.45 (((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((nil = nil) | (~inRange(N!2, nil)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(nil, N!2))), 0) | (~(nil = cons(tptp_fun_K_1(nil, N!2), tptp_fun_T_0(nil, N!2)))) | (~$greatereq(tptp_fun_K_1(nil, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(nil, N!2))))))) | (~(inRange(N!2, nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T))))))))))) <=> ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | inRange(N!2, nil))),
% 0.20/0.46 inference(transitivity,[status(thm)],[151, 136])).
% 0.20/0.46 tff(153,plain,
% 0.20/0.46 ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((nil = nil) | (~inRange(N!2, nil)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(nil, N!2))), 0) | (~(nil = cons(tptp_fun_K_1(nil, N!2), tptp_fun_T_0(nil, N!2)))) | (~$greatereq(tptp_fun_K_1(nil, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(nil, N!2))))))) | (~(inRange(N!2, nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T))))))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(154,plain,
% 0.20/0.46 ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | inRange(N!2, nil)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.46 tff(155,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[154, 25, 135])).
% 0.20/0.46 % SZS output end Proof
%------------------------------------------------------------------------------