TSTP Solution File: DAT103_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT103_1 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 14:36:45 EDT 2022
% Result : Theorem 0.15s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : DAT103_1 : TPTP v8.1.0. Released v6.1.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n013.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Aug 31 01:48:47 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.35 Usage: tptp [options] [-file:]file
% 0.15/0.35 -h, -? prints this message.
% 0.15/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.35 -m, -model generate model.
% 0.15/0.35 -p, -proof generate proof.
% 0.15/0.35 -c, -core generate unsat core of named formulas.
% 0.15/0.35 -st, -statistics display statistics.
% 0.15/0.35 -t:timeout set timeout (in second).
% 0.15/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.35 -<param>:<value> configuration parameter and value.
% 0.15/0.35 -o:<output-file> file to place output in.
% 0.15/0.40 % SZS status Theorem
% 0.15/0.40 % SZS output start Proof
% 0.15/0.40 tff(head_type, type, (
% 0.15/0.40 head: list > $int)).
% 0.15/0.40 tff(cons_type, type, (
% 0.15/0.40 cons: ( $int * list ) > list)).
% 0.15/0.40 tff(tptp_fun_T_0_type, type, (
% 0.15/0.40 tptp_fun_T_0: ( list * $int ) > list)).
% 0.15/0.40 tff(tptp_fun_N_2_type, type, (
% 0.15/0.40 tptp_fun_N_2: $int)).
% 0.15/0.40 tff(tptp_fun_L_3_type, type, (
% 0.15/0.40 tptp_fun_L_3: list)).
% 0.15/0.40 tff(tptp_fun_K_1_type, type, (
% 0.15/0.40 tptp_fun_K_1: ( list * $int ) > $int)).
% 0.15/0.40 tff(inRange_type, type, (
% 0.15/0.40 inRange: ( $int * list ) > $o)).
% 0.15/0.40 tff(nil_type, type, (
% 0.15/0.40 nil: list)).
% 0.15/0.40 tff(1,plain,
% 0.15/0.40 (^[K: $int, L: list] : refl(($sum(K, $product(-1, head(cons(K, L)))) = 0) <=> ($sum(K, $product(-1, head(cons(K, L)))) = 0))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(2,plain,
% 0.15/0.40 (![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0) <=> ![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0)),
% 0.15/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.15/0.40 tff(3,plain,
% 0.15/0.40 (^[K: $int, L: list] : trans(monotonicity(rewrite($sum(head(cons(K, L)), $product(-1, K)) = $sum($product(-1, K), head(cons(K, L)))), (($sum(head(cons(K, L)), $product(-1, K)) = 0) <=> ($sum($product(-1, K), head(cons(K, L))) = 0))), rewrite(($sum($product(-1, K), head(cons(K, L))) = 0) <=> ($sum(K, $product(-1, head(cons(K, L)))) = 0)), (($sum(head(cons(K, L)), $product(-1, K)) = 0) <=> ($sum(K, $product(-1, head(cons(K, L)))) = 0)))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(4,plain,
% 0.15/0.40 (![K: $int, L: list] : ($sum(head(cons(K, L)), $product(-1, K)) = 0) <=> ![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0)),
% 0.15/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.15/0.40 tff(5,plain,
% 0.15/0.40 (^[K: $int, L: list] : rewrite((head(cons(K, L)) = K) <=> ($sum(head(cons(K, L)), $product(-1, K)) = 0))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(6,plain,
% 0.15/0.40 (![K: $int, L: list] : (head(cons(K, L)) = K) <=> ![K: $int, L: list] : ($sum(head(cons(K, L)), $product(-1, K)) = 0)),
% 0.15/0.40 inference(quant_intro,[status(thm)],[5])).
% 0.15/0.40 tff(7,plain,
% 0.15/0.40 (![K: $int, L: list] : (head(cons(K, L)) = K) <=> ![K: $int, L: list] : (head(cons(K, L)) = K)),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(8,axiom,(![K: $int, L: list] : (head(cons(K, L)) = K)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l1')).
% 0.15/0.40 tff(9,plain,
% 0.15/0.40 (![K: $int, L: list] : (head(cons(K, L)) = K)),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.15/0.40 tff(10,plain,
% 0.15/0.40 (![K: $int, L: list] : ($sum(head(cons(K, L)), $product(-1, K)) = 0)),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.15/0.40 tff(11,plain,
% 0.15/0.40 (![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0)),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.15/0.40 tff(12,plain,(
% 0.15/0.40 ![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0)),
% 0.15/0.40 inference(skolemize,[status(sab)],[11])).
% 0.15/0.40 tff(13,plain,
% 0.15/0.40 (![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0)),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.15/0.40 tff(14,plain,
% 0.15/0.40 ((~![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0)) | ($sum(tptp_fun_K_1(L!3, N!2), $product(-1, head(cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2))))) = 0)),
% 0.15/0.40 inference(quant_inst,[status(thm)],[])).
% 0.15/0.40 tff(15,plain,
% 0.15/0.40 ($sum(tptp_fun_K_1(L!3, N!2), $product(-1, head(cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2))))) = 0),
% 0.15/0.40 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.15/0.40 tff(16,plain,
% 0.15/0.40 ((~($sum(tptp_fun_K_1(L!3, N!2), $product(-1, head(cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2))))) = 0)) | $greatereq($sum(tptp_fun_K_1(L!3, N!2), $product(-1, head(cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2))))), 0)),
% 0.15/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.15/0.40 tff(17,plain,
% 0.15/0.40 ($greatereq($sum(tptp_fun_K_1(L!3, N!2), $product(-1, head(cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2))))), 0)),
% 0.15/0.40 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.15/0.40 tff(18,plain,
% 0.15/0.40 (^[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)))))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 (![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))))))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 (^[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)))))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(21,plain,
% 0.21/0.40 (![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))))))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 (![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))))))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[21, 19])).
% 0.21/0.40 tff(23,plain,
% 0.21/0.40 (^[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))))))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(24,plain,
% 0.21/0.40 (![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))))))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.40 tff(25,plain,
% 0.21/0.40 (^[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)))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 (![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))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 (^[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)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 (![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))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[27])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 (^[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)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 (![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))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 (![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))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (^[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)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 (![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))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.41 tff(34,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')).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (![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))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (![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))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (![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))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[36, 30])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (![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))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[37, 28])).
% 0.21/0.41 tff(39,plain,(
% 0.21/0.41 ![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))))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[38])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (![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))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[39, 26])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (![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))))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[40, 24])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (![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))))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[41, 22])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (((~![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))))))))))) | (~((~((L!3 = nil) | (~inRange(N!2, L!3)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2))))))) | (~(inRange(N!2, L!3) | (~((L!3 = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(L!3 = 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))))))))))) | (~((~((L!3 = nil) | (~inRange(N!2, L!3)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2))))))) | (~(inRange(N!2, L!3) | (~((L!3 = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(L!3 = cons(K, T))) | (~inRange(N!2, T)))))))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 ((~((~((L!3 = nil) | (~inRange(N!2, L!3)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2))))))) | (~(inRange(N!2, L!3) | (~((L!3 = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(L!3 = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T)))))))))) <=> (~((~((L!3 = nil) | (~inRange(N!2, L!3)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2))))))) | (~(inRange(N!2, L!3) | (~((L!3 = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(L!3 = cons(K, T))) | (~inRange(N!2, T))))))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (((~![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))))))))))) | (~((~((L!3 = nil) | (~inRange(N!2, L!3)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2))))))) | (~(inRange(N!2, L!3) | (~((L!3 = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(L!3 = cons(K, T))) | (~$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))))))))))) | (~((~((L!3 = nil) | (~inRange(N!2, L!3)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2))))))) | (~(inRange(N!2, L!3) | (~((L!3 = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(L!3 = cons(K, T))) | (~inRange(N!2, T)))))))))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[44])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (((~![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))))))))))) | (~((~((L!3 = nil) | (~inRange(N!2, L!3)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2))))))) | (~(inRange(N!2, L!3) | (~((L!3 = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(L!3 = cons(K, T))) | (~$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))))))))))) | (~((~((L!3 = nil) | (~inRange(N!2, L!3)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2))))))) | (~(inRange(N!2, L!3) | (~((L!3 = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(L!3 = cons(K, T))) | (~inRange(N!2, T)))))))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[45, 43])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 ((~![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))))))))))) | (~((~((L!3 = nil) | (~inRange(N!2, L!3)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2))))))) | (~(inRange(N!2, L!3) | (~((L!3 = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N!2)), 0) | (~(L!3 = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N!2, T))))))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 ((~![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))))))))))) | (~((~((L!3 = nil) | (~inRange(N!2, L!3)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2))))))) | (~(inRange(N!2, L!3) | (~((L!3 = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(L!3 = cons(K, T))) | (~inRange(N!2, T))))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (~((~((L!3 = nil) | (~inRange(N!2, L!3)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2))))))) | (~(inRange(N!2, L!3) | (~((L!3 = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(L!3 = cons(K, T))) | (~inRange(N!2, T)))))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[48, 42])).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (((~((L!3 = nil) | (~inRange(N!2, L!3)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2))))))) | (~(inRange(N!2, L!3) | (~((L!3 = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | $greatereq($sum(K, $product(-1, N!2)), 0) | (~(L!3 = cons(K, T))) | (~inRange(N!2, T))))))))) | ((L!3 = nil) | (~inRange(N!2, L!3)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2))))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 ((L!3 = nil) | (~inRange(N!2, L!3)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.21/0.42 tff(52,plain,
% 0.21/0.42 (^[L: list, N: $int] : rewrite(((~(L = nil)) & inRange(N, L) & (~$lesseq(1, $sum(N, $product(-1, head(L)))))) <=> ((~(L = nil)) & inRange(N, L) & (~$greatereq($sum(N, $product(-1, head(L))), 1))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 (?[L: list, N: $int] : ((~(L = nil)) & inRange(N, L) & (~$lesseq(1, $sum(N, $product(-1, head(L)))))) <=> ?[L: list, N: $int] : ((~(L = nil)) & inRange(N, L) & (~$greatereq($sum(N, $product(-1, head(L))), 1)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[52])).
% 0.21/0.42 tff(54,plain,
% 0.21/0.42 (?[L: list, N: $int] : ((~(L = nil)) & inRange(N, L) & (~$lesseq(1, $sum(N, $product(-1, head(L)))))) <=> ?[L: list, N: $int] : ((~(L = nil)) & inRange(N, L) & (~$lesseq(1, $sum(N, $product(-1, head(L))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 ((~(~?[L: list, N: $int] : ((~(L = nil)) & inRange(N, L) & (~$lesseq(1, $sum(N, $product(-1, head(L)))))))) <=> ?[L: list, N: $int] : ((~(L = nil)) & inRange(N, L) & (~$lesseq(1, $sum(N, $product(-1, head(L))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(56,plain,
% 0.21/0.42 ((~?[L: list, N: $int] : (((~(L = nil)) & inRange(N, L)) & $less($difference(N, head(L)), 1))) <=> (~?[L: list, N: $int] : ((~(L = nil)) & inRange(N, L) & (~$lesseq(1, $sum(N, $product(-1, head(L)))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(57,plain,
% 0.21/0.42 ((~(~?[L: list, N: $int] : (((~(L = nil)) & inRange(N, L)) & $less($difference(N, head(L)), 1)))) <=> (~(~?[L: list, N: $int] : ((~(L = nil)) & inRange(N, L) & (~$lesseq(1, $sum(N, $product(-1, head(L))))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[56])).
% 0.21/0.42 tff(58,plain,
% 0.21/0.42 ((~(~?[L: list, N: $int] : (((~(L = nil)) & inRange(N, L)) & $less($difference(N, head(L)), 1)))) <=> ?[L: list, N: $int] : ((~(L = nil)) & inRange(N, L) & (~$lesseq(1, $sum(N, $product(-1, head(L))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[57, 55])).
% 0.21/0.42 tff(59,axiom,(~(~?[L: list, N: $int] : (((~(L = nil)) & inRange(N, L)) & $less($difference(N, head(L)), 1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c')).
% 0.21/0.42 tff(60,plain,
% 0.21/0.42 (?[L: list, N: $int] : ((~(L = nil)) & inRange(N, L) & (~$lesseq(1, $sum(N, $product(-1, head(L))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.42 tff(61,plain,
% 0.21/0.42 (?[L: list, N: $int] : ((~(L = nil)) & inRange(N, L) & (~$lesseq(1, $sum(N, $product(-1, head(L))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[60, 54])).
% 0.21/0.42 tff(62,plain,
% 0.21/0.42 (?[L: list, N: $int] : ((~(L = nil)) & inRange(N, L) & (~$greatereq($sum(N, $product(-1, head(L))), 1)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[61, 53])).
% 0.21/0.42 tff(63,plain,(
% 0.21/0.42 (~(L!3 = nil)) & inRange(N!2, L!3) & (~$greatereq($sum(N!2, $product(-1, head(L!3))), 1))),
% 0.21/0.42 inference(skolemize,[status(sab)],[62])).
% 0.21/0.42 tff(64,plain,
% 0.21/0.42 (inRange(N!2, L!3)),
% 0.21/0.42 inference(and_elim,[status(thm)],[63])).
% 0.21/0.42 tff(65,plain,
% 0.21/0.42 (~(L!3 = nil)),
% 0.21/0.42 inference(and_elim,[status(thm)],[63])).
% 0.21/0.42 tff(66,plain,
% 0.21/0.42 ((~((L!3 = nil) | (~inRange(N!2, L!3)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2))))))) | (L!3 = nil) | (~inRange(N!2, L!3)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2)))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(67,plain,
% 0.21/0.42 ((~((L!3 = nil) | (~inRange(N!2, L!3)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2))))))) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[66, 65, 64])).
% 0.21/0.42 tff(68,plain,
% 0.21/0.42 (~($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[67, 51])).
% 0.21/0.42 tff(69,plain,
% 0.21/0.42 (($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2)))) | (~$lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(70,plain,
% 0.21/0.42 (~$lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.21/0.42 tff(71,plain,
% 0.21/0.42 (~$greatereq($sum(N!2, $product(-1, head(L!3))), 1)),
% 0.21/0.42 inference(and_elim,[status(thm)],[63])).
% 0.21/0.42 tff(72,plain,
% 0.21/0.42 (($lesseq($sum(N!2, $product(-1, tptp_fun_K_1(L!3, N!2))), 0) | (~(L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))) | (~$greatereq(tptp_fun_K_1(L!3, N!2), 0)) | (~inRange(N!2, tptp_fun_T_0(L!3, N!2)))) | (L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 (L!3 = cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[72, 68])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 (cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)) = L!3),
% 0.21/0.42 inference(symmetry,[status(thm)],[73])).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 (head(cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2))) = head(L!3)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[74])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 (head(L!3) = head(cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2)))),
% 0.21/0.42 inference(symmetry,[status(thm)],[75])).
% 0.21/0.42 tff(77,plain,
% 0.21/0.42 ((~(head(L!3) = head(cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2))))) | $lesseq($sum(head(L!3), $product(-1, head(cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2))))), 0)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 ($lesseq($sum(head(L!3), $product(-1, head(cons(tptp_fun_K_1(L!3, N!2), tptp_fun_T_0(L!3, N!2))))), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.21/0.42 tff(79,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[78, 71, 70, 17])).
% 0.21/0.42 % SZS output end Proof
%------------------------------------------------------------------------------