TSTP Solution File: DAT104_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT104_1 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 14:36:45 EDT 2022
% Result : Theorem 0.21s 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT104_1 : TPTP v8.1.0. Released v6.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 01:56:10 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 % SZS output start Proof
% 0.21/0.47 tff(nil_type, type, (
% 0.21/0.47 nil: list)).
% 0.21/0.47 tff(cons_type, type, (
% 0.21/0.47 cons: ( $int * list ) > list)).
% 0.21/0.47 tff(tail_type, type, (
% 0.21/0.47 tail: list > list)).
% 0.21/0.47 tff(head_type, type, (
% 0.21/0.47 head: list > $int)).
% 0.21/0.47 tff(inRange_type, type, (
% 0.21/0.47 inRange: ( $int * list ) > $o)).
% 0.21/0.47 tff(tptp_fun_T_0_type, type, (
% 0.21/0.47 tptp_fun_T_0: ( list * $int ) > list)).
% 0.21/0.47 tff(tptp_fun_K_1_type, type, (
% 0.21/0.47 tptp_fun_K_1: ( list * $int ) > $int)).
% 0.21/0.47 tff(1,plain,
% 0.21/0.47 (^[K: $int, L: list] : refl((~(cons(K, L) = nil)) <=> (~(cons(K, L) = nil)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(2,plain,
% 0.21/0.47 (![K: $int, L: list] : (~(cons(K, L) = nil)) <=> ![K: $int, L: list] : (~(cons(K, L) = nil))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.47 tff(3,plain,
% 0.21/0.47 (![K: $int, L: list] : (~(cons(K, L) = nil)) <=> ![K: $int, L: list] : (~(cons(K, L) = nil))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(4,axiom,(![K: $int, L: list] : (~(cons(K, L) = nil))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l4')).
% 0.21/0.47 tff(5,plain,
% 0.21/0.47 (![K: $int, L: list] : (~(cons(K, L) = nil))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.47 tff(6,plain,(
% 0.21/0.47 ![K: $int, L: list] : (~(cons(K, L) = nil))),
% 0.21/0.47 inference(skolemize,[status(sab)],[5])).
% 0.21/0.47 tff(7,plain,
% 0.21/0.47 (![K: $int, L: list] : (~(cons(K, L) = nil))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.47 tff(8,plain,
% 0.21/0.47 ((~![K: $int, L: list] : (~(cons(K, L) = nil))) | (~(cons(0, nil) = nil))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(9,plain,
% 0.21/0.47 (~(cons(0, nil) = nil)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.47 tff(10,plain,
% 0.21/0.47 (^[L: list] : refl(((L = nil) | (L = cons(head(L), tail(L)))) <=> ((L = nil) | (L = cons(head(L), tail(L)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(11,plain,
% 0.21/0.47 (![L: list] : ((L = nil) | (L = cons(head(L), tail(L)))) <=> ![L: list] : ((L = nil) | (L = cons(head(L), tail(L))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.47 tff(12,plain,
% 0.21/0.47 (![L: list] : ((L = nil) | (L = cons(head(L), tail(L)))) <=> ![L: list] : ((L = nil) | (L = cons(head(L), tail(L))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(13,axiom,(![L: list] : ((L = nil) | (L = cons(head(L), tail(L))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l3')).
% 0.21/0.47 tff(14,plain,
% 0.21/0.47 (![L: list] : ((L = nil) | (L = cons(head(L), tail(L))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.47 tff(15,plain,(
% 0.21/0.47 ![L: list] : ((L = nil) | (L = cons(head(L), tail(L))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[14])).
% 0.21/0.47 tff(16,plain,
% 0.21/0.47 (![L: list] : ((L = nil) | (L = cons(head(L), tail(L))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.21/0.47 tff(17,plain,
% 0.21/0.47 (((~![L: list] : ((L = nil) | (L = cons(head(L), tail(L))))) | ((cons(0, nil) = nil) | (cons(0, nil) = cons(head(cons(0, nil)), tail(cons(0, nil)))))) <=> ((~![L: list] : ((L = nil) | (L = cons(head(L), tail(L))))) | (cons(0, nil) = nil) | (cons(0, nil) = cons(head(cons(0, nil)), tail(cons(0, nil)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(18,plain,
% 0.21/0.47 ((~![L: list] : ((L = nil) | (L = cons(head(L), tail(L))))) | ((cons(0, nil) = nil) | (cons(0, nil) = cons(head(cons(0, nil)), tail(cons(0, nil)))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(19,plain,
% 0.21/0.47 ((~![L: list] : ((L = nil) | (L = cons(head(L), tail(L))))) | (cons(0, nil) = nil) | (cons(0, nil) = cons(head(cons(0, nil)), tail(cons(0, nil))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.47 tff(20,plain,
% 0.21/0.47 (cons(0, nil) = cons(head(cons(0, nil)), tail(cons(0, nil)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 0.21/0.47 tff(21,plain,
% 0.21/0.47 (cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil)),
% 0.21/0.47 inference(symmetry,[status(thm)],[20])).
% 0.21/0.47 tff(22,assumption,(![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))), introduced(assumption)).
% 0.21/0.47 tff(23,plain,
% 0.21/0.47 (^[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)))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(24,plain,
% 0.21/0.47 (![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))))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.47 tff(25,plain,
% 0.21/0.47 (^[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)))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(26,plain,
% 0.21/0.47 (![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))))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.47 tff(27,plain,
% 0.21/0.47 (![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))))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[26, 24])).
% 0.21/0.47 tff(28,plain,
% 0.21/0.47 (^[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))))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(29,plain,
% 0.21/0.47 (![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))))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.47 tff(30,plain,
% 0.21/0.47 (^[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)))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(31,plain,
% 0.21/0.47 (![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))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.47 tff(32,plain,
% 0.21/0.47 (^[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)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(33,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.47 tff(34,plain,
% 0.21/0.47 (^[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)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(35,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.47 tff(36,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(37,plain,
% 0.21/0.47 (^[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)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(38,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.47 tff(39,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/sandbox/benchmark/theBenchmark.p','inRange')).
% 0.21/0.47 tff(40,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.47 tff(41,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.21/0.47 tff(42,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[41, 35])).
% 0.21/0.47 tff(43,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[42, 33])).
% 0.21/0.47 tff(44,plain,(
% 0.21/0.47 ![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))))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[43])).
% 0.21/0.47 tff(45,plain,
% 0.21/0.47 (![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))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[44, 31])).
% 0.21/0.47 tff(46,plain,
% 0.21/0.47 (![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))))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[45, 29])).
% 0.21/0.47 tff(47,plain,
% 0.21/0.47 (![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))))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[46, 27])).
% 0.21/0.47 tff(48,plain,
% 0.21/0.47 (((~![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(1, 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(1, nil))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(49,plain,
% 0.21/0.47 ((~(~inRange(1, nil))) <=> inRange(1, nil)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(50,plain,
% 0.21/0.47 (($false | (~inRange(1, nil))) <=> (~inRange(1, nil))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(51,plain,
% 0.21/0.47 ((~(inRange($sum(0, $product(-1, -1)), nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, $sum(0, $product(-1, -1)))), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange($sum(0, $product(-1, -1)), T)))))))) <=> (~inRange(1, nil))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(52,plain,
% 0.21/0.47 ((~$true) <=> $false),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(53,plain,
% 0.21/0.47 (($true | (~inRange(1, nil)) | (~((~inRange(1, tptp_fun_T_0(nil, 1))) | $greatereq(tptp_fun_K_1(nil, 1), 1) | (~$greatereq(tptp_fun_K_1(nil, 1), 0)) | (~(nil = cons(tptp_fun_K_1(nil, 1), tptp_fun_T_0(nil, 1))))))) <=> $true),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(54,plain,
% 0.21/0.47 ((~($lesseq($sum($sum(0, $product(-1, -1)), $product(-1, tptp_fun_K_1(nil, $sum(0, $product(-1, -1))))), 0) | (~(nil = cons(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), tptp_fun_T_0(nil, $sum(0, $product(-1, -1)))))) | (~$greatereq(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), 0)) | (~inRange($sum(0, $product(-1, -1)), tptp_fun_T_0(nil, $sum(0, $product(-1, -1))))))) <=> (~((~inRange(1, tptp_fun_T_0(nil, 1))) | $greatereq(tptp_fun_K_1(nil, 1), 1) | (~$greatereq(tptp_fun_K_1(nil, 1), 0)) | (~(nil = cons(tptp_fun_K_1(nil, 1), tptp_fun_T_0(nil, 1))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(55,plain,
% 0.21/0.47 ((~inRange($sum(0, $product(-1, -1)), nil)) <=> (~inRange(1, nil))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(56,plain,
% 0.21/0.47 ((nil = nil) <=> $true),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(57,plain,
% 0.21/0.47 (((nil = nil) | (~inRange($sum(0, $product(-1, -1)), nil)) | (~($lesseq($sum($sum(0, $product(-1, -1)), $product(-1, tptp_fun_K_1(nil, $sum(0, $product(-1, -1))))), 0) | (~(nil = cons(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), tptp_fun_T_0(nil, $sum(0, $product(-1, -1)))))) | (~$greatereq(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), 0)) | (~inRange($sum(0, $product(-1, -1)), tptp_fun_T_0(nil, $sum(0, $product(-1, -1)))))))) <=> ($true | (~inRange(1, nil)) | (~((~inRange(1, tptp_fun_T_0(nil, 1))) | $greatereq(tptp_fun_K_1(nil, 1), 1) | (~$greatereq(tptp_fun_K_1(nil, 1), 0)) | (~(nil = cons(tptp_fun_K_1(nil, 1), tptp_fun_T_0(nil, 1)))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[56, 55, 54])).
% 0.21/0.47 tff(58,plain,
% 0.21/0.47 (((nil = nil) | (~inRange($sum(0, $product(-1, -1)), nil)) | (~($lesseq($sum($sum(0, $product(-1, -1)), $product(-1, tptp_fun_K_1(nil, $sum(0, $product(-1, -1))))), 0) | (~(nil = cons(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), tptp_fun_T_0(nil, $sum(0, $product(-1, -1)))))) | (~$greatereq(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), 0)) | (~inRange($sum(0, $product(-1, -1)), tptp_fun_T_0(nil, $sum(0, $product(-1, -1)))))))) <=> $true),
% 0.21/0.47 inference(transitivity,[status(thm)],[57, 53])).
% 0.21/0.47 tff(59,plain,
% 0.21/0.47 ((~((nil = nil) | (~inRange($sum(0, $product(-1, -1)), nil)) | (~($lesseq($sum($sum(0, $product(-1, -1)), $product(-1, tptp_fun_K_1(nil, $sum(0, $product(-1, -1))))), 0) | (~(nil = cons(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), tptp_fun_T_0(nil, $sum(0, $product(-1, -1)))))) | (~$greatereq(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), 0)) | (~inRange($sum(0, $product(-1, -1)), tptp_fun_T_0(nil, $sum(0, $product(-1, -1))))))))) <=> (~$true)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[58])).
% 0.21/0.48 tff(60,plain,
% 0.21/0.48 ((~((nil = nil) | (~inRange($sum(0, $product(-1, -1)), nil)) | (~($lesseq($sum($sum(0, $product(-1, -1)), $product(-1, tptp_fun_K_1(nil, $sum(0, $product(-1, -1))))), 0) | (~(nil = cons(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), tptp_fun_T_0(nil, $sum(0, $product(-1, -1)))))) | (~$greatereq(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), 0)) | (~inRange($sum(0, $product(-1, -1)), tptp_fun_T_0(nil, $sum(0, $product(-1, -1))))))))) <=> $false),
% 0.21/0.48 inference(transitivity,[status(thm)],[59, 52])).
% 0.21/0.48 tff(61,plain,
% 0.21/0.48 (((~((nil = nil) | (~inRange($sum(0, $product(-1, -1)), nil)) | (~($lesseq($sum($sum(0, $product(-1, -1)), $product(-1, tptp_fun_K_1(nil, $sum(0, $product(-1, -1))))), 0) | (~(nil = cons(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), tptp_fun_T_0(nil, $sum(0, $product(-1, -1)))))) | (~$greatereq(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), 0)) | (~inRange($sum(0, $product(-1, -1)), tptp_fun_T_0(nil, $sum(0, $product(-1, -1))))))))) | (~(inRange($sum(0, $product(-1, -1)), nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, $sum(0, $product(-1, -1)))), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange($sum(0, $product(-1, -1)), T))))))))) <=> ($false | (~inRange(1, nil)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[60, 51])).
% 0.21/0.48 tff(62,plain,
% 0.21/0.48 (((~((nil = nil) | (~inRange($sum(0, $product(-1, -1)), nil)) | (~($lesseq($sum($sum(0, $product(-1, -1)), $product(-1, tptp_fun_K_1(nil, $sum(0, $product(-1, -1))))), 0) | (~(nil = cons(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), tptp_fun_T_0(nil, $sum(0, $product(-1, -1)))))) | (~$greatereq(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), 0)) | (~inRange($sum(0, $product(-1, -1)), tptp_fun_T_0(nil, $sum(0, $product(-1, -1))))))))) | (~(inRange($sum(0, $product(-1, -1)), nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, $sum(0, $product(-1, -1)))), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange($sum(0, $product(-1, -1)), T))))))))) <=> (~inRange(1, nil))),
% 0.21/0.48 inference(transitivity,[status(thm)],[61, 50])).
% 0.21/0.48 tff(63,plain,
% 0.21/0.48 ((~((~((nil = nil) | (~inRange($sum(0, $product(-1, -1)), nil)) | (~($lesseq($sum($sum(0, $product(-1, -1)), $product(-1, tptp_fun_K_1(nil, $sum(0, $product(-1, -1))))), 0) | (~(nil = cons(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), tptp_fun_T_0(nil, $sum(0, $product(-1, -1)))))) | (~$greatereq(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), 0)) | (~inRange($sum(0, $product(-1, -1)), tptp_fun_T_0(nil, $sum(0, $product(-1, -1))))))))) | (~(inRange($sum(0, $product(-1, -1)), nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, $sum(0, $product(-1, -1)))), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange($sum(0, $product(-1, -1)), T)))))))))) <=> (~(~inRange(1, nil)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[62])).
% 0.21/0.48 tff(64,plain,
% 0.21/0.48 ((~((~((nil = nil) | (~inRange($sum(0, $product(-1, -1)), nil)) | (~($lesseq($sum($sum(0, $product(-1, -1)), $product(-1, tptp_fun_K_1(nil, $sum(0, $product(-1, -1))))), 0) | (~(nil = cons(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), tptp_fun_T_0(nil, $sum(0, $product(-1, -1)))))) | (~$greatereq(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), 0)) | (~inRange($sum(0, $product(-1, -1)), tptp_fun_T_0(nil, $sum(0, $product(-1, -1))))))))) | (~(inRange($sum(0, $product(-1, -1)), nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, $sum(0, $product(-1, -1)))), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange($sum(0, $product(-1, -1)), T)))))))))) <=> inRange(1, nil)),
% 0.21/0.48 inference(transitivity,[status(thm)],[63, 49])).
% 0.21/0.48 tff(65,plain,
% 0.21/0.48 (((~![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($sum(0, $product(-1, -1)), nil)) | (~($lesseq($sum($sum(0, $product(-1, -1)), $product(-1, tptp_fun_K_1(nil, $sum(0, $product(-1, -1))))), 0) | (~(nil = cons(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), tptp_fun_T_0(nil, $sum(0, $product(-1, -1)))))) | (~$greatereq(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), 0)) | (~inRange($sum(0, $product(-1, -1)), tptp_fun_T_0(nil, $sum(0, $product(-1, -1))))))))) | (~(inRange($sum(0, $product(-1, -1)), nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, $sum(0, $product(-1, -1)))), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange($sum(0, $product(-1, -1)), 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(1, nil))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[64])).
% 0.21/0.48 tff(66,plain,
% 0.21/0.48 (((~![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($sum(0, $product(-1, -1)), nil)) | (~($lesseq($sum($sum(0, $product(-1, -1)), $product(-1, tptp_fun_K_1(nil, $sum(0, $product(-1, -1))))), 0) | (~(nil = cons(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), tptp_fun_T_0(nil, $sum(0, $product(-1, -1)))))) | (~$greatereq(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), 0)) | (~inRange($sum(0, $product(-1, -1)), tptp_fun_T_0(nil, $sum(0, $product(-1, -1))))))))) | (~(inRange($sum(0, $product(-1, -1)), nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, $sum(0, $product(-1, -1)))), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange($sum(0, $product(-1, -1)), 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(1, nil))),
% 0.21/0.48 inference(transitivity,[status(thm)],[65, 48])).
% 0.21/0.48 tff(67,plain,
% 0.21/0.48 ((~![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($sum(0, $product(-1, -1)), nil)) | (~($lesseq($sum($sum(0, $product(-1, -1)), $product(-1, tptp_fun_K_1(nil, $sum(0, $product(-1, -1))))), 0) | (~(nil = cons(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), tptp_fun_T_0(nil, $sum(0, $product(-1, -1)))))) | (~$greatereq(tptp_fun_K_1(nil, $sum(0, $product(-1, -1))), 0)) | (~inRange($sum(0, $product(-1, -1)), tptp_fun_T_0(nil, $sum(0, $product(-1, -1))))))))) | (~(inRange($sum(0, $product(-1, -1)), nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, $sum(0, $product(-1, -1)))), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange($sum(0, $product(-1, -1)), T))))))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(68,plain,
% 0.21/0.48 ((~![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(1, nil)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.48 tff(69,plain,
% 0.21/0.48 (inRange(1, nil)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[68, 47])).
% 0.21/0.48 tff(70,plain,
% 0.21/0.48 (((~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))) | ((~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)))) <=> ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(71,plain,
% 0.21/0.48 (($false | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)) | $false) <=> ((~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(72,plain,
% 0.21/0.48 ($greatereq(0, 1) <=> $false),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(73,plain,
% 0.21/0.48 ($greatereq(0, 0) <=> $true),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(74,plain,
% 0.21/0.48 ((~$greatereq(0, 0)) <=> (~$true)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[73])).
% 0.21/0.48 tff(75,plain,
% 0.21/0.48 ((~$greatereq(0, 0)) <=> $false),
% 0.21/0.48 inference(transitivity,[status(thm)],[74, 52])).
% 0.21/0.48 tff(76,plain,
% 0.21/0.48 (((~$greatereq(0, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)) | $greatereq(0, 1)) <=> ($false | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)) | $false)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[75, 72])).
% 0.21/0.48 tff(77,plain,
% 0.21/0.48 (((~$greatereq(0, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)) | $greatereq(0, 1)) <=> ((~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[76, 71])).
% 0.21/0.48 tff(78,plain,
% 0.21/0.48 (((~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))) | ((~$greatereq(0, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)) | $greatereq(0, 1))) <=> ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))) | ((~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[77])).
% 0.21/0.48 tff(79,plain,
% 0.21/0.48 (((~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))) | ((~$greatereq(0, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)) | $greatereq(0, 1))) <=> ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[78, 70])).
% 0.21/0.48 tff(80,plain,
% 0.21/0.48 ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))) | ((~$greatereq(0, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)) | $greatereq(0, 1))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(81,plain,
% 0.21/0.48 ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.21/0.48 tff(82,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[81, 69, 22, 21])).
% 0.21/0.48 tff(83,plain,(~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(84,plain,
% 0.21/0.48 (((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1)))) | ![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(85,plain,
% 0.21/0.48 ((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.21/0.48 tff(86,plain,
% 0.21/0.48 (((~![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))))))))))) | (~((~((~((~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 0)) | $greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 1) | (~inRange(1, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1)))))) | (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))))) | inRange(1, cons(head(cons(0, nil)), tail(cons(0, 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))))))))))) | (~((~((~((~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 0)) | $greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 1) | (~inRange(1, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1)))))) | (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))))) | inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(87,plain,
% 0.21/0.48 ((~((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange($product(-1, -1), cons(head(cons(0, nil)), tail(cons(0, nil))))) | (~($lesseq($sum($product(-1, -1), $product(-1, tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), $product(-1, -1)))), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), $product(-1, -1)), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), $product(-1, -1))))) | (~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), $product(-1, -1)), 0)) | (~inRange($product(-1, -1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), $product(-1, -1)))))))) | (~(inRange($product(-1, -1), cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, $product(-1, -1))), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange($product(-1, -1), T)))))))))) <=> (~((~((~((~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 0)) | $greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 1) | (~inRange(1, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1)))))) | (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))))) | inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(88,plain,
% 0.21/0.48 (((~![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(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange($product(-1, -1), cons(head(cons(0, nil)), tail(cons(0, nil))))) | (~($lesseq($sum($product(-1, -1), $product(-1, tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), $product(-1, -1)))), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), $product(-1, -1)), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), $product(-1, -1))))) | (~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), $product(-1, -1)), 0)) | (~inRange($product(-1, -1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), $product(-1, -1)))))))) | (~(inRange($product(-1, -1), cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, $product(-1, -1))), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange($product(-1, -1), 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))))))))))) | (~((~((~((~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 0)) | $greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 1) | (~inRange(1, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1)))))) | (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))))) | inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[87])).
% 0.21/0.48 tff(89,plain,
% 0.21/0.48 (((~![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(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange($product(-1, -1), cons(head(cons(0, nil)), tail(cons(0, nil))))) | (~($lesseq($sum($product(-1, -1), $product(-1, tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), $product(-1, -1)))), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), $product(-1, -1)), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), $product(-1, -1))))) | (~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), $product(-1, -1)), 0)) | (~inRange($product(-1, -1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), $product(-1, -1)))))))) | (~(inRange($product(-1, -1), cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, $product(-1, -1))), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange($product(-1, -1), 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))))))))))) | (~((~((~((~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 0)) | $greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 1) | (~inRange(1, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1)))))) | (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))))) | inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[88, 86])).
% 0.21/0.48 tff(90,plain,
% 0.21/0.48 ((~![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(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange($product(-1, -1), cons(head(cons(0, nil)), tail(cons(0, nil))))) | (~($lesseq($sum($product(-1, -1), $product(-1, tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), $product(-1, -1)))), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), $product(-1, -1)), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), $product(-1, -1))))) | (~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), $product(-1, -1)), 0)) | (~inRange($product(-1, -1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), $product(-1, -1)))))))) | (~(inRange($product(-1, -1), cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, $product(-1, -1))), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange($product(-1, -1), T))))))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(91,plain,
% 0.21/0.49 ((~![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))))))))))) | (~((~((~((~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 0)) | $greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 1) | (~inRange(1, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1)))))) | (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))))) | inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.49 tff(92,plain,
% 0.21/0.49 (~((~((~((~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 0)) | $greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 1) | (~inRange(1, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1)))))) | (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))))) | inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[91, 47])).
% 0.21/0.49 tff(93,plain,
% 0.21/0.49 (((~((~((~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 0)) | $greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 1) | (~inRange(1, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1)))))) | (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))))) | inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | ((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))))) | inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(94,plain,
% 0.21/0.49 ((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))))) | inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.21/0.49 tff(95,plain,
% 0.21/0.49 ((~((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))))) | inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))))) | inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(96,plain,
% 0.21/0.49 ((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))))) | inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.21/0.49 tff(97,plain,
% 0.21/0.49 (inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[96, 85])).
% 0.21/0.49 tff(98,plain,
% 0.21/0.49 (^[N: $int, L: list] : refl(((~inRange(N, L)) | inRange($sum(-1, N), L)) <=> ((~inRange(N, L)) | inRange($sum(-1, N), L)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(99,plain,
% 0.21/0.49 (![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L)) <=> ![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[98])).
% 0.21/0.49 tff(100,plain,
% 0.21/0.49 (![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L)) <=> ![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(101,plain,
% 0.21/0.49 ((~(~![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L)))) <=> ![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(102,plain,
% 0.21/0.49 ((~![N: $int, L: list] : (inRange(N, L) => inRange($difference(N, 1), L))) <=> (~![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(103,plain,
% 0.21/0.49 ((~(~![N: $int, L: list] : (inRange(N, L) => inRange($difference(N, 1), L)))) <=> (~(~![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[102])).
% 0.21/0.49 tff(104,plain,
% 0.21/0.49 ((~(~![N: $int, L: list] : (inRange(N, L) => inRange($difference(N, 1), L)))) <=> ![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L))),
% 0.21/0.49 inference(transitivity,[status(thm)],[103, 101])).
% 0.21/0.49 tff(105,axiom,(~(~![N: $int, L: list] : (inRange(N, L) => inRange($difference(N, 1), L)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c')).
% 0.21/0.49 tff(106,plain,
% 0.21/0.49 (![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.21/0.49 tff(107,plain,
% 0.21/0.49 (![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[106, 100])).
% 0.21/0.49 tff(108,plain,(
% 0.21/0.49 ![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L))),
% 0.21/0.49 inference(skolemize,[status(sab)],[107])).
% 0.21/0.49 tff(109,plain,
% 0.21/0.49 (![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[108, 99])).
% 0.21/0.49 tff(110,plain,
% 0.21/0.49 (((~![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L))) | ((~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil)))))) <=> ((~![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L))) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil)))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(111,plain,
% 0.21/0.49 (((~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | inRange($sum(-1, 1), cons(head(cons(0, nil)), tail(cons(0, nil))))) <=> ((~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil)))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(112,plain,
% 0.21/0.49 (((~![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L))) | ((~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | inRange($sum(-1, 1), cons(head(cons(0, nil)), tail(cons(0, nil)))))) <=> ((~![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L))) | ((~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[111])).
% 0.21/0.49 tff(113,plain,
% 0.21/0.49 (((~![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L))) | ((~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | inRange($sum(-1, 1), cons(head(cons(0, nil)), tail(cons(0, nil)))))) <=> ((~![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L))) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil)))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[112, 110])).
% 0.21/0.49 tff(114,plain,
% 0.21/0.49 ((~![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L))) | ((~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | inRange($sum(-1, 1), cons(head(cons(0, nil)), tail(cons(0, nil)))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(115,plain,
% 0.21/0.49 ((~![N: $int, L: list] : ((~inRange(N, L)) | inRange($sum(-1, N), L))) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.21/0.49 tff(116,plain,
% 0.21/0.49 (inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[115, 109, 97])).
% 0.21/0.49 tff(117,plain,
% 0.21/0.49 ((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) <=> (cons(0, nil) = nil)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[21])).
% 0.21/0.49 tff(118,plain,
% 0.21/0.49 ((cons(0, nil) = nil) <=> (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil)),
% 0.21/0.49 inference(symmetry,[status(thm)],[117])).
% 0.21/0.49 tff(119,plain,
% 0.21/0.49 ((~(cons(0, nil) = nil)) <=> (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = nil))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[118])).
% 0.21/0.49 tff(120,plain,
% 0.21/0.49 (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = nil)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[9, 119])).
% 0.21/0.49 tff(121,plain,
% 0.21/0.49 ((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil)))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(122,plain,
% 0.21/0.49 (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil))))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[121, 120, 116])).
% 0.21/0.49 tff(123,plain,
% 0.21/0.49 (((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~(inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = nil))))) | ((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil))))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(124,plain,
% 0.21/0.49 ((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~(inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = nil))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.21/0.49 tff(125,plain,
% 0.21/0.49 (((~![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(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~(inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = 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))))))))))) | (~((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~(inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = nil)))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(126,plain,
% 0.21/0.49 ((~((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil))))) | (~($lesseq($sum(0, $product(-1, tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 0))), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 0), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 0)))) | (~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 0), 0)) | (~inRange(0, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 0))))))) | (~(inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, 0)), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(0, T)))))))))) <=> (~((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~(inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = nil))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(127,plain,
% 0.21/0.49 (((~![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(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil))))) | (~($lesseq($sum(0, $product(-1, tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 0))), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 0), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 0)))) | (~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 0), 0)) | (~inRange(0, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 0))))))) | (~(inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, 0)), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(0, 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(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~(inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = nil)))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[126])).
% 0.21/0.49 tff(128,plain,
% 0.21/0.49 (((~![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(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil))))) | (~($lesseq($sum(0, $product(-1, tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 0))), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 0), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 0)))) | (~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 0), 0)) | (~inRange(0, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 0))))))) | (~(inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, 0)), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(0, 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(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~(inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = nil)))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[127, 125])).
% 0.21/0.49 tff(129,plain,
% 0.21/0.49 ((~![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(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil))))) | (~($lesseq($sum(0, $product(-1, tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 0))), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 0), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 0)))) | (~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 0), 0)) | (~inRange(0, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 0))))))) | (~(inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, 0)), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(0, T))))))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(130,plain,
% 0.21/0.49 ((~![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(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~(inRange(0, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = nil))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.21/0.49 tff(131,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[130, 47, 124])).
% 0.21/0.49 % SZS output end Proof
%------------------------------------------------------------------------------