TSTP Solution File: SWV161+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV161+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:10:11 EDT 2022
% Result : Theorem 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV161+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n017.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 : Sun Sep 4 01:02:09 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.
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 tff(succ_type, type, (
% 0.21/0.44 succ: $i > $i)).
% 0.21/0.44 tff(tptp_minus_1_type, type, (
% 0.21/0.44 tptp_minus_1: $i)).
% 0.21/0.44 tff(sum_type, type, (
% 0.21/0.44 sum: ( $i * $i * $i ) > $i)).
% 0.21/0.44 tff(a_select3_type, type, (
% 0.21/0.44 a_select3: ( $i * $i * $i ) > $i)).
% 0.21/0.44 tff(tptp_sum_index_type, type, (
% 0.21/0.44 tptp_sum_index: $i)).
% 0.21/0.44 tff(tptp_fun_B_13_type, type, (
% 0.21/0.44 tptp_fun_B_13: $i)).
% 0.21/0.44 tff(q_type, type, (
% 0.21/0.44 q: $i)).
% 0.21/0.44 tff(pv10_type, type, (
% 0.21/0.44 pv10: $i)).
% 0.21/0.44 tff(n1_type, type, (
% 0.21/0.44 n1: $i)).
% 0.21/0.44 tff(n0_type, type, (
% 0.21/0.44 n0: $i)).
% 0.21/0.44 tff(gt_type, type, (
% 0.21/0.44 gt: ( $i * $i ) > $o)).
% 0.21/0.44 tff(leq_type, type, (
% 0.21/0.44 leq: ( $i * $i ) > $o)).
% 0.21/0.44 tff(pred_type, type, (
% 0.21/0.44 pred: $i > $i)).
% 0.21/0.44 tff(n4_type, type, (
% 0.21/0.44 n4: $i)).
% 0.21/0.44 tff(n135299_type, type, (
% 0.21/0.44 n135299: $i)).
% 0.21/0.44 tff(1,plain,
% 0.21/0.44 ((succ(n0) = n1) <=> (succ(succ(tptp_minus_1)) = sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, pv10, tptp_sum_index)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(2,plain,
% 0.21/0.44 ((succ(n0) = n1) <=> (succ(n0) = n1)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(3,axiom,(succ(n0) = n1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','successor_1')).
% 0.21/0.44 tff(4,plain,
% 0.21/0.44 (succ(n0) = n1),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.44 tff(5,plain,
% 0.21/0.44 (succ(succ(tptp_minus_1)) = sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, pv10, tptp_sum_index))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.44 tff(6,plain,
% 0.21/0.44 (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, pv10, tptp_sum_index)) = succ(succ(tptp_minus_1))),
% 0.21/0.44 inference(symmetry,[status(thm)],[5])).
% 0.21/0.44 tff(7,plain,
% 0.21/0.44 (^[X: $i, Y: $i] : refl((leq(X, pred(Y)) <=> gt(Y, X)) <=> (leq(X, pred(Y)) <=> gt(Y, X)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(8,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[7])).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(10,axiom,(![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_gt_pred')).
% 0.21/0.44 tff(11,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.21/0.44 tff(12,plain,(
% 0.21/0.44 ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.21/0.44 inference(skolemize,[status(sab)],[11])).
% 0.21/0.44 tff(13,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.21/0.44 tff(14,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(B!13, pred(pv10)) <=> gt(pv10, B!13))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(15,plain,
% 0.21/0.44 (leq(B!13, pred(pv10)) <=> gt(pv10, B!13)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.21/0.44 tff(16,plain,
% 0.21/0.44 ((~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, pv10))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))))) <=> (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, pv10))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(17,plain,
% 0.21/0.44 ((~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, pv10))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, pv10, tptp_sum_index))))) <=> (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, pv10))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(18,plain,
% 0.21/0.44 ((~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, pv10))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, pv10, tptp_sum_index))))) <=> (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, pv10))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, pv10, tptp_sum_index)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(19,plain,
% 0.21/0.45 ((~![B: $i] : ((~(leq(n0, B) & leq(B, pv10))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))) <=> (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, pv10))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, pv10, tptp_sum_index)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(20,plain,
% 0.21/0.45 ((~![B: $i] : ((~(leq(n0, B) & leq(B, pv10))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))) <=> (~![B: $i] : ((~(leq(n0, B) & leq(B, pv10))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(21,plain,
% 0.21/0.45 ((~(((((sum(n0, n4, a_select3(q, pv10, tptp_sum_index)) = n1) & leq(n0, pv10)) & leq(pv10, n135299)) & ![A: $i] : ((leq(n0, A) & leq(A, pred(pv10))) => (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1))) => ![B: $i] : ((leq(n0, B) & leq(B, pv10)) => (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)))) <=> (~((~((sum(n0, n4, a_select3(q, pv10, tptp_sum_index)) = n1) & leq(n0, pv10) & leq(pv10, n135299) & ![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1)))) | ![B: $i] : ((~(leq(n0, B) & leq(B, pv10))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(22,axiom,(~(((((sum(n0, n4, a_select3(q, pv10, tptp_sum_index)) = n1) & leq(n0, pv10)) & leq(pv10, n135299)) & ![A: $i] : ((leq(n0, A) & leq(A, pred(pv10))) => (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1))) => ![B: $i] : ((leq(n0, B) & leq(B, pv10)) => (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cl5_nebula_norm_0011')).
% 0.21/0.45 tff(23,plain,
% 0.21/0.45 (~((~((sum(n0, n4, a_select3(q, pv10, tptp_sum_index)) = n1) & leq(n0, pv10) & leq(pv10, n135299) & ![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1)))) | ![B: $i] : ((~(leq(n0, B) & leq(B, pv10))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.21/0.45 tff(24,plain,
% 0.21/0.45 (~![B: $i] : ((~(leq(n0, B) & leq(B, pv10))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))),
% 0.21/0.45 inference(or_elim,[status(thm)],[23])).
% 0.21/0.45 tff(25,plain,
% 0.21/0.45 (~![B: $i] : ((~(leq(n0, B) & leq(B, pv10))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.21/0.45 tff(26,plain,
% 0.21/0.45 (~![B: $i] : ((~(leq(n0, B) & leq(B, pv10))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.21/0.45 tff(27,plain,
% 0.21/0.45 (~![B: $i] : ((~(leq(n0, B) & leq(B, pv10))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[26, 20])).
% 0.21/0.45 tff(28,plain,
% 0.21/0.45 (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, pv10))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, pv10, tptp_sum_index))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.21/0.45 tff(29,plain,
% 0.21/0.45 (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, pv10))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, pv10, tptp_sum_index))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.21/0.45 tff(30,plain,
% 0.21/0.45 (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, pv10))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[29, 17])).
% 0.21/0.45 tff(31,plain,
% 0.21/0.45 (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, pv10))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[30, 16])).
% 0.21/0.45 tff(32,plain,
% 0.21/0.45 (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, pv10))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[31, 16])).
% 0.21/0.45 tff(33,plain,
% 0.21/0.45 (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, pv10))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[32, 16])).
% 0.21/0.45 tff(34,plain,(
% 0.21/0.45 ~((~(leq(succ(tptp_minus_1), B!13) & leq(B!13, pv10))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B!13, tptp_sum_index)) = succ(succ(tptp_minus_1))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[33])).
% 0.21/0.45 tff(35,plain,
% 0.21/0.45 (~(sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B!13, tptp_sum_index)) = succ(succ(tptp_minus_1)))),
% 0.21/0.45 inference(or_elim,[status(thm)],[34])).
% 0.21/0.45 tff(36,plain,
% 0.21/0.45 (leq(succ(tptp_minus_1), B!13) & leq(B!13, pv10)),
% 0.21/0.45 inference(or_elim,[status(thm)],[34])).
% 0.21/0.45 tff(37,plain,
% 0.21/0.45 (leq(succ(tptp_minus_1), B!13)),
% 0.21/0.45 inference(and_elim,[status(thm)],[36])).
% 0.21/0.45 tff(38,plain,
% 0.21/0.45 (^[A: $i] : refl(((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10)))) <=> ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(39,plain,
% 0.21/0.45 (![A: $i] : ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10)))) <=> ![A: $i] : ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[38])).
% 0.21/0.45 tff(40,plain,
% 0.21/0.45 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), A) & leq(A, pred(pv10))) <=> (~((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10)))))), ((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) <=> (~(~((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10)))))))), rewrite((~(~((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10)))))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))))), ((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10)))))), (((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1)))) <=> (((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1)))))), rewrite((((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1)))) <=> ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))))), (((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1)))) <=> ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(41,plain,
% 0.21/0.45 (![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1)))) <=> ![A: $i] : ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[40])).
% 0.21/0.45 tff(42,plain,
% 0.21/0.45 (^[A: $i] : rewrite(((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, pv10, tptp_sum_index)))) <=> ((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(43,plain,
% 0.21/0.45 (![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, pv10, tptp_sum_index)))) <=> ![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.45 tff(44,plain,
% 0.21/0.45 (^[A: $i] : rewrite(((~(leq(n0, A) & leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1)) <=> ((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, pv10, tptp_sum_index)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(45,plain,
% 0.21/0.45 (![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1)) <=> ![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, pv10, tptp_sum_index))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.45 tff(46,plain,
% 0.21/0.45 (![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1)) <=> ![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(47,plain,
% 0.21/0.45 ((sum(n0, n4, a_select3(q, pv10, tptp_sum_index)) = n1) & leq(n0, pv10) & leq(pv10, n135299) & ![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1))),
% 0.21/0.45 inference(or_elim,[status(thm)],[23])).
% 0.21/0.45 tff(48,plain,
% 0.21/0.45 (![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1))),
% 0.21/0.45 inference(and_elim,[status(thm)],[47])).
% 0.21/0.45 tff(49,plain,
% 0.21/0.45 (![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[48, 46])).
% 0.21/0.45 tff(50,plain,
% 0.21/0.45 (![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, pv10, tptp_sum_index))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.21/0.45 tff(51,plain,
% 0.21/0.45 (![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.21/0.46 tff(52,plain,(
% 0.21/0.46 ![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[51])).
% 0.21/0.46 tff(53,plain,
% 0.21/0.46 (![A: $i] : ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[52, 41])).
% 0.21/0.46 tff(54,plain,
% 0.21/0.46 (![A: $i] : ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[53, 39])).
% 0.21/0.46 tff(55,plain,
% 0.21/0.46 (((~![A: $i] : ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))))) | ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B!13, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B!13)) | (~leq(B!13, pred(pv10))))) <=> ((~![A: $i] : ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B!13, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B!13)) | (~leq(B!13, pred(pv10))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(56,plain,
% 0.21/0.46 ((~![A: $i] : ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))))) | ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B!13, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B!13)) | (~leq(B!13, pred(pv10))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(57,plain,
% 0.21/0.46 ((~![A: $i] : ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, A, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B!13, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B!13)) | (~leq(B!13, pred(pv10)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.21/0.46 tff(58,plain,
% 0.21/0.46 (~leq(B!13, pred(pv10))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[57, 54, 37, 35])).
% 0.21/0.46 tff(59,plain,
% 0.21/0.46 ((~(leq(B!13, pred(pv10)) <=> gt(pv10, B!13))) | leq(B!13, pred(pv10)) | (~gt(pv10, B!13))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(60,plain,
% 0.21/0.46 ((~(leq(B!13, pred(pv10)) <=> gt(pv10, B!13))) | (~gt(pv10, B!13))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.21/0.46 tff(61,plain,
% 0.21/0.46 (~gt(pv10, B!13)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[60, 15])).
% 0.21/0.46 tff(62,plain,
% 0.21/0.46 (leq(B!13, pv10)),
% 0.21/0.46 inference(and_elim,[status(thm)],[36])).
% 0.21/0.46 tff(63,plain,
% 0.21/0.46 (^[X: $i, Y: $i] : refl(((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(64,plain,
% 0.21/0.46 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.46 tff(65,plain,
% 0.21/0.46 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & (~(X = Y))) <=> (~((~leq(X, Y)) | (X = Y)))), ((~(leq(X, Y) & (~(X = Y)))) <=> (~(~((~leq(X, Y)) | (X = Y)))))), rewrite((~(~((~leq(X, Y)) | (X = Y)))) <=> ((~leq(X, Y)) | (X = Y))), ((~(leq(X, Y) & (~(X = Y)))) <=> ((~leq(X, Y)) | (X = Y)))), (((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> (((~leq(X, Y)) | (X = Y)) | gt(Y, X)))), rewrite((((~leq(X, Y)) | (X = Y)) | gt(Y, X)) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y)))), (((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(66,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[65])).
% 0.21/0.47 tff(67,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(68,plain,
% 0.21/0.47 (^[X: $i, Y: $i] : rewrite(((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(69,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[68])).
% 0.21/0.47 tff(70,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_gt2')).
% 0.21/0.47 tff(71,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.47 tff(72,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.21/0.47 tff(73,plain,(
% 0.21/0.47 ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.21/0.47 inference(skolemize,[status(sab)],[72])).
% 0.21/0.47 tff(74,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.21/0.47 tff(75,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[74, 64])).
% 0.21/0.47 tff(76,plain,
% 0.21/0.47 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((B!13 = pv10) | gt(pv10, B!13) | (~leq(B!13, pv10)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (B!13 = pv10) | gt(pv10, B!13) | (~leq(B!13, pv10)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(77,plain,
% 0.21/0.47 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((B!13 = pv10) | gt(pv10, B!13) | (~leq(B!13, pv10)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(78,plain,
% 0.21/0.47 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (B!13 = pv10) | gt(pv10, B!13) | (~leq(B!13, pv10))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.47 tff(79,plain,
% 0.21/0.47 ((B!13 = pv10) | gt(pv10, B!13)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[78, 75, 62])).
% 0.21/0.47 tff(80,plain,
% 0.21/0.47 (B!13 = pv10),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[79, 61])).
% 0.21/0.47 tff(81,plain,
% 0.21/0.47 (a_select3(q, B!13, tptp_sum_index) = a_select3(q, pv10, tptp_sum_index)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[80])).
% 0.21/0.47 tff(82,plain,
% 0.21/0.47 (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B!13, tptp_sum_index)) = sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, pv10, tptp_sum_index))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[81])).
% 0.21/0.47 tff(83,plain,
% 0.21/0.47 (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B!13, tptp_sum_index)) = succ(succ(tptp_minus_1))),
% 0.21/0.47 inference(transitivity,[status(thm)],[82, 6])).
% 0.21/0.47 tff(84,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[35, 83])).
% 0.21/0.47 % SZS output end Proof
%------------------------------------------------------------------------------