TSTP Solution File: SWV048+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV048+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n011.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 Aug 31 22:54:42 EDT 2023
% Result : Theorem 15.39s 2.83s
% Output : Proof 19.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV048+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 09:45:41 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.78/1.40 Prover 4: Preprocessing ...
% 5.30/1.43 Prover 1: Preprocessing ...
% 5.40/1.45 Prover 0: Preprocessing ...
% 5.40/1.45 Prover 2: Preprocessing ...
% 5.40/1.45 Prover 3: Preprocessing ...
% 5.40/1.45 Prover 6: Preprocessing ...
% 5.40/1.45 Prover 5: Preprocessing ...
% 11.57/2.28 Prover 1: Warning: ignoring some quantifiers
% 11.57/2.32 Prover 3: Warning: ignoring some quantifiers
% 12.14/2.35 Prover 4: Warning: ignoring some quantifiers
% 12.14/2.36 Prover 3: Constructing countermodel ...
% 12.43/2.38 Prover 1: Constructing countermodel ...
% 12.43/2.38 Prover 6: Proving ...
% 12.90/2.44 Prover 4: Constructing countermodel ...
% 13.09/2.48 Prover 5: Proving ...
% 13.09/2.48 Prover 0: Proving ...
% 13.09/2.55 Prover 2: Proving ...
% 15.39/2.83 Prover 3: proved (2170ms)
% 15.39/2.83
% 15.39/2.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.39/2.83
% 15.39/2.84 Prover 5: stopped
% 15.39/2.84 Prover 2: stopped
% 15.39/2.84 Prover 0: stopped
% 15.39/2.86 Prover 6: stopped
% 16.09/2.87 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 16.09/2.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 16.09/2.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 16.09/2.87 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 16.09/2.87 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 16.63/2.99 Prover 1: Found proof (size 21)
% 16.63/2.99 Prover 1: proved (2346ms)
% 16.63/2.99 Prover 4: stopped
% 17.22/3.04 Prover 10: Preprocessing ...
% 17.70/3.07 Prover 13: Preprocessing ...
% 17.70/3.09 Prover 7: Preprocessing ...
% 17.70/3.09 Prover 8: Preprocessing ...
% 17.70/3.09 Prover 11: Preprocessing ...
% 17.70/3.13 Prover 10: stopped
% 17.70/3.15 Prover 7: stopped
% 18.40/3.17 Prover 11: stopped
% 18.40/3.22 Prover 13: stopped
% 18.88/3.27 Prover 8: Warning: ignoring some quantifiers
% 19.06/3.28 Prover 8: Constructing countermodel ...
% 19.11/3.30 Prover 8: stopped
% 19.11/3.30
% 19.11/3.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.11/3.30
% 19.17/3.31 % SZS output start Proof for theBenchmark
% 19.19/3.31 Assumptions after simplification:
% 19.19/3.31 ---------------------------------
% 19.19/3.31
% 19.19/3.31 (cl5_nebula_norm_0016)
% 19.19/3.34 $i(x) & $i(pv81) & $i(pv78) & $i(pv35) & $i(pv79) & $i(q) & $i(n135300) &
% 19.19/3.34 $i(n5) & $i(n1) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 19.19/3.34 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (times(v4, v5)
% 19.19/3.34 = v6 & minus(n135300, n1) = v0 & minus(n5, n1) = v2 & minus(n0, n1) = v3 &
% 19.19/3.34 sum(n0, v3, v6) = v7 & sum(n0, v0, v1) = pv78 & a_select3(q, pv81, pv35) =
% 19.19/3.34 v4 & a_select3(q, pv79, pv35) = v1 & a_select2(x, pv81) = v5 & leq(pv35, v2)
% 19.19/3.34 = 0 & leq(n0, pv35) = 0 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 19.19/3.34 $i(v2) & $i(v1) & $i(v0) & ((pv78 = n0 & ~ true) | ( ~ (v7 = n0) & ~ (pv78
% 19.19/3.34 = n0))))
% 19.19/3.34
% 19.19/3.34 (gt_3_tptp_minus_1)
% 19.19/3.34 gt(n3, tptp_minus_1) = 0 & $i(n3) & $i(tptp_minus_1)
% 19.19/3.34
% 19.19/3.34 (pred_minus_1)
% 19.19/3.34 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) |
% 19.19/3.34 (pred(v0) = v1 & $i(v1)))
% 19.19/3.34
% 19.19/3.34 (pred_succ)
% 19.19/3.34 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0)
% 19.19/3.34
% 19.19/3.34 (succ_tptp_minus_1)
% 19.19/3.34 succ(tptp_minus_1) = n0 & $i(tptp_minus_1) & $i(n0)
% 19.19/3.34
% 19.19/3.34 (sum_plus_base)
% 19.19/3.34 $i(tptp_minus_1) & $i(n0) & ! [v0: $i] : ! [v1: $i] : (v1 = n0 | ~ (sum(n0,
% 19.19/3.34 tptp_minus_1, v0) = v1) | ~ $i(v0))
% 19.19/3.34
% 19.19/3.34 (ttrue)
% 19.19/3.34 true
% 19.19/3.34
% 19.19/3.34 (function-axioms)
% 19.19/3.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 19.19/3.35 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 19.19/3.35 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 19.19/3.35 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 19.19/3.35 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 19.19/3.35 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 19.19/3.35 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 19.19/3.35 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 19.19/3.35 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 19.19/3.35 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 19.19/3.35 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 19.19/3.35 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (times(v3, v2) = v1) | ~ (times(v3,
% 19.19/3.35 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 19.19/3.35 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, v2) = v0)) & ! [v0: $i] : !
% 19.19/3.35 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~
% 19.19/3.35 (plus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 19.19/3.35 : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) | ~ (tptp_mmul(v3, v2) = v0)) & !
% 19.19/3.35 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 19.19/3.35 (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = v0)) & ! [v0: $i] : !
% 19.19/3.35 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_madd(v3, v2) = v1)
% 19.19/3.35 | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 19.19/3.35 ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ (dim(v3, v2) = v0)) & !
% 19.19/3.35 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 19.19/3.35 (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, v2) = v0)) & !
% 19.19/3.35 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 19.19/3.35 (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: $i] : !
% 19.19/3.35 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (uniform_int_rnd(v3, v2)
% 19.19/3.35 = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 19.19/3.35 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (geq(v3,
% 19.19/3.35 v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 19.19/3.35 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (lt(v3,
% 19.19/3.35 v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 19.19/3.35 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2)
% 19.19/3.35 = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 19.19/3.35 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) =
% 19.19/3.35 v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 19.19/3.35 (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 19.19/3.35 : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ (trans(v2) = v0)) & !
% 19.19/3.35 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~
% 19.19/3.35 (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 19.19/3.35 (pred(v2) = v1) | ~ (pred(v2) = v0))
% 19.19/3.35
% 19.19/3.35 Further assumptions not needed in the proof:
% 19.19/3.35 --------------------------------------------
% 19.19/3.35 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 19.19/3.35 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 19.19/3.35 finite_domain_5, gt_0_tptp_minus_1, gt_135300_0, gt_135300_1, gt_135300_2,
% 19.19/3.35 gt_135300_3, gt_135300_4, gt_135300_5, gt_135300_tptp_minus_1, gt_1_0,
% 19.19/3.35 gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2,
% 19.19/3.35 gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2,
% 19.19/3.35 gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, leq_geq, leq_gt1,
% 19.19/3.35 leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv,
% 19.19/3.35 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add,
% 19.19/3.35 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans,
% 19.19/3.35 matrix_symm_update_diagonal, reflexivity_leq, sel2_update_1, sel2_update_2,
% 19.19/3.35 sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_l,
% 19.19/3.35 succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r,
% 19.19/3.35 succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, succ_pred,
% 19.19/3.35 successor_1, successor_2, successor_3, successor_4, successor_5,
% 19.19/3.35 sum_plus_base_float, totality, transitivity_gt, transitivity_leq,
% 19.19/3.35 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 19.19/3.35
% 19.19/3.35 Those formulas are unsatisfiable:
% 19.19/3.35 ---------------------------------
% 19.19/3.35
% 19.19/3.35 Begin of proof
% 19.19/3.36 |
% 19.19/3.36 | ALPHA: (sum_plus_base) implies:
% 19.19/3.36 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = n0 | ~ (sum(n0, tptp_minus_1, v0) =
% 19.19/3.36 | v1) | ~ $i(v0))
% 19.19/3.36 |
% 19.19/3.36 | ALPHA: (succ_tptp_minus_1) implies:
% 19.19/3.36 | (2) succ(tptp_minus_1) = n0
% 19.19/3.36 |
% 19.19/3.36 | ALPHA: (pred_minus_1) implies:
% 19.19/3.36 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) |
% 19.19/3.36 | (pred(v0) = v1 & $i(v1)))
% 19.19/3.36 |
% 19.19/3.36 | ALPHA: (gt_3_tptp_minus_1) implies:
% 19.19/3.36 | (4) $i(tptp_minus_1)
% 19.19/3.36 |
% 19.19/3.36 | ALPHA: (cl5_nebula_norm_0016) implies:
% 19.19/3.36 | (5) $i(n0)
% 19.19/3.36 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 19.19/3.36 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (times(v4, v5) = v6 &
% 19.19/3.36 | minus(n135300, n1) = v0 & minus(n5, n1) = v2 & minus(n0, n1) = v3 &
% 19.19/3.36 | sum(n0, v3, v6) = v7 & sum(n0, v0, v1) = pv78 & a_select3(q, pv81,
% 19.19/3.36 | pv35) = v4 & a_select3(q, pv79, pv35) = v1 & a_select2(x, pv81) =
% 19.19/3.36 | v5 & leq(pv35, v2) = 0 & leq(n0, pv35) = 0 & $i(v7) & $i(v6) & $i(v5)
% 19.19/3.36 | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((pv78 = n0 & ~ true)
% 19.19/3.36 | | ( ~ (v7 = n0) & ~ (pv78 = n0))))
% 19.19/3.36 |
% 19.19/3.36 | ALPHA: (function-axioms) implies:
% 19.19/3.36 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1)
% 19.19/3.36 | | ~ (pred(v2) = v0))
% 19.19/3.36 |
% 19.19/3.36 | DELTA: instantiating (6) with fresh symbols all_61_0, all_61_1, all_61_2,
% 19.19/3.36 | all_61_3, all_61_4, all_61_5, all_61_6, all_61_7 gives:
% 19.19/3.36 | (8) times(all_61_3, all_61_2) = all_61_1 & minus(n135300, n1) = all_61_7 &
% 19.19/3.36 | minus(n5, n1) = all_61_5 & minus(n0, n1) = all_61_4 & sum(n0, all_61_4,
% 19.19/3.36 | all_61_1) = all_61_0 & sum(n0, all_61_7, all_61_6) = pv78 &
% 19.19/3.36 | a_select3(q, pv81, pv35) = all_61_3 & a_select3(q, pv79, pv35) =
% 19.19/3.36 | all_61_6 & a_select2(x, pv81) = all_61_2 & leq(pv35, all_61_5) = 0 &
% 19.19/3.36 | leq(n0, pv35) = 0 & $i(all_61_0) & $i(all_61_1) & $i(all_61_2) &
% 19.19/3.36 | $i(all_61_3) & $i(all_61_4) & $i(all_61_5) & $i(all_61_6) &
% 19.19/3.36 | $i(all_61_7) & ((pv78 = n0 & ~ true) | ( ~ (all_61_0 = n0) & ~ (pv78
% 19.19/3.36 | = n0)))
% 19.19/3.36 |
% 19.19/3.36 | ALPHA: (8) implies:
% 19.19/3.36 | (9) $i(all_61_1)
% 19.19/3.36 | (10) sum(n0, all_61_4, all_61_1) = all_61_0
% 19.19/3.36 | (11) minus(n0, n1) = all_61_4
% 19.19/3.36 | (12) (pv78 = n0 & ~ true) | ( ~ (all_61_0 = n0) & ~ (pv78 = n0))
% 19.19/3.36 |
% 19.19/3.36 | BETA: splitting (12) gives:
% 19.19/3.36 |
% 19.19/3.36 | Case 1:
% 19.19/3.36 | |
% 19.19/3.36 | | (13) pv78 = n0 & ~ true
% 19.19/3.36 | |
% 19.19/3.36 | | ALPHA: (13) implies:
% 19.19/3.36 | | (14) ~ true
% 19.19/3.36 | |
% 19.19/3.37 | | PRED_UNIFY: (14), (ttrue) imply:
% 19.19/3.37 | | (15) $false
% 19.19/3.37 | |
% 19.19/3.37 | | CLOSE: (15) is inconsistent.
% 19.19/3.37 | |
% 19.19/3.37 | Case 2:
% 19.19/3.37 | |
% 19.19/3.37 | | (16) ~ (all_61_0 = n0) & ~ (pv78 = n0)
% 19.19/3.37 | |
% 19.19/3.37 | | ALPHA: (16) implies:
% 19.19/3.37 | | (17) ~ (all_61_0 = n0)
% 19.19/3.37 | |
% 19.19/3.37 | | GROUND_INST: instantiating (pred_succ) with tptp_minus_1, n0, simplifying
% 19.19/3.37 | | with (2), (4) gives:
% 19.19/3.37 | | (18) pred(n0) = tptp_minus_1
% 19.19/3.37 | |
% 19.19/3.37 | | GROUND_INST: instantiating (3) with n0, all_61_4, simplifying with (5), (11)
% 19.19/3.37 | | gives:
% 19.19/3.37 | | (19) pred(n0) = all_61_4 & $i(all_61_4)
% 19.19/3.37 | |
% 19.19/3.37 | | ALPHA: (19) implies:
% 19.19/3.37 | | (20) pred(n0) = all_61_4
% 19.19/3.37 | |
% 19.19/3.37 | | GROUND_INST: instantiating (7) with tptp_minus_1, all_61_4, n0, simplifying
% 19.19/3.37 | | with (18), (20) gives:
% 19.19/3.37 | | (21) all_61_4 = tptp_minus_1
% 19.19/3.37 | |
% 19.19/3.37 | | REDUCE: (10), (21) imply:
% 19.19/3.37 | | (22) sum(n0, tptp_minus_1, all_61_1) = all_61_0
% 19.19/3.37 | |
% 19.19/3.37 | | GROUND_INST: instantiating (1) with all_61_1, all_61_0, simplifying with
% 19.19/3.37 | | (9), (22) gives:
% 19.19/3.37 | | (23) all_61_0 = n0
% 19.19/3.37 | |
% 19.19/3.37 | | REDUCE: (17), (23) imply:
% 19.19/3.37 | | (24) $false
% 19.19/3.37 | |
% 19.19/3.37 | | CLOSE: (24) is inconsistent.
% 19.19/3.37 | |
% 19.19/3.37 | End of split
% 19.19/3.37 |
% 19.19/3.37 End of proof
% 19.19/3.37 % SZS output end Proof for theBenchmark
% 19.19/3.37
% 19.19/3.37 2745ms
%------------------------------------------------------------------------------