TSTP Solution File: SEU267+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU267+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n014.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 17:43:45 EDT 2023
% Result : Theorem 68.54s 9.92s
% Output : Proof 87.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU267+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.34 % Computer : n014.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Wed Aug 23 18:51:04 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 7.84/1.87 Prover 3: Preprocessing ...
% 7.84/1.87 Prover 0: Preprocessing ...
% 7.84/1.88 Prover 5: Preprocessing ...
% 8.51/1.90 Prover 4: Preprocessing ...
% 8.51/1.90 Prover 1: Preprocessing ...
% 8.51/1.91 Prover 2: Preprocessing ...
% 8.51/1.92 Prover 6: Preprocessing ...
% 25.00/4.13 Prover 1: Warning: ignoring some quantifiers
% 26.19/4.30 Prover 6: Proving ...
% 26.19/4.31 Prover 3: Warning: ignoring some quantifiers
% 26.19/4.31 Prover 1: Constructing countermodel ...
% 26.19/4.32 Prover 5: Proving ...
% 26.77/4.36 Prover 3: Constructing countermodel ...
% 35.31/5.50 Prover 2: Proving ...
% 41.77/6.53 Prover 4: Warning: ignoring some quantifiers
% 44.53/6.74 Prover 4: Constructing countermodel ...
% 52.13/7.72 Prover 0: Proving ...
% 68.54/9.92 Prover 5: proved (9283ms)
% 68.54/9.92
% 68.54/9.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 68.54/9.92
% 68.54/9.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 68.54/9.92 Prover 6: stopped
% 68.54/9.92 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 68.54/9.94 Prover 3: stopped
% 68.54/9.94 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 69.07/9.96 Prover 0: stopped
% 69.07/9.97 Prover 2: stopped
% 69.07/9.97 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 69.07/9.99 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 73.02/10.48 Prover 7: Preprocessing ...
% 73.26/10.51 Prover 8: Preprocessing ...
% 73.26/10.53 Prover 10: Preprocessing ...
% 73.47/10.53 Prover 13: Preprocessing ...
% 73.47/10.56 Prover 11: Preprocessing ...
% 76.98/11.05 Prover 10: Warning: ignoring some quantifiers
% 77.64/11.11 Prover 10: Constructing countermodel ...
% 78.64/11.25 Prover 7: Warning: ignoring some quantifiers
% 79.27/11.30 Prover 8: Warning: ignoring some quantifiers
% 79.27/11.34 Prover 13: Warning: ignoring some quantifiers
% 79.27/11.36 Prover 7: Constructing countermodel ...
% 79.27/11.37 Prover 8: Constructing countermodel ...
% 79.94/11.44 Prover 13: Constructing countermodel ...
% 81.55/11.61 Prover 1: Found proof (size 32)
% 81.55/11.61 Prover 1: proved (10988ms)
% 81.55/11.62 Prover 13: stopped
% 81.55/11.62 Prover 8: stopped
% 81.55/11.62 Prover 7: stopped
% 81.55/11.62 Prover 4: stopped
% 81.55/11.62 Prover 10: stopped
% 86.17/12.71 Prover 11: Warning: ignoring some quantifiers
% 86.50/12.86 Prover 11: Constructing countermodel ...
% 86.50/12.89 Prover 11: stopped
% 86.50/12.89
% 86.50/12.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 86.50/12.89
% 86.50/12.90 % SZS output start Proof for theBenchmark
% 86.50/12.92 Assumptions after simplification:
% 86.50/12.92 ---------------------------------
% 86.50/12.92
% 86.50/12.92 (d1_mcart_1)
% 87.33/12.97 ! [v0: $i] : ! [v1: $i] : ( ~ (pair_first(v0) = v1) | ~ $i(v0) | ! [v2:
% 87.33/12.97 $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v3) = v0) | ~ $i(v3) | ~
% 87.33/12.97 $i(v2)) | ( ? [v2: $i] : (v2 = v1 | ~ $i(v2) | ? [v3: $i] : ? [v4: $i]
% 87.33/12.97 : ( ~ (v3 = v2) & ordered_pair(v3, v4) = v0 & $i(v4) & $i(v3))) & ( ~
% 87.33/12.97 $i(v1) | ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ (ordered_pair(v2, v3)
% 87.33/12.97 = v0) | ~ $i(v3) | ~ $i(v2)))))
% 87.33/12.97
% 87.33/12.97 (d2_mcart_1)
% 87.33/12.98 ! [v0: $i] : ! [v1: $i] : ( ~ (pair_second(v0) = v1) | ~ $i(v0) | ! [v2:
% 87.33/12.98 $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v3) = v0) | ~ $i(v3) | ~
% 87.33/12.98 $i(v2)) | ( ? [v2: $i] : (v2 = v1 | ~ $i(v2) | ? [v3: $i] : ? [v4: $i]
% 87.33/12.98 : ( ~ (v4 = v2) & ordered_pair(v3, v4) = v0 & $i(v4) & $i(v3))) & ( ~
% 87.33/12.98 $i(v1) | ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (ordered_pair(v2, v3)
% 87.33/12.98 = v0) | ~ $i(v3) | ~ $i(v2)))))
% 87.33/12.98
% 87.33/12.98 (t7_mcart_1)
% 87.33/12.98 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 87.33/12.98 (pair_second(v2) = v4 & pair_first(v2) = v3 & ordered_pair(v0, v1) = v2 &
% 87.33/12.98 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v4 = v1) | ~ (v3 = v0)))
% 87.33/12.98
% 87.33/12.98 Further assumptions not needed in the proof:
% 87.33/12.98 --------------------------------------------
% 87.44/12.99 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_funct_1, cc1_ordinal1,
% 87.44/12.99 cc1_relat_1, cc1_relset_1, cc2_funct_1, cc2_ordinal1, cc3_ordinal1,
% 87.44/12.99 commutativity_k2_tarski, commutativity_k2_xboole_0, commutativity_k3_xboole_0,
% 87.44/12.99 connectedness_r1_ordinal1, d10_relat_1, d10_xboole_0, d11_relat_1, d12_funct_1,
% 87.44/12.99 d12_relat_1, d12_relat_2, d13_funct_1, d13_relat_1, d14_relat_1, d14_relat_2,
% 87.44/12.99 d16_relat_2, d1_enumset1, d1_ordinal1, d1_relat_1, d1_relat_2, d1_relset_1,
% 87.44/12.99 d1_setfam_1, d1_tarski, d1_wellord1, d1_xboole_0, d1_zfmisc_1, d2_ordinal1,
% 87.44/12.99 d2_relat_1, d2_subset_1, d2_tarski, d2_wellord1, d2_xboole_0, d2_zfmisc_1,
% 87.44/12.99 d3_ordinal1, d3_relat_1, d3_tarski, d3_wellord1, d3_xboole_0, d4_funct_1,
% 87.44/12.99 d4_ordinal1, d4_relat_1, d4_relat_2, d4_subset_1, d4_tarski, d4_wellord1,
% 87.44/12.99 d4_xboole_0, d5_funct_1, d5_relat_1, d5_subset_1, d5_tarski, d5_wellord1,
% 87.44/12.99 d6_ordinal1, d6_relat_1, d6_relat_2, d6_wellord1, d7_relat_1, d7_wellord1,
% 87.44/12.99 d7_xboole_0, d8_funct_1, d8_relat_1, d8_relat_2, d8_setfam_1, d8_xboole_0,
% 87.44/12.99 d9_funct_1, d9_relat_2, dt_k10_relat_1, dt_k1_enumset1, dt_k1_funct_1,
% 87.44/12.99 dt_k1_mcart_1, dt_k1_ordinal1, dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski,
% 87.44/12.99 dt_k1_wellord1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_funct_1, dt_k2_mcart_1,
% 87.44/12.99 dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski, dt_k2_wellord1, dt_k2_xboole_0,
% 87.44/12.99 dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0,
% 87.44/12.99 dt_k4_relat_1, dt_k4_relset_1, dt_k4_tarski, dt_k4_xboole_0, dt_k5_relat_1,
% 87.44/12.99 dt_k5_relset_1, dt_k5_setfam_1, dt_k6_relat_1, dt_k6_setfam_1, dt_k6_subset_1,
% 87.44/12.99 dt_k7_relat_1, dt_k7_setfam_1, dt_k8_relat_1, dt_k9_relat_1, dt_m1_relset_1,
% 87.44/12.99 dt_m1_subset_1, dt_m2_relset_1, existence_m1_relset_1, existence_m1_subset_1,
% 87.44/12.99 existence_m2_relset_1, fc10_relat_1, fc11_relat_1, fc12_relat_1, fc13_relat_1,
% 87.44/12.99 fc1_funct_1, fc1_ordinal1, fc1_relat_1, fc1_subset_1, fc1_xboole_0,
% 87.44/12.99 fc1_zfmisc_1, fc2_funct_1, fc2_ordinal1, fc2_relat_1, fc2_subset_1,
% 87.44/12.99 fc2_xboole_0, fc3_funct_1, fc3_ordinal1, fc3_relat_1, fc3_subset_1,
% 87.44/12.99 fc3_xboole_0, fc4_funct_1, fc4_ordinal1, fc4_relat_1, fc4_subset_1, fc5_funct_1,
% 87.44/12.99 fc5_relat_1, fc6_relat_1, fc7_relat_1, fc8_relat_1, fc9_relat_1,
% 87.44/12.99 idempotence_k2_xboole_0, idempotence_k3_xboole_0, involutiveness_k3_subset_1,
% 87.44/12.99 involutiveness_k4_relat_1, involutiveness_k7_setfam_1,
% 87.44/12.99 irreflexivity_r2_xboole_0, l1_wellord1, l1_zfmisc_1, l23_zfmisc_1, l25_zfmisc_1,
% 87.44/12.99 l28_zfmisc_1, l29_wellord1, l2_wellord1, l2_zfmisc_1, l32_xboole_1, l3_subset_1,
% 87.44/12.99 l3_wellord1, l3_zfmisc_1, l4_wellord1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1,
% 87.44/12.99 l71_subset_1, l82_funct_1, rc1_funct_1, rc1_ordinal1, rc1_relat_1, rc1_subset_1,
% 87.44/12.99 rc1_xboole_0, rc2_funct_1, rc2_ordinal1, rc2_relat_1, rc2_subset_1,
% 87.44/12.99 rc2_xboole_0, rc3_funct_1, rc3_ordinal1, rc3_relat_1, rc4_funct_1,
% 87.44/12.99 redefinition_k4_relset_1, redefinition_k5_relset_1, redefinition_k5_setfam_1,
% 87.44/12.99 redefinition_k6_setfam_1, redefinition_k6_subset_1, redefinition_m2_relset_1,
% 87.44/12.99 redefinition_r1_ordinal1, reflexivity_r1_ordinal1, reflexivity_r1_tarski,
% 87.44/12.99 symmetry_r1_xboole_0, t106_zfmisc_1, t10_ordinal1, t10_zfmisc_1, t115_relat_1,
% 87.44/12.99 t116_relat_1, t117_relat_1, t118_relat_1, t118_zfmisc_1, t119_relat_1,
% 87.44/12.99 t119_zfmisc_1, t12_relset_1, t12_xboole_1, t136_zfmisc_1, t140_relat_1,
% 87.44/12.99 t143_relat_1, t144_relat_1, t145_funct_1, t145_relat_1, t146_funct_1,
% 87.44/12.99 t146_relat_1, t147_funct_1, t14_relset_1, t160_relat_1, t166_relat_1,
% 87.44/12.99 t167_relat_1, t16_relset_1, t16_wellord1, t174_relat_1, t178_relat_1,
% 87.44/12.99 t17_wellord1, t17_xboole_1, t18_wellord1, t19_wellord1, t19_xboole_1, t1_boole,
% 87.44/12.99 t1_subset, t1_xboole_1, t1_zfmisc_1, t20_relat_1, t20_wellord1, t21_funct_1,
% 87.44/12.99 t21_ordinal1, t21_relat_1, t21_wellord1, t22_funct_1, t22_relset_1,
% 87.44/12.99 t22_wellord1, t23_funct_1, t23_ordinal1, t23_relset_1, t23_wellord1,
% 87.44/12.99 t24_ordinal1, t24_wellord1, t25_relat_1, t25_wellord1, t26_xboole_1,
% 87.44/12.99 t28_xboole_1, t2_boole, t2_subset, t2_tarski, t2_xboole_1, t30_relat_1,
% 87.44/12.99 t31_ordinal1, t31_wellord1, t32_ordinal1, t32_wellord1, t33_ordinal1,
% 87.44/12.99 t33_xboole_1, t33_zfmisc_1, t34_funct_1, t35_funct_1, t36_xboole_1, t37_relat_1,
% 87.44/12.99 t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1, t39_wellord1, t39_xboole_1,
% 87.44/12.99 t39_zfmisc_1, t3_boole, t3_ordinal1, t3_subset, t3_xboole_0, t3_xboole_1,
% 87.44/12.99 t40_xboole_1, t41_ordinal1, t42_ordinal1, t43_subset_1, t44_relat_1,
% 87.44/12.99 t45_relat_1, t45_xboole_1, t46_relat_1, t46_setfam_1, t46_zfmisc_1, t47_relat_1,
% 87.44/12.99 t47_setfam_1, t48_setfam_1, t48_xboole_1, t49_wellord1, t4_boole, t4_subset,
% 87.44/12.99 t4_xboole_0, t50_subset_1, t53_wellord1, t54_funct_1, t54_subset_1,
% 87.44/12.99 t54_wellord1, t55_funct_1, t56_relat_1, t57_funct_1, t5_subset, t5_wellord1,
% 87.44/12.99 t60_relat_1, t60_xboole_1, t62_funct_1, t63_xboole_1, t64_relat_1, t65_relat_1,
% 87.44/12.99 t65_zfmisc_1, t68_funct_1, t69_enumset1, t6_boole, t6_zfmisc_1, t70_funct_1,
% 87.44/12.99 t71_relat_1, t72_funct_1, t74_relat_1, t7_boole, t7_tarski, t7_xboole_1,
% 87.44/12.99 t83_xboole_1, t86_relat_1, t88_relat_1, t8_boole, t8_funct_1, t8_wellord1,
% 87.44/12.99 t8_xboole_1, t8_zfmisc_1, t90_relat_1, t92_zfmisc_1, t94_relat_1, t99_relat_1,
% 87.44/12.99 t99_zfmisc_1, t9_tarski, t9_zfmisc_1
% 87.44/12.99
% 87.44/12.99 Those formulas are unsatisfiable:
% 87.44/12.99 ---------------------------------
% 87.44/12.99
% 87.44/12.99 Begin of proof
% 87.44/12.99 |
% 87.44/12.99 | DELTA: instantiating (t7_mcart_1) with fresh symbols all_332_0, all_332_1,
% 87.44/12.99 | all_332_2, all_332_3, all_332_4 gives:
% 87.44/12.99 | (1) pair_second(all_332_2) = all_332_0 & pair_first(all_332_2) = all_332_1
% 87.44/12.99 | & ordered_pair(all_332_4, all_332_3) = all_332_2 & $i(all_332_0) &
% 87.44/12.99 | $i(all_332_1) & $i(all_332_2) & $i(all_332_3) & $i(all_332_4) & ( ~
% 87.44/12.99 | (all_332_0 = all_332_3) | ~ (all_332_1 = all_332_4))
% 87.44/12.99 |
% 87.44/12.99 | ALPHA: (1) implies:
% 87.44/13.00 | (2) $i(all_332_4)
% 87.44/13.00 | (3) $i(all_332_3)
% 87.44/13.00 | (4) $i(all_332_2)
% 87.44/13.00 | (5) $i(all_332_1)
% 87.44/13.00 | (6) $i(all_332_0)
% 87.44/13.00 | (7) ordered_pair(all_332_4, all_332_3) = all_332_2
% 87.44/13.00 | (8) pair_first(all_332_2) = all_332_1
% 87.44/13.00 | (9) pair_second(all_332_2) = all_332_0
% 87.44/13.00 | (10) ~ (all_332_0 = all_332_3) | ~ (all_332_1 = all_332_4)
% 87.44/13.00 |
% 87.44/13.00 | GROUND_INST: instantiating (d1_mcart_1) with all_332_2, all_332_1, simplifying
% 87.44/13.00 | with (4), (8) gives:
% 87.44/13.00 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v1) = all_332_2) |
% 87.44/13.00 | ~ $i(v1) | ~ $i(v0)) | ( ? [v0: any] : (v0 = all_332_1 | ~ $i(v0)
% 87.44/13.00 | | ? [v1: any] : ? [v2: $i] : ( ~ (v1 = v0) & ordered_pair(v1,
% 87.44/13.00 | v2) = all_332_2 & $i(v2) & $i(v1))) & ( ~ $i(all_332_1) | !
% 87.44/13.00 | [v0: any] : ! [v1: $i] : (v0 = all_332_1 | ~ (ordered_pair(v0,
% 87.44/13.00 | v1) = all_332_2) | ~ $i(v1) | ~ $i(v0))))
% 87.44/13.01 |
% 87.44/13.01 | GROUND_INST: instantiating (d2_mcart_1) with all_332_2, all_332_0, simplifying
% 87.44/13.01 | with (4), (9) gives:
% 87.44/13.01 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v1) = all_332_2) |
% 87.44/13.01 | ~ $i(v1) | ~ $i(v0)) | ( ? [v0: any] : (v0 = all_332_0 | ~ $i(v0)
% 87.44/13.01 | | ? [v1: $i] : ? [v2: any] : ( ~ (v2 = v0) & ordered_pair(v1,
% 87.44/13.01 | v2) = all_332_2 & $i(v2) & $i(v1))) & ( ~ $i(all_332_0) | !
% 87.44/13.01 | [v0: $i] : ! [v1: any] : (v1 = all_332_0 | ~ (ordered_pair(v0,
% 87.44/13.01 | v1) = all_332_2) | ~ $i(v1) | ~ $i(v0))))
% 87.44/13.01 |
% 87.44/13.01 | BETA: splitting (10) gives:
% 87.44/13.01 |
% 87.44/13.01 | Case 1:
% 87.44/13.01 | |
% 87.44/13.01 | | (13) ~ (all_332_0 = all_332_3)
% 87.44/13.01 | |
% 87.44/13.01 | | BETA: splitting (12) gives:
% 87.44/13.01 | |
% 87.44/13.01 | | Case 1:
% 87.44/13.01 | | |
% 87.44/13.01 | | | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v1) = all_332_2)
% 87.44/13.01 | | | | ~ $i(v1) | ~ $i(v0))
% 87.44/13.01 | | |
% 87.44/13.01 | | | GROUND_INST: instantiating (14) with all_332_4, all_332_3, simplifying
% 87.44/13.01 | | | with (2), (3), (7) gives:
% 87.44/13.01 | | | (15) $false
% 87.44/13.01 | | |
% 87.44/13.01 | | | CLOSE: (15) is inconsistent.
% 87.44/13.01 | | |
% 87.44/13.01 | | Case 2:
% 87.44/13.01 | | |
% 87.44/13.02 | | | (16) ? [v0: any] : (v0 = all_332_0 | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 87.44/13.02 | | | any] : ( ~ (v2 = v0) & ordered_pair(v1, v2) = all_332_2 &
% 87.44/13.02 | | | $i(v2) & $i(v1))) & ( ~ $i(all_332_0) | ! [v0: $i] : ! [v1:
% 87.44/13.02 | | | any] : (v1 = all_332_0 | ~ (ordered_pair(v0, v1) = all_332_2)
% 87.44/13.02 | | | | ~ $i(v1) | ~ $i(v0)))
% 87.44/13.02 | | |
% 87.44/13.02 | | | ALPHA: (16) implies:
% 87.44/13.02 | | | (17) ~ $i(all_332_0) | ! [v0: $i] : ! [v1: any] : (v1 = all_332_0 |
% 87.44/13.02 | | | ~ (ordered_pair(v0, v1) = all_332_2) | ~ $i(v1) | ~ $i(v0))
% 87.44/13.02 | | |
% 87.60/13.02 | | | BETA: splitting (17) gives:
% 87.60/13.02 | | |
% 87.60/13.02 | | | Case 1:
% 87.60/13.02 | | | |
% 87.60/13.02 | | | | (18) ~ $i(all_332_0)
% 87.60/13.02 | | | |
% 87.60/13.02 | | | | PRED_UNIFY: (6), (18) imply:
% 87.60/13.02 | | | | (19) $false
% 87.60/13.02 | | | |
% 87.60/13.02 | | | | CLOSE: (19) is inconsistent.
% 87.60/13.02 | | | |
% 87.60/13.02 | | | Case 2:
% 87.60/13.02 | | | |
% 87.60/13.02 | | | | (20) ! [v0: $i] : ! [v1: any] : (v1 = all_332_0 | ~
% 87.60/13.02 | | | | (ordered_pair(v0, v1) = all_332_2) | ~ $i(v1) | ~ $i(v0))
% 87.60/13.02 | | | |
% 87.60/13.02 | | | | GROUND_INST: instantiating (20) with all_332_4, all_332_3, simplifying
% 87.60/13.02 | | | | with (2), (3), (7) gives:
% 87.60/13.02 | | | | (21) all_332_0 = all_332_3
% 87.60/13.02 | | | |
% 87.60/13.02 | | | | REDUCE: (13), (21) imply:
% 87.60/13.02 | | | | (22) $false
% 87.60/13.02 | | | |
% 87.60/13.02 | | | | CLOSE: (22) is inconsistent.
% 87.60/13.02 | | | |
% 87.60/13.02 | | | End of split
% 87.60/13.02 | | |
% 87.60/13.02 | | End of split
% 87.60/13.02 | |
% 87.60/13.02 | Case 2:
% 87.60/13.02 | |
% 87.60/13.02 | | (23) all_332_0 = all_332_3
% 87.60/13.02 | | (24) ~ (all_332_1 = all_332_4)
% 87.60/13.02 | |
% 87.60/13.02 | | BETA: splitting (11) gives:
% 87.60/13.02 | |
% 87.60/13.02 | | Case 1:
% 87.60/13.02 | | |
% 87.60/13.02 | | | (25) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v1) = all_332_2)
% 87.60/13.02 | | | | ~ $i(v1) | ~ $i(v0))
% 87.60/13.02 | | |
% 87.60/13.02 | | | GROUND_INST: instantiating (25) with all_332_4, all_332_3, simplifying
% 87.60/13.02 | | | with (2), (3), (7) gives:
% 87.60/13.02 | | | (26) $false
% 87.60/13.02 | | |
% 87.60/13.02 | | | CLOSE: (26) is inconsistent.
% 87.60/13.02 | | |
% 87.60/13.02 | | Case 2:
% 87.60/13.02 | | |
% 87.60/13.02 | | | (27) ? [v0: any] : (v0 = all_332_1 | ~ $i(v0) | ? [v1: any] : ?
% 87.60/13.02 | | | [v2: $i] : ( ~ (v1 = v0) & ordered_pair(v1, v2) = all_332_2 &
% 87.60/13.03 | | | $i(v2) & $i(v1))) & ( ~ $i(all_332_1) | ! [v0: any] : ! [v1:
% 87.60/13.03 | | | $i] : (v0 = all_332_1 | ~ (ordered_pair(v0, v1) = all_332_2)
% 87.60/13.03 | | | | ~ $i(v1) | ~ $i(v0)))
% 87.60/13.03 | | |
% 87.60/13.03 | | | ALPHA: (27) implies:
% 87.60/13.03 | | | (28) ~ $i(all_332_1) | ! [v0: any] : ! [v1: $i] : (v0 = all_332_1 |
% 87.60/13.03 | | | ~ (ordered_pair(v0, v1) = all_332_2) | ~ $i(v1) | ~ $i(v0))
% 87.60/13.03 | | |
% 87.60/13.03 | | | BETA: splitting (28) gives:
% 87.60/13.03 | | |
% 87.60/13.03 | | | Case 1:
% 87.60/13.03 | | | |
% 87.60/13.03 | | | | (29) ~ $i(all_332_1)
% 87.60/13.03 | | | |
% 87.60/13.03 | | | | PRED_UNIFY: (5), (29) imply:
% 87.60/13.03 | | | | (30) $false
% 87.60/13.03 | | | |
% 87.60/13.03 | | | | CLOSE: (30) is inconsistent.
% 87.60/13.03 | | | |
% 87.60/13.03 | | | Case 2:
% 87.60/13.03 | | | |
% 87.60/13.03 | | | | (31) ! [v0: any] : ! [v1: $i] : (v0 = all_332_1 | ~
% 87.60/13.03 | | | | (ordered_pair(v0, v1) = all_332_2) | ~ $i(v1) | ~ $i(v0))
% 87.60/13.03 | | | |
% 87.60/13.03 | | | | GROUND_INST: instantiating (31) with all_332_4, all_332_3, simplifying
% 87.60/13.03 | | | | with (2), (3), (7) gives:
% 87.60/13.03 | | | | (32) all_332_1 = all_332_4
% 87.60/13.03 | | | |
% 87.60/13.03 | | | | REDUCE: (24), (32) imply:
% 87.60/13.03 | | | | (33) $false
% 87.60/13.03 | | | |
% 87.60/13.03 | | | | CLOSE: (33) is inconsistent.
% 87.60/13.03 | | | |
% 87.60/13.03 | | | End of split
% 87.60/13.03 | | |
% 87.60/13.03 | | End of split
% 87.60/13.03 | |
% 87.60/13.03 | End of split
% 87.60/13.03 |
% 87.60/13.03 End of proof
% 87.60/13.03 % SZS output end Proof for theBenchmark
% 87.60/13.03
% 87.60/13.03 12421ms
%------------------------------------------------------------------------------