%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n021.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 04:11:37 EDT 2023 % Result : Theorem 38.28s 5.95s % Output : Proof 59.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.35 % Computer : n021.cluster.edu % 0.12/0.35 % Model : x86_64 x86_64 % 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.35 % Memory : 8042.1875MB % 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.35 % CPULimit : 300 % 0.12/0.35 % WCLimit : 300 % 0.12/0.35 % DateTime : Sun Aug 27 15:17:12 EDT 2023 % 0.12/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 15.45/2.87 Prover 6: Preprocessing ... % 15.45/2.87 Prover 3: Preprocessing ... % 15.45/2.89 Prover 4: Preprocessing ... % 15.45/2.93 Prover 5: Preprocessing ... % 15.45/3.01 Prover 1: Preprocessing ... % 16.43/3.05 Prover 2: Preprocessing ... % 16.43/3.09 Prover 0: Preprocessing ... % 36.08/5.62 Prover 1: Warning: ignoring some quantifiers % 36.08/5.76 Prover 3: Warning: ignoring some quantifiers % 37.18/5.81 Prover 6: Proving ... % 37.18/5.86 Prover 3: Constructing countermodel ... % 37.18/5.90 Prover 1: Constructing countermodel ... % 38.28/5.95 Prover 6: proved (5277ms) % 38.28/5.95 % 38.28/5.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 38.28/5.95 % 38.28/5.95 Prover 3: proved (5295ms) % 38.28/5.95 % 38.28/5.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 38.28/5.95 % 38.28/5.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 38.28/5.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 41.98/6.45 Prover 4: Warning: ignoring some quantifiers % 44.37/6.72 Prover 8: Preprocessing ... % 44.61/6.75 Prover 4: Constructing countermodel ... % 44.61/6.80 Prover 7: Preprocessing ... % 46.21/6.96 Prover 0: Proving ... % 46.21/6.96 Prover 0: stopped % 46.34/6.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 47.44/7.21 Prover 5: Proving ... % 47.44/7.21 Prover 5: stopped % 47.44/7.23 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 52.83/7.92 Prover 2: Proving ... % 52.83/7.92 Prover 2: stopped % 52.83/7.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 53.87/8.00 Prover 10: Preprocessing ... % 53.87/8.01 Prover 1: Found proof (size 12) % 53.87/8.01 Prover 1: proved (7365ms) % 53.87/8.01 Prover 4: stopped % 55.02/8.22 Prover 11: Preprocessing ... % 55.63/8.24 Prover 10: stopped % 55.98/8.33 Prover 7: Warning: ignoring some quantifiers % 56.47/8.36 Prover 8: Warning: ignoring some quantifiers % 57.69/8.52 Prover 7: Constructing countermodel ... % 57.69/8.52 Prover 7: stopped % 57.69/8.53 Prover 8: Constructing countermodel ... % 57.69/8.53 Prover 8: stopped % 57.69/8.54 Prover 11: stopped % 57.86/8.56 Prover 13: Preprocessing ... % 59.07/8.90 Prover 13: stopped % 59.07/8.90 % 59.07/8.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 59.07/8.90 % 59.07/8.90 % SZS output start Proof for theBenchmark % 59.40/8.94 Assumptions after simplification: % 59.40/8.94 --------------------------------- % 59.40/8.95 % 59.40/8.95 (axiom4) % 59.40/8.97 ZF$(y$) & ZF_set$(a$) & ? [v0: ZF_set_bool_fun$] : (member$a(y$) = v0 & % 59.40/8.97 fun_app$c(v0, a$) = 0 & ZF_set_bool_fun$(v0)) % 59.40/8.97 % 59.40/8.97 (conjecture3) % 59.40/8.98 ZF$(y$) & ZF_set_ZF_fun$(implode$) & ZF_ZF_set_fun$(f$) & ZF_set$(a$) & ? % 59.40/8.98 [v0: ZF_set_bool_fun$] : ? [v1: int] : ? [v2: ZF_set$] : ? [v3: ZF$] : ( ~ % 59.40/8.98 (v1 = 0) & fun_app$e(implode$, v2) = v3 & fun_app$f(f$, y$) = v2 & % 59.40/8.98 member$a(y$) = v0 & fun_app$c(v0, a$) = v1 & ZF$(v3) & ZF_set_bool_fun$(v0) % 59.40/8.98 & ZF_set$(v2)) % 59.40/8.98 % 59.62/8.98 (function-axioms) % 59.62/9.03 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Nat_set$] : % 59.62/9.03 ! [v3: Nat_ZF_fun$] : (v1 = v0 | ~ (inj_on$(v3, v2) = v1) | ~ (inj_on$(v3, % 59.62/9.03 v2) = v0)) & ! [v0: ZF$] : ! [v1: ZF$] : ! [v2: ZF_bool_fun$] : ! % 59.62/9.03 [v3: ZF$] : (v1 = v0 | ~ (sep$(v3, v2) = v1) | ~ (sep$(v3, v2) = v0)) & ! % 59.62/9.03 [v0: ZF$] : ! [v1: ZF$] : ! [v2: ZF_ZF_fun$] : ! [v3: ZF$] : (v1 = v0 | ~ % 59.62/9.03 (lambda$(v3, v2) = v1) | ~ (lambda$(v3, v2) = v0)) & ! [v0: ZF_ZF_fun$] : % 59.62/9.03 ! [v1: ZF_ZF_fun$] : ! [v2: ZF_ZF_fun$] : ! [v3: ZF_ZF_fun$] : (v1 = v0 | ~ % 59.62/9.03 (comp$b(v3, v2) = v1) | ~ (comp$b(v3, v2) = v0)) & ! [v0: Nat_nat_fun$] : % 59.62/9.03 ! [v1: Nat_nat_fun$] : ! [v2: Nat_nat_fun$] : ! [v3: Nat_nat_fun$] : (v1 = % 59.62/9.03 v0 | ~ (comp$a(v3, v2) = v1) | ~ (comp$a(v3, v2) = v0)) & ! [v0: % 59.62/9.03 ZF_ZF_fun$] : ! [v1: ZF_ZF_fun$] : ! [v2: ZF_nat_fun$] : ! [v3: % 59.62/9.03 Nat_ZF_fun$] : (v1 = v0 | ~ (comp$(v3, v2) = v1) | ~ (comp$(v3, v2) = v0)) % 59.62/9.03 & ! [v0: Nat_set$] : ! [v1: Nat_set$] : ! [v2: Nat_set$] : ! [v3: % 59.62/9.03 Nat_set$] : (v1 = v0 | ~ (sup$c(v3, v2) = v1) | ~ (sup$c(v3, v2) = v0)) & % 59.62/9.03 ! [v0: ZF_set_set$] : ! [v1: ZF_set_set$] : ! [v2: ZF_set_set$] : ! [v3: % 59.62/9.03 ZF_set_set$] : (v1 = v0 | ~ (sup$a(v3, v2) = v1) | ~ (sup$a(v3, v2) = v0)) % 59.62/9.03 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 59.62/9.03 ZF_int_fun$] : ! [v3: ZF_ZF_prod_set$] : (v1 = v0 | ~ (relChain$b(v3, v2) % 59.62/9.03 = v1) | ~ (relChain$b(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! % 59.62/9.03 [v2: ZF$] : ! [v3: ZF_int_fun$] : (v1 = v0 | ~ (fun_app$aj(v3, v2) = v1) | % 59.62/9.03 ~ (fun_app$aj(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 59.62/9.03 MultipleValueBool] : ! [v2: ZF_ZF_ZF_prod_set_fun$] : ! [v3: % 59.62/9.03 ZF_ZF_prod_set$] : (v1 = v0 | ~ (relChain$a(v3, v2) = v1) | ~ % 59.62/9.03 (relChain$a(v3, v2) = v0)) & ! [v0: ZF_ZF_prod_set$] : ! [v1: % 59.62/9.03 ZF_ZF_prod_set$] : ! [v2: ZF$] : ! [v3: ZF_ZF_ZF_prod_set_fun$] : (v1 = v0 % 59.62/9.03 | ~ (fun_app$ai(v3, v2) = v1) | ~ (fun_app$ai(v3, v2) = v0)) & ! [v0: % 59.62/9.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: ZF_ZF_set_fun$] : % 59.62/9.03 ! [v3: ZF_ZF_prod_set$] : (v1 = v0 | ~ (relChain$(v3, v2) = v1) | ~ % 59.62/9.03 (relChain$(v3, v2) = v0)) & ! [v0: Nat_ZF_fun$] : ! [v1: Nat_ZF_fun$] : ! % 59.62/9.03 [v2: ZF$] : ! [v3: ZF_ZF_prod_set$] : (v1 = v0 | ~ (ext_ZF_n$(v3, v2) = v1) % 59.62/9.03 | ~ (ext_ZF_n$(v3, v2) = v0)) & ! [v0: ZF_set_bool_fun$] : ! [v1: % 59.62/9.03 ZF_set_bool_fun$] : ! [v2: ZF_ZF_set_fun$] : ! [v3: ZF_set_ZF_fun$] : (v1 % 59.62/9.03 = v0 | ~ (type_definition$c(v3, v2) = v1) | ~ (type_definition$c(v3, v2) = % 59.62/9.03 v0)) & ! [v0: ZF_set_bool_fun$] : ! [v1: ZF_set_bool_fun$] : ! [v2: % 59.62/9.03 ZF_ZF_fun$] : ! [v3: ZF_ZF_fun$] : (v1 = v0 | ~ (type_definition$b(v3, v2) % 59.62/9.03 = v1) | ~ (type_definition$b(v3, v2) = v0)) & ! [v0: % 59.62/9.03 ZF_set_set_bool_fun$] : ! [v1: ZF_set_set_bool_fun$] : ! [v2: % 59.62/9.03 ZF_set_ZF_fun$] : ! [v3: ZF_ZF_set_fun$] : (v1 = v0 | ~ % 59.62/9.03 (type_definition$a(v3, v2) = v1) | ~ (type_definition$a(v3, v2) = v0)) & ! % 59.62/9.03 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 59.62/9.03 ZF_ZF_prod_zet$] : ! [v3: ZF_ZF_prod$] : (v1 = v0 | ~ (zin$b(v3, v2) = v1) % 59.62/9.03 | ~ (zin$b(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 59.62/9.03 MultipleValueBool] : ! [v2: ZF_set_zet$] : ! [v3: ZF_set$] : (v1 = v0 | ~ % 59.62/9.03 (zin$a(v3, v2) = v1) | ~ (zin$a(v3, v2) = v0)) & ! [v0: ZF_zet$] : ! [v1: % 59.62/9.03 ZF_zet$] : ! [v2: ZF_zet$] : ! [v3: ZF_zet$] : (v1 = v0 | ~ (zunion$(v3, % 59.62/9.03 v2) = v1) | ~ (zunion$(v3, v2) = v0)) & ! [v0: ZF_set_set_bool_fun$] : % 59.62/9.03 ! [v1: ZF_set_set_bool_fun$] : ! [v2: ZF_set_ZF_zet_fun$] : ! [v3: % 59.62/9.03 ZF_zet_ZF_set_fun$] : (v1 = v0 | ~ (type_definition$(v3, v2) = v1) | ~ % 59.62/9.03 (type_definition$(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 59.62/9.03 MultipleValueBool] : ! [v2: ZF_zet$] : ! [v3: ZF_zet_bool_fun$] : (v1 = v0 % 59.62/9.03 | ~ (fun_app$ah(v3, v2) = v1) | ~ (fun_app$ah(v3, v2) = v0)) & ! [v0: % 59.62/9.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Int_set$] : ! % 59.62/9.03 [v3: Int_int_fun$] : (v1 = v0 | ~ (strict_mono_on$c(v3, v2) = v1) | ~ % 59.62/9.03 (strict_mono_on$c(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 59.62/9.03 MultipleValueBool] : ! [v2: Int_set$] : ! [v3: Int_ZF_ZF_prod_set_fun$] : % 59.62/9.03 (v1 = v0 | ~ (strict_mono_on$b(v3, v2) = v1) | ~ (strict_mono_on$b(v3, v2) = % 59.62/9.03 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 59.62/9.03 Int_set$] : ! [v3: Int_ZF_set_fun$] : (v1 = v0 | ~ (strict_mono_on$a(v3, % 59.62/9.03 v2) = v1) | ~ (strict_mono_on$a(v3, v2) = v0)) & ! [v0: % 59.62/9.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Int_set$] : ! % 59.62/9.03 [v3: int] : (v1 = v0 | ~ (member$e(v3, v2) = v1) | ~ (member$e(v3, v2) = % 59.62/9.03 v0)) & ! [v0: ZF$] : ! [v1: ZF$] : ! [v2: ZF_ZF_fun$] : ! [v3: ZF$] : % 59.62/9.03 (v1 = v0 | ~ (repl$(v3, v2) = v1) | ~ (repl$(v3, v2) = v0)) & ! [v0: % 59.62/9.03 ZF_zet$] : ! [v1: ZF_zet$] : ! [v2: ZF_set$] : ! [v3: ZF_set_ZF_zet_fun$] % 59.62/9.03 : (v1 = v0 | ~ (fun_app$ag(v3, v2) = v1) | ~ (fun_app$ag(v3, v2) = v0)) & ! % 59.62/9.03 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Nat_set$] : ! % 59.62/9.03 [v3: Nat_nat_fun$] : (v1 = v0 | ~ (strict_mono_on$(v3, v2) = v1) | ~ % 59.62/9.03 (strict_mono_on$(v3, v2) = v0)) & ! [v0: ZF_ZF_prod_ZF_ZF_prod_fun$] : ! % 59.62/9.03 [v1: ZF_ZF_prod_ZF_ZF_prod_fun$] : ! [v2: ZF_ZF_prod_ZF_ZF_prod_fun$] : ! % 59.62/9.03 [v3: ZF_ZF_prod_set$] : (v1 = v0 | ~ (inv_into$k(v3, v2) = v1) | ~ % 59.62/9.03 (inv_into$k(v3, v2) = v0)) & ! [v0: ZF_ZF_prod_ZF_set_fun$] : ! [v1: % 59.62/9.03 ZF_ZF_prod_ZF_set_fun$] : ! [v2: ZF_set_ZF_ZF_prod_fun$] : ! [v3: % 59.62/9.03 ZF_set_set$] : (v1 = v0 | ~ (inv_into$j(v3, v2) = v1) | ~ (inv_into$j(v3, % 59.62/9.03 v2) = v0)) & ! [v0: ZF_ZF_prod_ZF_fun$] : ! [v1: ZF_ZF_prod_ZF_fun$] : % 59.62/9.03 ! [v2: ZF_ZF_ZF_prod_fun$] : ! [v3: ZF_set$] : (v1 = v0 | ~ (inv_into$i(v3, % 59.62/9.03 v2) = v1) | ~ (inv_into$i(v3, v2) = v0)) & ! [v0: % 59.62/9.03 ZF_set_ZF_ZF_prod_fun$] : ! [v1: ZF_set_ZF_ZF_prod_fun$] : ! [v2: % 59.62/9.03 ZF_ZF_prod_ZF_set_fun$] : ! [v3: ZF_ZF_prod_set$] : (v1 = v0 | ~ % 59.62/9.03 (inv_into$h(v3, v2) = v1) | ~ (inv_into$h(v3, v2) = v0)) & ! [v0: % 59.62/9.03 ZF_set_ZF_set_fun$] : ! [v1: ZF_set_ZF_set_fun$] : ! [v2: % 59.62/9.03 ZF_set_ZF_set_fun$] : ! [v3: ZF_set_set$] : (v1 = v0 | ~ (inv_into$g(v3, % 59.62/9.03 v2) = v1) | ~ (inv_into$g(v3, v2) = v0)) & ! [v0: ZF_ZF_ZF_prod_fun$] % 59.62/9.03 : ! [v1: ZF_ZF_ZF_prod_fun$] : ! [v2: ZF_ZF_prod_ZF_fun$] : ! [v3: % 59.62/9.04 ZF_ZF_prod_set$] : (v1 = v0 | ~ (inv_into$f(v3, v2) = v1) | ~ % 59.62/9.04 (inv_into$f(v3, v2) = v0)) & ! [v0: ZF_ZF_set_fun$] : ! [v1: % 59.62/9.04 ZF_ZF_set_fun$] : ! [v2: ZF_set_ZF_fun$] : ! [v3: ZF_set_set$] : (v1 = v0 % 59.62/9.04 | ~ (inv_into$e(v3, v2) = v1) | ~ (inv_into$e(v3, v2) = v0)) & ! [v0: % 59.62/9.04 Nat_nat_fun$] : ! [v1: Nat_nat_fun$] : ! [v2: Nat_nat_fun$] : ! [v3: % 59.62/9.04 Nat_set$] : (v1 = v0 | ~ (inv_into$d(v3, v2) = v1) | ~ (inv_into$d(v3, v2) % 59.62/9.04 = v0)) & ! [v0: ZF_nat_fun$] : ! [v1: ZF_nat_fun$] : ! [v2: % 59.62/9.04 Nat_ZF_fun$] : ! [v3: Nat_set$] : (v1 = v0 | ~ (inv_into$c(v3, v2) = v1) | % 59.62/9.04 ~ (inv_into$c(v3, v2) = v0)) & ! [v0: Nat_ZF_fun$] : ! [v1: Nat_ZF_fun$] % 59.62/9.04 : ! [v2: ZF_nat_fun$] : ! [v3: ZF_set$] : (v1 = v0 | ~ (inv_into$b(v3, v2) % 59.62/9.04 = v1) | ~ (inv_into$b(v3, v2) = v0)) & ! [v0: ZF_ZF_fun$] : ! [v1: % 59.62/9.04 ZF_ZF_fun$] : ! [v2: ZF_ZF_fun$] : ! [v3: ZF_set$] : (v1 = v0 | ~ % 59.62/9.04 (inv_into$a(v3, v2) = v1) | ~ (inv_into$a(v3, v2) = v0)) & ! [v0: % 59.62/9.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: ZF_set_set_set$] : % 59.62/9.04 ! [v3: ZF_set_set$] : (v1 = v0 | ~ (member$d(v3, v2) = v1) | ~ % 59.62/9.04 (member$d(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 59.62/9.04 MultipleValueBool] : ! [v2: Nat_set$] : ! [v3: Nat_set$] : (v1 = v0 | ~ % 59.62/9.04 (less_eq$d(v3, v2) = v1) | ~ (less_eq$d(v3, v2) = v0)) & ! [v0: % 59.62/9.04 Int_bool_fun$] : ! [v1: Int_bool_fun$] : ! [v2: int] : ! [v3: % 59.62/9.04 Int_int_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$af(v3, v2) = v1) | ~ % 59.62/9.04 (fun_app$af(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 59.62/9.04 MultipleValueBool] : ! [v2: int] : ! [v3: Int_bool_fun$] : (v1 = v0 | ~ % 59.62/9.04 (fun_app$ae(v3, v2) = v1) | ~ (fun_app$ae(v3, v2) = v0)) & ! [v0: % 59.62/9.04 Nat_bool_fun$] : ! [v1: Nat_bool_fun$] : ! [v2: Nat$] : ! [v3: % 59.62/9.04 Nat_nat_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$ad(v3, v2) = v1) | ~ % 59.62/9.04 (fun_app$ad(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : ! % 59.62/9.04 [v3: Int_int_fun$] : (v1 = v0 | ~ (fun_app$ac(v3, v2) = v1) | ~ % 59.62/9.04 (fun_app$ac(v3, v2) = v0)) & ! [v0: ZF_ZF_prod_set$] : ! [v1: % 59.62/9.04 ZF_ZF_prod_set$] : ! [v2: int] : ! [v3: Int_ZF_ZF_prod_set_fun$] : (v1 = % 59.62/9.04 v0 | ~ (fun_app$ab(v3, v2) = v1) | ~ (fun_app$ab(v3, v2) = v0)) & ! [v0: % 59.62/9.04 ZF_set$] : ! [v1: ZF_set$] : ! [v2: int] : ! [v3: Int_ZF_set_fun$] : (v1 % 59.62/9.04 = v0 | ~ (fun_app$aa(v3, v2) = v1) | ~ (fun_app$aa(v3, v2) = v0)) & ! % 59.62/9.04 [v0: int] : ! [v1: int] : ! [v2: ZF_ZF_prod_set$] : ! [v3: % 59.62/9.04 ZF_ZF_prod_set_int_fun$] : (v1 = v0 | ~ (fun_app$z(v3, v2) = v1) | ~ % 59.62/9.04 (fun_app$z(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: ZF_set$] : % 59.62/9.04 ! [v3: ZF_set_int_fun$] : (v1 = v0 | ~ (fun_app$y(v3, v2) = v1) | ~ % 59.62/9.04 (fun_app$y(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 59.62/9.04 MultipleValueBool] : ! [v2: Nat$] : ! [v3: Nat_bool_fun$] : (v1 = v0 | ~ % 59.62/9.04 (fun_app$x(v3, v2) = v1) | ~ (fun_app$x(v3, v2) = v0)) & ! [v0: % 59.62/9.04 ZF_set_ZF_fun$] : ! [v1: ZF_set_ZF_fun$] : ! [v2: ZF_ZF_set_fun$] : ! % 59.62/9.04 [v3: ZF_set$] : (v1 = v0 | ~ (inv_into$(v3, v2) = v1) | ~ (inv_into$(v3, v2) % 59.62/9.04 = v0)) & ! [v0: ZF_zet$] : ! [v1: ZF_zet$] : ! [v2: ZF_zet$] : ! [v3: % 59.62/9.04 ZF_ZF_fun$] : (v1 = v0 | ~ (zimage$a(v3, v2) = v1) | ~ (zimage$a(v3, v2) = % 59.62/9.04 v0)) & ! [v0: ZF_set_zet$] : ! [v1: ZF_set_zet$] : ! [v2: ZF_zet$] : ! % 59.62/9.04 [v3: ZF_ZF_set_fun$] : (v1 = v0 | ~ (zimage$(v3, v2) = v1) | ~ (zimage$(v3, % 59.62/9.04 v2) = v0)) & ! [v0: ZF_ZF_prod$] : ! [v1: ZF_ZF_prod$] : ! [v2: Nat$] % 59.62/9.04 : ! [v3: Nat_ZF_ZF_prod_fun$] : (v1 = v0 | ~ (fun_app$w(v3, v2) = v1) | ~ % 59.62/9.04 (fun_app$w(v3, v2) = v0)) & ! [v0: ZF_ZF_prod_set$] : ! [v1: % 59.62/9.04 ZF_ZF_prod_set$] : ! [v2: Nat_set$] : ! [v3: Nat_ZF_ZF_prod_fun$] : (v1 = % 59.62/9.04 v0 | ~ (image$m(v3, v2) = v1) | ~ (image$m(v3, v2) = v0)) & ! [v0: % 59.62/9.04 ZF_set$] : ! [v1: ZF_set$] : ! [v2: Nat$] : ! [v3: Nat_ZF_set_fun$] : (v1 % 59.62/9.04 = v0 | ~ (fun_app$v(v3, v2) = v1) | ~ (fun_app$v(v3, v2) = v0)) & ! [v0: % 59.62/9.04 ZF_set_set$] : ! [v1: ZF_set_set$] : ! [v2: Nat_set$] : ! [v3: % 59.62/9.04 Nat_ZF_set_fun$] : (v1 = v0 | ~ (image$l(v3, v2) = v1) | ~ (image$l(v3, % 59.62/9.04 v2) = v0)) & ! [v0: Nat_set$] : ! [v1: Nat_set$] : ! [v2: Nat_set$] : % 59.62/9.04 ! [v3: Nat_nat_fun$] : (v1 = v0 | ~ (image$k(v3, v2) = v1) | ~ (image$k(v3, % 59.62/9.04 v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat$] : ! [v3: % 59.62/9.04 Nat_nat_fun$] : (v1 = v0 | ~ (fun_app$u(v3, v2) = v1) | ~ (fun_app$u(v3, % 59.62/9.04 v2) = v0)) & ! [v0: ZF_set$] : ! [v1: ZF_set$] : ! [v2: Nat_set$] : % 59.62/9.04 ! [v3: Nat_ZF_fun$] : (v1 = v0 | ~ (image$j(v3, v2) = v1) | ~ (image$j(v3, % 59.62/9.04 v2) = v0)) & ! [v0: ZF$] : ! [v1: ZF$] : ! [v2: Nat$] : ! [v3: % 59.62/9.04 Nat_ZF_fun$] : (v1 = v0 | ~ (fun_app$t(v3, v2) = v1) | ~ (fun_app$t(v3, % 59.62/9.04 v2) = v0)) & ! [v0: Nat_set$] : ! [v1: Nat_set$] : ! [v2: ZF_set$] : % 59.62/9.04 ! [v3: ZF_nat_fun$] : (v1 = v0 | ~ (image$i(v3, v2) = v1) | ~ (image$i(v3, % 59.62/9.04 v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: ZF$] : ! [v3: % 59.62/9.04 ZF_nat_fun$] : (v1 = v0 | ~ (fun_app$s(v3, v2) = v1) | ~ (fun_app$s(v3, % 59.62/9.04 v2) = v0)) & ! [v0: ZF_ZF_prod_set$] : ! [v1: ZF_ZF_prod_set$] : ! % 59.62/9.04 [v2: ZF_ZF_prod_set$] : ! [v3: ZF_ZF_prod_set_ZF_ZF_prod_set_fun$] : (v1 = v0 % 59.62/9.04 | ~ (fun_app$r(v3, v2) = v1) | ~ (fun_app$r(v3, v2) = v0)) & ! [v0: % 59.62/9.04 ZF_ZF_prod$] : ! [v1: ZF_ZF_prod$] : ! [v2: ZF_ZF_prod$] : ! [v3: % 59.62/9.04 ZF_ZF_prod_ZF_ZF_prod_fun$] : (v1 = v0 | ~ (fun_app$q(v3, v2) = v1) | ~ % 59.62/9.04 (fun_app$q(v3, v2) = v0)) & ! [v0: ZF_set_set$] : ! [v1: ZF_set_set$] : ! % 59.62/9.04 [v2: ZF_ZF_prod_set$] : ! [v3: ZF_ZF_prod_ZF_set_fun$] : (v1 = v0 | ~ % 59.62/9.04 (image$g(v3, v2) = v1) | ~ (image$g(v3, v2) = v0)) & ! [v0: ZF_set$] : ! % 59.62/9.04 [v1: ZF_set$] : ! [v2: ZF_ZF_prod$] : ! [v3: ZF_ZF_prod_ZF_set_fun$] : (v1 = % 59.62/9.04 v0 | ~ (fun_app$p(v3, v2) = v1) | ~ (fun_app$p(v3, v2) = v0)) & ! [v0: % 59.62/9.04 ZF_set$] : ! [v1: ZF_set$] : ! [v2: ZF_ZF_prod_set$] : ! [v3: % 59.62/9.04 ZF_ZF_prod_set_ZF_set_fun$] : (v1 = v0 | ~ (fun_app$o(v3, v2) = v1) | ~ % 59.62/9.04 (fun_app$o(v3, v2) = v0)) & ! [v0: ZF$] : ! [v1: ZF$] : ! [v2: % 59.62/9.04 ZF_ZF_prod$] : ! [v3: ZF_ZF_prod_ZF_fun$] : (v1 = v0 | ~ (fun_app$n(v3, % 59.62/9.04 v2) = v1) | ~ (fun_app$n(v3, v2) = v0)) & ! [v0: ZF_ZF_prod_set$] : ! % 59.62/9.04 [v1: ZF_ZF_prod_set$] : ! [v2: ZF_set_set$] : ! [v3: ZF_set_ZF_ZF_prod_fun$] % 59.62/9.04 : (v1 = v0 | ~ (image$e(v3, v2) = v1) | ~ (image$e(v3, v2) = v0)) & ! [v0: % 59.62/9.04 ZF_ZF_prod$] : ! [v1: ZF_ZF_prod$] : ! [v2: ZF_set$] : ! [v3: % 59.62/9.04 ZF_set_ZF_ZF_prod_fun$] : (v1 = v0 | ~ (fun_app$m(v3, v2) = v1) | ~ % 59.62/9.04 (fun_app$m(v3, v2) = v0)) & ! [v0: ZF_set_set$] : ! [v1: ZF_set_set$] : ! % 59.62/9.04 [v2: ZF_set_set$] : ! [v3: ZF_set_ZF_set_fun$] : (v1 = v0 | ~ (image$d(v3, % 59.62/9.04 v2) = v1) | ~ (image$d(v3, v2) = v0)) & ! [v0: ZF_set$] : ! [v1: % 59.62/9.04 ZF_set$] : ! [v2: ZF_set_set$] : ! [v3: ZF_set_set_ZF_set_fun$] : (v1 = v0 % 59.62/9.04 | ~ (fun_app$l(v3, v2) = v1) | ~ (fun_app$l(v3, v2) = v0)) & ! [v0: % 59.62/9.04 ZF_ZF_prod_set$] : ! [v1: ZF_ZF_prod_set$] : ! [v2: ZF_set$] : ! [v3: % 59.62/9.04 ZF_set_ZF_ZF_prod_set_fun$] : (v1 = v0 | ~ (fun_app$k(v3, v2) = v1) | ~ % 59.62/9.04 (fun_app$k(v3, v2) = v0)) & ! [v0: ZF_ZF_prod$] : ! [v1: ZF_ZF_prod$] : ! % 59.62/9.04 [v2: ZF$] : ! [v3: ZF_ZF_ZF_prod_fun$] : (v1 = v0 | ~ (fun_app$j(v3, v2) = % 59.62/9.04 v1) | ~ (fun_app$j(v3, v2) = v0)) & ! [v0: ZF_set$] : ! [v1: ZF_set$] : % 59.62/9.04 ! [v2: ZF_set$] : ! [v3: ZF_set_ZF_set_fun$] : (v1 = v0 | ~ (fun_app$i(v3, % 59.62/9.04 v2) = v1) | ~ (fun_app$i(v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 59.62/9.04 ! [v1: MultipleValueBool] : ! [v2: Nat_set$] : ! [v3: Nat$] : (v1 = v0 | ~ % 59.62/9.04 (member$c(v3, v2) = v1) | ~ (member$c(v3, v2) = v0)) & ! [v0: ZF_set$] : % 59.62/9.04 ! [v1: ZF_set$] : ! [v2: ZF_zet$] : ! [v3: ZF_zet_ZF_set_fun$] : (v1 = v0 | % 59.62/9.04 ~ (fun_app$h(v3, v2) = v1) | ~ (fun_app$h(v3, v2) = v0)) & ! [v0: ZF$] : % 59.62/9.04 ! [v1: ZF$] : ! [v2: ZF$] : ! [v3: ZF_ZF_fun$] : (v1 = v0 | ~ % 59.62/9.04 (fun_app$g(v3, v2) = v1) | ~ (fun_app$g(v3, v2) = v0)) & ! [v0: ZF$] : ! % 59.62/9.04 [v1: ZF$] : ! [v2: ZF_set$] : ! [v3: ZF_set_ZF_fun$] : (v1 = v0 | ~ % 59.62/9.04 (fun_app$e(v3, v2) = v1) | ~ (fun_app$e(v3, v2) = v0)) & ! [v0: % 59.62/9.04 ZF_set_set$] : ! [v1: ZF_set_set$] : ! [v2: ZF_set$] : ! [v3: % 59.62/9.04 ZF_ZF_set_fun$] : (v1 = v0 | ~ (image$(v3, v2) = v1) | ~ (image$(v3, v2) = % 59.62/9.04 v0)) & ! [v0: ZF_set$] : ! [v1: ZF_set$] : ! [v2: ZF$] : ! [v3: % 59.62/9.04 ZF_ZF_set_fun$] : (v1 = v0 | ~ (fun_app$f(v3, v2) = v1) | ~ (fun_app$f(v3, % 59.62/9.04 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 59.62/9.04 ! [v2: ZF_set_set$] : ! [v3: ZF_set_set_bool_fun$] : (v1 = v0 | ~ % 59.62/9.04 (fun_app$d(v3, v2) = v1) | ~ (fun_app$d(v3, v2) = v0)) & ! [v0: % 59.62/9.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: ZF$] : ! [v3: % 59.62/9.04 ZF_bool_fun$] : (v1 = v0 | ~ (fun_app$b(v3, v2) = v1) | ~ (fun_app$b(v3, % 59.62/9.04 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 59.62/9.04 ! [v2: ZF_set$] : ! [v3: ZF_set_bool_fun$] : (v1 = v0 | ~ (fun_app$c(v3, v2) % 59.62/9.04 = v1) | ~ (fun_app$c(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 59.62/9.04 [v1: MultipleValueBool] : ! [v2: ZF_ZF_prod$] : ! [v3: ZF_ZF_prod_bool_fun$] % 59.62/9.04 : (v1 = v0 | ~ (fun_app$(v3, v2) = v1) | ~ (fun_app$(v3, v2) = v0)) & ! % 59.62/9.04 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 59.62/9.04 ZF_ZF_prod_set$] : ! [v3: ZF_ZF_prod_set_bool_fun$] : (v1 = v0 | ~ % 59.62/9.04 (fun_app$a(v3, v2) = v1) | ~ (fun_app$a(v3, v2) = v0)) & ! [v0: % 59.62/9.04 ZF_set_bool_fun$] : ! [v1: ZF_set_bool_fun$] : ! [v2: ZF_ZF_set_fun$] : % 59.62/9.04 (v1 = v0 | ~ (inj_on$a(v2) = v1) | ~ (inj_on$a(v2) = v0)) & ! [v0: % 59.62/9.04 ZF_ZF_fun$] : ! [v1: ZF_ZF_fun$] : ! [v2: ZF$] : (v1 = v0 | ~ (opair$(v2) % 59.62/9.04 = v1) | ~ (opair$(v2) = v0)) & ! [v0: ZF_ZF_fun$] : ! [v1: ZF_ZF_fun$] % 59.62/9.04 : ! [v2: ZF$] : (v1 = v0 | ~ (upair$(v2) = v1) | ~ (upair$(v2) = v0)) & ! % 59.62/9.04 [v0: ZF_ZF_fun$] : ! [v1: ZF_ZF_fun$] : ! [v2: ZF$] : (v1 = v0 | ~ % 59.62/9.04 (app$(v2) = v1) | ~ (app$(v2) = v0)) & ! [v0: ZF_ZF_fun$] : ! [v1: % 59.62/9.04 ZF_ZF_fun$] : ! [v2: ZF$] : (v1 = v0 | ~ (pFun$(v2) = v1) | ~ (pFun$(v2) % 59.62/9.04 = v0)) & ! [v0: ZF_ZF_fun$] : ! [v1: ZF_ZF_fun$] : ! [v2: ZF$] : (v1 = % 59.62/9.04 v0 | ~ (fun$(v2) = v1) | ~ (fun$(v2) = v0)) & ! [v0: ZF_bool_fun$] : ! % 59.62/9.04 [v1: ZF_bool_fun$] : ! [v2: ZF$] : (v1 = v0 | ~ (subset$(v2) = v1) | ~ % 59.62/9.04 (subset$(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: int] : (v1 = % 59.62/9.04 v0 | ~ (nat$a(v2) = v1) | ~ (nat$a(v2) = v0)) & ! [v0: ZF_ZF_fun$] : ! % 59.62/9.04 [v1: ZF_ZF_fun$] : ! [v2: ZF$] : (v1 = v0 | ~ (union$(v2) = v1) | ~ % 59.62/9.04 (union$(v2) = v0)) & ! [v0: ZF_ZF_fun$] : ! [v1: ZF_ZF_fun$] : ! [v2: % 59.62/9.04 ZF$] : (v1 = v0 | ~ (cartProd$(v2) = v1) | ~ (cartProd$(v2) = v0)) & ! % 59.62/9.04 [v0: int] : ! [v1: int] : ! [v2: Nat$] : (v1 = v0 | ~ (of_nat$(v2) = v1) | % 59.62/9.04 ~ (of_nat$(v2) = v0)) & ! [v0: Int_int_fun$] : ! [v1: Int_int_fun$] : ! % 59.62/9.04 [v2: int] : (v1 = v0 | ~ (sup$d(v2) = v1) | ~ (sup$d(v2) = v0)) & ! [v0: % 59.62/9.04 ZF_ZF_prod_set_ZF_ZF_prod_set_fun$] : ! [v1: % 59.62/9.04 ZF_ZF_prod_set_ZF_ZF_prod_set_fun$] : ! [v2: ZF_ZF_prod_set$] : (v1 = v0 | % 59.62/9.04 ~ (sup$b(v2) = v1) | ~ (sup$b(v2) = v0)) & ! [v0: ZF$] : ! [v1: ZF$] : ! % 59.62/9.04 [v2: Nat_ZF_fun$] : (v1 = v0 | ~ (seqSum$(v2) = v1) | ~ (seqSum$(v2) = v0)) % 59.62/9.04 & ! [v0: ZF_set_ZF_set_fun$] : ! [v1: ZF_set_ZF_set_fun$] : ! [v2: ZF_set$] % 59.62/9.04 : (v1 = v0 | ~ (sup$(v2) = v1) | ~ (sup$(v2) = v0)) & ! [v0: ZF_ZF_fun$] : % 59.62/9.04 ! [v1: ZF_ZF_fun$] : ! [v2: ZF_ZF_prod_set$] : (v1 = v0 | ~ % 59.62/9.04 (ext_ZF_hull$(v2) = v1) | ~ (ext_ZF_hull$(v2) = v0)) & ! [v0: % 59.62/9.04 ZF_zet_bool_fun$] : ! [v1: ZF_zet_bool_fun$] : ! [v2: ZF_zet$] : (v1 = v0 % 59.62/9.04 | ~ (zsubset$(v2) = v1) | ~ (zsubset$(v2) = v0)) & ! [v0: % 59.62/9.04 ZF_ZF_prod_set$] : ! [v1: ZF_ZF_prod_set$] : ! [v2: ZF_ZF_prod_zet$] : (v1 % 59.62/9.04 = v0 | ~ (rep_zet$b(v2) = v1) | ~ (rep_zet$b(v2) = v0)) & ! [v0: % 59.62/9.04 ZF_ZF_ZF_prod_fun$] : ! [v1: ZF_ZF_ZF_prod_fun$] : ! [v2: ZF$] : (v1 = v0 % 59.62/9.04 | ~ (pair$(v2) = v1) | ~ (pair$(v2) = v0)) & ! [v0: MultipleValueBool] : % 59.62/9.04 ! [v1: MultipleValueBool] : ! [v2: Nat_nat_fun$] : (v1 = v0 | ~ % 59.62/9.04 (bijection$a(v2) = v1) | ~ (bijection$a(v2) = v0)) & ! [v0: % 59.62/9.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: ZF_ZF_fun$] : (v1 % 59.62/9.04 = v0 | ~ (bijection$(v2) = v1) | ~ (bijection$(v2) = v0)) & ! [v0: % 59.62/9.04 ZF_zet_bool_fun$] : ! [v1: ZF_zet_bool_fun$] : ! [v2: ZF$] : (v1 = v0 | ~ % 59.62/9.04 (zin$(v2) = v1) | ~ (zin$(v2) = v0)) & ! [v0: ZF_set_zet$] : ! [v1: % 59.62/9.04 ZF_set_zet$] : ! [v2: ZF_set_set$] : (v1 = v0 | ~ (abs_zet$(v2) = v1) | ~ % 59.62/9.04 (abs_zet$(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 59.62/9.04 MultipleValueBool] : ! [v2: Int_int_fun$] : (v1 = v0 | ~ % 59.62/9.04 (strict_mono$c(v2) = v1) | ~ (strict_mono$c(v2) = v0)) & ! [v0: % 59.62/9.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 59.62/9.04 Int_ZF_ZF_prod_set_fun$] : (v1 = v0 | ~ (strict_mono$b(v2) = v1) | ~ % 59.62/9.04 (strict_mono$b(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 59.62/9.04 MultipleValueBool] : ! [v2: Int_ZF_set_fun$] : (v1 = v0 | ~ % 59.62/9.04 (strict_mono$a(v2) = v1) | ~ (strict_mono$a(v2) = v0)) & ! [v0: % 59.62/9.04 ZF_set_set_bool_fun$] : ! [v1: ZF_set_set_bool_fun$] : ! [v2: ZF_set_set$] % 59.62/9.04 : (v1 = v0 | ~ (less_eq$b(v2) = v1) | ~ (less_eq$b(v2) = v0)) & ! [v0: % 59.62/9.04 ZF_ZF_prod_set$] : ! [v1: ZF_ZF_prod_set$] : ! [v2: ZF_ZF_prod_bool_fun$] % 59.62/9.04 : (v1 = v0 | ~ (collect$c(v2) = v1) | ~ (collect$c(v2) = v0)) & ! [v0: % 59.62/9.04 ZF_set_set$] : ! [v1: ZF_set_set$] : ! [v2: ZF_set_bool_fun$] : (v1 = v0 | % 59.62/9.04 ~ (collect$b(v2) = v1) | ~ (collect$b(v2) = v0)) & ! [v0: % 59.62/9.04 ZF_ZF_prod_set_bool_fun$] : ! [v1: ZF_ZF_prod_set_bool_fun$] : ! [v2: % 59.62/9.04 ZF_ZF_prod_set$] : (v1 = v0 | ~ (less_eq$a(v2) = v1) | ~ (less_eq$a(v2) = % 59.62/9.04 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 59.62/9.04 Nat_nat_fun$] : (v1 = v0 | ~ (strict_mono$(v2) = v1) | ~ (strict_mono$(v2) % 59.62/9.04 = v0)) & ! [v0: ZF_set_set$] : ! [v1: ZF_set_set$] : ! [v2: % 59.62/9.04 ZF_set_zet$] : (v1 = v0 | ~ (rep_zet$a(v2) = v1) | ~ (rep_zet$a(v2) = v0)) % 59.62/9.04 & ! [v0: ZF_zet$] : ! [v1: ZF_zet$] : ! [v2: ZF$] : (v1 = v0 | ~ % 59.62/9.04 (zexplode$(v2) = v1) | ~ (zexplode$(v2) = v0)) & ! [v0: ZF_set_bool_fun$] % 59.62/9.04 : ! [v1: ZF_set_bool_fun$] : ! [v2: ZF_set$] : (v1 = v0 | ~ (less_eq$(v2) = % 59.62/9.04 v1) | ~ (less_eq$(v2) = v0)) & ! [v0: ZF_bool_fun$] : ! [v1: % 59.62/9.04 ZF_bool_fun$] : ! [v2: ZF$] : (v1 = v0 | ~ (elem$(v2) = v1) | ~ % 59.62/9.04 (elem$(v2) = v0)) & ! [v0: Nat_set$] : ! [v1: Nat_set$] : ! [v2: % 59.62/9.04 Nat_bool_fun$] : (v1 = v0 | ~ (collect$a(v2) = v1) | ~ (collect$a(v2) = % 59.62/9.04 v0)) & ! [v0: ZF_set$] : ! [v1: ZF_set$] : ! [v2: ZF_bool_fun$] : (v1 = % 59.62/9.04 v0 | ~ (collect$(v2) = v1) | ~ (collect$(v2) = v0)) & ! [v0: % 59.62/9.04 ZF_ZF_prod_set_ZF_ZF_prod_set_fun$] : ! [v1: % 59.62/9.04 ZF_ZF_prod_set_ZF_ZF_prod_set_fun$] : ! [v2: ZF_ZF_prod_ZF_ZF_prod_fun$] : % 59.62/9.04 (v1 = v0 | ~ (image$h(v2) = v1) | ~ (image$h(v2) = v0)) & ! [v0: % 59.62/9.04 ZF_ZF_prod_set_ZF_set_fun$] : ! [v1: ZF_ZF_prod_set_ZF_set_fun$] : ! [v2: % 59.62/9.04 ZF_ZF_prod_ZF_fun$] : (v1 = v0 | ~ (image$f(v2) = v1) | ~ (image$f(v2) = % 59.62/9.04 v0)) & ! [v0: ZF_set_set_ZF_set_fun$] : ! [v1: ZF_set_set_ZF_set_fun$] : % 59.62/9.04 ! [v2: ZF_set_ZF_fun$] : (v1 = v0 | ~ (image$c(v2) = v1) | ~ (image$c(v2) = % 59.62/9.04 v0)) & ! [v0: ZF_set_ZF_ZF_prod_set_fun$] : ! [v1: % 59.62/9.04 ZF_set_ZF_ZF_prod_set_fun$] : ! [v2: ZF_ZF_ZF_prod_fun$] : (v1 = v0 | ~ % 59.62/9.04 (image$b(v2) = v1) | ~ (image$b(v2) = v0)) & ! [v0: ZF_set_ZF_set_fun$] : % 59.62/9.04 ! [v1: ZF_set_ZF_set_fun$] : ! [v2: ZF_ZF_fun$] : (v1 = v0 | ~ (image$a(v2) % 59.62/9.04 = v1) | ~ (image$a(v2) = v0)) & ! [v0: ZF$] : ! [v1: ZF$] : ! [v2: % 59.62/9.04 ZF_zet$] : (v1 = v0 | ~ (zimplode$(v2) = v1) | ~ (zimplode$(v2) = v0)) & % 59.62/9.04 ! [v0: ZF_ZF_set_fun$] : ! [v1: ZF_ZF_set_fun$] : ! [v2: ZF_ZF_prod_set$] : % 59.62/9.04 (v1 = v0 | ~ (ext$(v2) = v1) | ~ (ext$(v2) = v0)) & ! [v0: ZF_ZF_fun$] : ! % 59.62/9.04 [v1: ZF_ZF_fun$] : ! [v2: ZF_ZF_prod_set$] : (v1 = v0 | ~ (ext_ZF$(v2) = v1) % 59.62/9.04 | ~ (ext_ZF$(v2) = v0)) & ! [v0: ZF_set_set_bool_fun$] : ! [v1: % 59.62/9.04 ZF_set_set_bool_fun$] : ! [v2: ZF_set$] : (v1 = v0 | ~ (member$b(v2) = v1) % 59.62/9.04 | ~ (member$b(v2) = v0)) & ! [v0: ZF_set_bool_fun$] : ! [v1: % 59.62/9.04 ZF_set_bool_fun$] : ! [v2: ZF_set_set$] : (v1 = v0 | ~ (uua$(v2) = v1) | % 59.62/9.04 ~ (uua$(v2) = v0)) & ! [v0: ZF_bool_fun$] : ! [v1: ZF_bool_fun$] : ! [v2: % 59.62/9.04 ZF_set$] : (v1 = v0 | ~ (uu$(v2) = v1) | ~ (uu$(v2) = v0)) & ! [v0: % 59.62/9.04 ZF_set_bool_fun$] : ! [v1: ZF_set_bool_fun$] : ! [v2: ZF$] : (v1 = v0 | ~ % 59.62/9.04 (member$a(v2) = v1) | ~ (member$a(v2) = v0)) & ! [v0: % 59.62/9.04 ZF_ZF_prod_bool_fun$] : ! [v1: ZF_ZF_prod_bool_fun$] : ! [v2: % 59.62/9.04 ZF_ZF_prod_set$] : (v1 = v0 | ~ (uub$(v2) = v1) | ~ (uub$(v2) = v0)) & ! % 59.62/9.04 [v0: ZF_ZF_prod_set_bool_fun$] : ! [v1: ZF_ZF_prod_set_bool_fun$] : ! [v2: % 59.62/9.04 ZF_ZF_prod$] : (v1 = v0 | ~ (member$(v2) = v1) | ~ (member$(v2) = v0)) % 59.62/9.04 % 59.62/9.04 Further assumptions not needed in the proof: % 59.62/9.04 -------------------------------------------- % 59.62/9.04 axiom0, axiom1, axiom10, axiom100, axiom101, axiom102, axiom103, axiom104, % 59.62/9.04 axiom105, axiom106, axiom107, axiom108, axiom109, axiom11, axiom110, axiom111, % 59.62/9.04 axiom112, axiom113, axiom114, axiom115, axiom116, axiom117, axiom118, axiom119, % 59.62/9.04 axiom12, axiom120, axiom121, axiom122, axiom123, axiom124, axiom125, axiom126, % 59.62/9.04 axiom127, axiom128, axiom129, axiom13, axiom130, axiom131, axiom132, axiom133, % 59.62/9.04 axiom134, axiom135, axiom136, axiom137, axiom138, axiom139, axiom14, axiom140, % 59.62/9.04 axiom141, axiom142, axiom143, axiom144, axiom145, axiom146, axiom147, axiom148, % 59.62/9.04 axiom149, axiom15, axiom150, axiom151, axiom152, axiom153, axiom154, axiom155, % 59.62/9.04 axiom156, axiom157, axiom158, axiom159, axiom16, axiom160, axiom161, axiom162, % 59.62/9.04 axiom163, axiom164, axiom165, axiom166, axiom167, axiom168, axiom169, axiom17, % 59.62/9.04 axiom170, axiom171, axiom172, axiom173, axiom174, axiom175, axiom176, axiom177, % 59.62/9.04 axiom178, axiom179, axiom18, axiom180, axiom181, axiom182, axiom183, axiom184, % 59.62/9.04 axiom185, axiom186, axiom187, axiom188, axiom189, axiom19, axiom190, axiom191, % 59.62/9.04 axiom192, axiom193, axiom194, axiom195, axiom196, axiom197, axiom198, axiom199, % 59.62/9.04 axiom2, axiom20, axiom200, axiom201, axiom202, axiom203, axiom204, axiom205, % 59.62/9.04 axiom206, axiom207, axiom208, axiom209, axiom21, axiom210, axiom211, axiom212, % 59.62/9.04 axiom213, axiom214, axiom215, axiom216, axiom217, axiom218, axiom219, axiom22, % 59.62/9.04 axiom220, axiom221, axiom222, axiom223, axiom224, axiom225, axiom226, axiom227, % 59.62/9.04 axiom228, axiom229, axiom23, axiom230, axiom231, axiom232, axiom233, axiom234, % 59.62/9.04 axiom235, axiom236, axiom237, axiom238, axiom239, axiom24, axiom240, axiom241, % 59.62/9.04 axiom242, axiom243, axiom244, axiom245, axiom246, axiom247, axiom248, axiom249, % 59.62/9.04 axiom25, axiom250, axiom251, axiom252, axiom253, axiom254, axiom255, axiom256, % 59.62/9.04 axiom257, axiom258, axiom259, axiom26, axiom260, axiom261, axiom262, axiom263, % 59.62/9.04 axiom264, axiom265, axiom266, axiom267, axiom268, axiom269, axiom27, axiom270, % 59.62/9.04 axiom271, axiom272, axiom273, axiom274, axiom275, axiom276, axiom277, axiom278, % 59.62/9.04 axiom279, axiom28, axiom280, axiom281, axiom282, axiom283, axiom284, axiom285, % 59.62/9.04 axiom286, axiom287, axiom288, axiom289, axiom29, axiom290, axiom291, axiom292, % 59.62/9.04 axiom293, axiom294, axiom295, axiom296, axiom297, axiom298, axiom299, axiom30, % 59.62/9.04 axiom300, axiom301, axiom302, axiom303, axiom304, axiom305, axiom306, axiom307, % 59.62/9.04 axiom308, axiom309, axiom31, axiom310, axiom311, axiom312, axiom313, axiom314, % 59.62/9.04 axiom315, axiom316, axiom317, axiom318, axiom319, axiom32, axiom320, axiom321, % 59.62/9.04 axiom322, axiom323, axiom324, axiom325, axiom326, axiom327, axiom328, axiom329, % 59.62/9.04 axiom33, axiom330, axiom331, axiom332, axiom333, axiom334, axiom335, axiom336, % 59.62/9.04 axiom337, axiom338, axiom339, axiom34, axiom340, axiom341, axiom342, axiom343, % 59.62/9.04 axiom344, axiom345, axiom346, axiom347, axiom348, axiom349, axiom35, axiom350, % 59.62/9.04 axiom351, axiom352, axiom353, axiom354, axiom355, axiom356, axiom357, axiom358, % 59.62/9.04 axiom359, axiom36, axiom360, axiom361, axiom362, axiom363, axiom364, axiom365, % 59.62/9.04 axiom366, axiom367, axiom368, axiom369, axiom37, axiom370, axiom371, axiom372, % 59.62/9.04 axiom373, axiom374, axiom375, axiom376, axiom377, axiom378, axiom379, axiom38, % 59.62/9.04 axiom380, axiom381, axiom382, axiom383, axiom384, axiom385, axiom386, axiom387, % 59.62/9.04 axiom388, axiom389, axiom39, axiom390, axiom391, axiom392, axiom393, axiom394, % 59.62/9.04 axiom395, axiom396, axiom397, axiom398, axiom399, axiom40, axiom400, axiom401, % 59.62/9.04 axiom402, axiom403, axiom404, axiom405, axiom406, axiom407, axiom408, axiom409, % 59.62/9.04 axiom41, axiom410, axiom411, axiom412, axiom413, axiom414, axiom415, axiom416, % 59.62/9.04 axiom417, axiom418, axiom419, axiom42, axiom420, axiom421, axiom422, axiom423, % 59.62/9.04 axiom424, axiom425, axiom426, axiom427, axiom428, axiom429, axiom43, axiom430, % 59.62/9.04 axiom431, axiom432, axiom433, axiom434, axiom435, axiom436, axiom437, axiom438, % 59.62/9.04 axiom439, axiom44, axiom440, axiom441, axiom442, axiom443, axiom444, axiom445, % 59.62/9.04 axiom446, axiom447, axiom448, axiom449, axiom45, axiom450, axiom451, axiom452, % 59.62/9.04 axiom453, axiom454, axiom455, axiom456, axiom457, axiom458, axiom459, axiom46, % 59.62/9.04 axiom460, axiom461, axiom462, axiom463, axiom464, axiom465, axiom466, axiom467, % 59.62/9.04 axiom468, axiom469, axiom47, axiom470, axiom471, axiom472, axiom473, axiom474, % 59.62/9.04 axiom475, axiom476, axiom477, axiom478, axiom479, axiom48, axiom480, axiom481, % 59.62/9.04 axiom482, axiom483, axiom484, axiom485, axiom486, axiom487, axiom488, axiom489, % 59.62/9.04 axiom49, axiom490, axiom491, axiom492, axiom493, axiom494, axiom495, axiom496, % 59.62/9.04 axiom497, axiom498, axiom499, axiom5, axiom50, axiom500, axiom501, axiom502, % 59.62/9.04 axiom503, axiom504, axiom505, axiom506, axiom507, axiom508, axiom509, axiom51, % 59.62/9.04 axiom510, axiom511, axiom512, axiom513, axiom514, axiom515, axiom516, axiom517, % 59.62/9.04 axiom518, axiom519, axiom52, axiom520, axiom521, axiom522, axiom523, axiom524, % 59.62/9.04 axiom525, axiom526, axiom527, axiom528, axiom529, axiom53, axiom530, axiom531, % 59.62/9.04 axiom532, axiom533, axiom534, axiom535, axiom536, axiom537, axiom538, axiom539, % 59.62/9.04 axiom54, axiom540, axiom541, axiom542, axiom543, axiom544, axiom545, axiom546, % 59.62/9.04 axiom547, axiom548, axiom549, axiom55, axiom550, axiom551, axiom552, axiom553, % 59.62/9.04 axiom554, axiom555, axiom556, axiom557, axiom558, axiom559, axiom56, axiom560, % 59.62/9.04 axiom561, axiom562, axiom563, axiom564, axiom565, axiom566, axiom567, axiom568, % 59.62/9.04 axiom569, axiom57, axiom570, axiom571, axiom572, axiom573, axiom574, axiom575, % 59.62/9.04 axiom576, axiom577, axiom578, axiom579, axiom58, axiom580, axiom581, axiom582, % 59.62/9.04 axiom583, axiom584, axiom585, axiom586, axiom587, axiom588, axiom589, axiom59, % 59.62/9.04 axiom590, axiom591, axiom592, axiom593, axiom594, axiom595, axiom596, axiom597, % 59.62/9.04 axiom598, axiom599, axiom6, axiom60, axiom600, axiom601, axiom602, axiom603, % 59.62/9.04 axiom604, axiom605, axiom606, axiom607, axiom608, axiom609, axiom61, axiom610, % 59.62/9.04 axiom611, axiom612, axiom613, axiom614, axiom615, axiom616, axiom617, axiom618, % 59.62/9.04 axiom619, axiom62, axiom620, axiom621, axiom622, axiom623, axiom624, axiom625, % 59.62/9.04 axiom626, axiom627, axiom628, axiom629, axiom63, axiom630, axiom631, axiom632, % 59.62/9.04 axiom633, axiom634, axiom635, axiom636, axiom637, axiom638, axiom639, axiom64, % 59.62/9.04 axiom640, axiom641, axiom642, axiom643, axiom644, axiom645, axiom65, axiom66, % 59.62/9.04 axiom67, axiom68, axiom69, axiom7, axiom70, axiom71, axiom72, axiom73, axiom74, % 59.62/9.04 axiom75, axiom76, axiom77, axiom78, axiom79, axiom8, axiom80, axiom81, axiom82, % 59.62/9.04 axiom83, axiom84, axiom85, axiom86, axiom87, axiom88, axiom89, axiom9, axiom90, % 59.62/9.04 axiom91, axiom92, axiom93, axiom94, axiom95, axiom96, axiom97, axiom98, axiom99 % 59.62/9.04 % 59.62/9.04 Those formulas are unsatisfiable: % 59.62/9.04 --------------------------------- % 59.62/9.04 % 59.62/9.04 Begin of proof % 59.62/9.04 | % 59.62/9.04 | ALPHA: (axiom4) implies: % 59.62/9.05 | (1) ? [v0: ZF_set_bool_fun$] : (member$a(y$) = v0 & fun_app$c(v0, a$) = 0 % 59.62/9.05 | & ZF_set_bool_fun$(v0)) % 59.62/9.05 | % 59.62/9.05 | ALPHA: (conjecture3) implies: % 59.62/9.05 | (2) ? [v0: ZF_set_bool_fun$] : ? [v1: int] : ? [v2: ZF_set$] : ? [v3: % 59.62/9.05 | ZF$] : ( ~ (v1 = 0) & fun_app$e(implode$, v2) = v3 & fun_app$f(f$, % 59.62/9.05 | y$) = v2 & member$a(y$) = v0 & fun_app$c(v0, a$) = v1 & ZF$(v3) & % 59.62/9.05 | ZF_set_bool_fun$(v0) & ZF_set$(v2)) % 59.62/9.05 | % 59.62/9.05 | ALPHA: (function-axioms) implies: % 59.62/9.05 | (3) ! [v0: ZF_set_bool_fun$] : ! [v1: ZF_set_bool_fun$] : ! [v2: ZF$] : % 59.62/9.05 | (v1 = v0 | ~ (member$a(v2) = v1) | ~ (member$a(v2) = v0)) % 59.62/9.05 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 59.62/9.05 | ZF_set$] : ! [v3: ZF_set_bool_fun$] : (v1 = v0 | ~ (fun_app$c(v3, % 59.62/9.05 | v2) = v1) | ~ (fun_app$c(v3, v2) = v0)) % 59.62/9.05 | % 59.62/9.05 | DELTA: instantiating (1) with fresh symbol all_615_0 gives: % 59.62/9.05 | (5) member$a(y$) = all_615_0 & fun_app$c(all_615_0, a$) = 0 & % 59.62/9.05 | ZF_set_bool_fun$(all_615_0) % 59.62/9.05 | % 59.62/9.05 | ALPHA: (5) implies: % 59.62/9.05 | (6) fun_app$c(all_615_0, a$) = 0 % 59.62/9.05 | (7) member$a(y$) = all_615_0 % 59.62/9.05 | % 59.62/9.05 | DELTA: instantiating (2) with fresh symbols all_688_0, all_688_1, all_688_2, % 59.62/9.05 | all_688_3 gives: % 59.62/9.05 | (8) ~ (all_688_2 = 0) & fun_app$e(implode$, all_688_1) = all_688_0 & % 59.62/9.05 | fun_app$f(f$, y$) = all_688_1 & member$a(y$) = all_688_3 & % 59.62/9.05 | fun_app$c(all_688_3, a$) = all_688_2 & ZF$(all_688_0) & % 59.62/9.05 | ZF_set_bool_fun$(all_688_3) & ZF_set$(all_688_1) % 59.62/9.05 | % 59.62/9.05 | ALPHA: (8) implies: % 59.62/9.05 | (9) ~ (all_688_2 = 0) % 59.62/9.05 | (10) fun_app$c(all_688_3, a$) = all_688_2 % 59.62/9.05 | (11) member$a(y$) = all_688_3 % 59.62/9.05 | % 59.62/9.05 | GROUND_INST: instantiating (3) with all_615_0, all_688_3, y$, simplifying with % 59.62/9.05 | (7), (11) gives: % 59.62/9.05 | (12) all_688_3 = all_615_0 % 59.62/9.05 | % 59.62/9.05 | REDUCE: (10), (12) imply: % 59.62/9.05 | (13) fun_app$c(all_615_0, a$) = all_688_2 % 59.62/9.05 | % 59.62/9.05 | GROUND_INST: instantiating (4) with 0, all_688_2, a$, all_615_0, simplifying % 59.62/9.05 | with (6), (13) gives: % 59.62/9.05 | (14) all_688_2 = 0 % 59.62/9.05 | % 59.62/9.05 | REDUCE: (9), (14) imply: % 59.62/9.05 | (15) $false % 59.62/9.06 | % 59.62/9.06 | CLOSE: (15) is inconsistent. % 59.62/9.06 | % 59.62/9.06 End of proof % 59.62/9.06 % SZS output end Proof for theBenchmark % 59.62/9.06 % 59.62/9.06 8430ms %------------------------------------------------------------------------------