%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU806^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n024.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 : Wed Jun 3 08:53:17 AM UTC 2026 % Result : Theorem 150.60s 150.90s % Output : Proof 150.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SEU806^2 : TPTP v9.2.1. Released v3.7.0. % 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n024.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 12:52:30 EDT 2026 % 0.07/0.25 % CPUTime : % 0.14/0.33 %----Proving TH0 % 150.60/150.90 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 150.60/150.90 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 150.60/150.90 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 150.60/150.90 --- Run --ho-elim --full-saturate-quant at 18s... % 150.60/150.90 % SZS status Theorem % 150.60/150.90 % SZS output start Proof % 150.60/150.90 ( % 150.60/150.90 (declare-sort $$unsorted 0) % 150.60/150.90 (declare-const tptp.in__Cong Bool) % 150.60/150.90 (declare-const tptp.emptyset $$unsorted) % 150.60/150.90 (declare-const tptp.setadjoinIL Bool) % 150.60/150.90 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 150.60/150.90 (declare-const tptp.uniqinunit Bool) % 150.60/150.90 (declare-const tptp.foundationAx Bool) % 150.60/150.90 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 150.60/150.90 (define @t1 () (@var "A" $$unsorted)) % 150.60/150.90 (define @t2 () (@var "Xx" $$unsorted)) % 150.60/150.90 (define @t3 () (_ tptp.in @t2)) % 150.60/150.90 (define @t4 () (_ @t3 @t1)) % 150.60/150.90 (define @t5 () (@var "B" $$unsorted)) % 150.60/150.90 (define @t6 () (_ @t3 @t5)) % 150.60/150.90 (define @t7 () (and @t6 @t4)) % 150.60/150.90 (define @t8 () (@list @t2)) % 150.60/150.90 (define @t9 () (exists @t8 @t7)) % 150.60/150.90 (define @t10 () (not @t9)) % 150.60/150.90 (define @t11 () (_ (_ tptp.in @t5) @t1)) % 150.60/150.90 (define @t12 () (and @t11 @t10)) % 150.60/150.90 (define @t13 () (@list @t5)) % 150.60/150.90 (define @t14 () (exists @t13 @t12)) % 150.60/150.90 (define @t15 () (exists @t8 @t4)) % 150.60/150.90 (define @t16 () (=> @t15 @t14)) % 150.60/150.90 (define @t17 () (@list @t1)) % 150.60/150.90 (define @t18 () (forall @t17 @t16)) % 150.60/150.90 (define @t19 () (= tptp.foundationAx @t18)) % 150.60/150.90 (define @t20 () (@var "Xy" $$unsorted)) % 150.60/150.90 (define @t21 () (_ (_ tptp.setadjoin @t2) @t20)) % 150.60/150.90 (define @t22 () (_ @t3 @t21)) % 150.60/150.90 (define @t23 () (@list @t2 @t20)) % 150.60/150.90 (define @t24 () (forall @t23 @t22)) % 150.60/150.90 (define @t25 () (= tptp.setadjoinIL @t24)) % 150.60/150.90 (define @t26 () (= @t2 @t20)) % 150.60/150.90 (define @t27 () (_ (_ tptp.setadjoin @t20) tptp.emptyset)) % 150.60/150.90 (define @t28 () (_ @t3 @t27)) % 150.60/150.90 (define @t29 () (forall @t23 (=> @t28 @t26))) % 150.60/150.90 (define @t30 () (= tptp.uniqinunit @t29)) % 150.60/150.90 (define @t31 () (_ (_ tptp.in @t20) @t5)) % 150.60/150.90 (define @t32 () (= @t4 @t31)) % 150.60/150.90 (define @t33 () (forall @t23 (=> @t26 @t32))) % 150.60/150.90 (define @t34 () (= @t1 @t5)) % 150.60/150.90 (define @t35 () (=> @t34 @t33)) % 150.60/150.90 (define @t36 () (@list @t1 @t5)) % 150.60/150.90 (define @t37 () (forall @t36 @t35)) % 150.60/150.90 (define @t38 () (= tptp.in__Cong @t37)) % 150.60/150.90 (define @t39 () (_ (_ tptp.in @t1) @t1)) % 150.60/150.90 (define @t40 () (not @t39)) % 150.60/150.90 (define @t41 () (forall @t17 @t40)) % 150.60/150.90 (define @t42 () (=> tptp.in__Cong @t41)) % 150.60/150.90 (define @t43 () (=> tptp.uniqinunit @t42)) % 150.60/150.90 (define @t44 () (=> tptp.setadjoinIL @t43)) % 150.60/150.90 (define @t45 () (=> tptp.foundationAx @t44)) % 150.60/150.90 (define @t46 () (not @t45)) % 150.60/150.90 (define @t47 () (@const 0 (@ho-elim-sort (-> $$unsorted $$unsorted Bool)))) % 150.60/150.90 (define @t48 () (@const 1 (-> (@ho-elim-sort (-> $$unsorted $$unsorted Bool)) $$unsorted (@ho-elim-sort (-> $$unsorted Bool))))) % 150.60/150.90 (define @t49 () (@const 2 (-> (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool))) % 150.60/150.90 (define @t50 () (forall @t17 (not (_ @t49 (_ @t48 @t47 @t1) @t1)))) % 150.60/150.90 (define @t51 () (@const 3 (@ho-elim-sort (-> $$unsorted $$unsorted $$unsorted)))) % 150.60/150.90 (define @t52 () (@const 4 (-> (@ho-elim-sort (-> $$unsorted $$unsorted $$unsorted)) $$unsorted (@ho-elim-sort (-> $$unsorted $$unsorted))))) % 150.60/150.90 (define @t53 () (@const 5 (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted $$unsorted))) % 150.60/150.90 (define @t54 () (_ @t48 @t47 @t2)) % 150.60/150.90 (define @t55 () (forall @t23 (or (not (_ @t49 @t54 (_ @t53 (_ @t52 @t51 @t20) tptp.emptyset))) @t26))) % 150.60/150.90 (define @t56 () (not (_ @t49 @t54 @t5))) % 150.60/150.90 (define @t57 () (_ @t48 @t47 @t5)) % 150.60/150.90 (define @t58 () (@var "BOUND_VARIABLE_7507" $$unsorted)) % 150.60/150.90 (define @t59 () (@list @t1 @t58)) % 150.60/150.90 (define @t60 () (tptp.in @t1 @t1)) % 150.60/150.90 (define @t61 () (forall @t17 (not @t60))) % 150.60/150.90 (define @t62 () (tptp.setadjoin @t20 tptp.emptyset)) % 150.60/150.90 (define @t63 () (tptp.in @t2 @t62)) % 150.60/150.90 (define @t64 () (forall @t23 (or (not @t63) @t26))) % 150.60/150.90 (define @t65 () (tptp.setadjoin @t2 @t20)) % 150.60/150.90 (define @t66 () (tptp.in @t2 @t65)) % 150.60/150.90 (define @t67 () (forall @t23 @t66)) % 150.60/150.90 (define @t68 () (tptp.in @t2 @t1)) % 150.60/150.90 (define @t69 () (not @t68)) % 150.60/150.90 (define @t70 () (tptp.in @t2 @t5)) % 150.60/150.90 (define @t71 () (forall @t8 (or (not @t70) @t69))) % 150.60/150.90 (define @t72 () (not @t71)) % 150.60/150.90 (define @t73 () (tptp.in @t5 @t1)) % 150.60/150.90 (define @t74 () (not (forall @t13 (or (not @t73) @t72)))) % 150.60/150.90 (define @t75 () (not (tptp.in @t58 @t1))) % 150.60/150.90 (define @t76 () (or @t75 @t74)) % 150.60/150.90 (define @t77 () (forall @t59 @t76)) % 150.60/150.90 (define @t78 () (=> @t64 (=> true @t61))) % 150.60/150.90 (define @t79 () (=> @t67 @t78)) % 150.60/150.90 (define @t80 () (=> @t77 @t79)) % 150.60/150.90 (define @t81 () (@var "BOUND_VARIABLE_7555" $$unsorted)) % 150.60/150.90 (define @t82 () (@list @t5 @t81)) % 150.60/150.90 (define @t83 () (tptp.in @t81 @t5)) % 150.60/150.90 (define @t84 () (not (= @t5 @t5))) % 150.60/150.90 (define @t85 () (or @t84 (= @t83 @t83))) % 150.60/150.90 (define @t86 () (= @t83 (tptp.in @t81 @t1))) % 150.60/150.90 (define @t87 () (not @t34)) % 150.60/150.90 (define @t88 () (or @t87 @t87 @t86)) % 150.60/150.90 (define @t89 () (or @t87 @t86)) % 150.60/150.90 (define @t90 () (forall @t17 @t89)) % 150.60/150.90 (define @t91 () (forall @t82 @t90)) % 150.60/150.90 (define @t92 () (forall (@list @t5 @t81 @t1) @t89)) % 150.60/150.90 (define @t93 () (forall (@list @t1 @t5 @t81) @t89)) % 150.60/150.90 (define @t94 () (@list @t81)) % 150.60/150.90 (define @t95 () (forall @t94 @t89)) % 150.60/150.90 (define @t96 () (forall @t94 @t86)) % 150.60/150.90 (define @t97 () (or @t87 @t96)) % 150.60/150.90 (define @t98 () (tptp.in @t20 @t1)) % 150.60/150.90 (define @t99 () (tptp.in @t20 @t5)) % 150.60/150.90 (define @t100 () (= @t99 @t98)) % 150.60/150.90 (define @t101 () (@list @t20)) % 150.60/150.90 (define @t102 () (forall @t101 @t100)) % 150.60/150.90 (define @t103 () (not (= @t20 @t20))) % 150.60/150.90 (define @t104 () (or @t103 (= @t98 @t99))) % 150.60/150.90 (define @t105 () (= @t68 @t99)) % 150.60/150.90 (define @t106 () (not @t26)) % 150.60/150.90 (define @t107 () (or @t106 @t106 @t105)) % 150.60/150.90 (define @t108 () (or @t106 @t105)) % 150.60/150.90 (define @t109 () (forall @t8 @t108)) % 150.60/150.90 (define @t110 () (forall @t101 @t109)) % 150.60/150.90 (define @t111 () (forall (@list @t20 @t2) @t108)) % 150.60/150.90 (define @t112 () (or @t106 @t32)) % 150.60/150.90 (define @t113 () (=> tptp.in__Cong @t61)) % 150.60/150.90 (define @t114 () (not @t28)) % 150.60/150.90 (define @t115 () (or @t114 @t26)) % 150.60/150.90 (define @t116 () (=> tptp.uniqinunit @t113)) % 150.60/150.90 (define @t117 () (=> tptp.setadjoinIL @t116)) % 150.60/150.90 (define @t118 () (@list @t58)) % 150.60/150.90 (define @t119 () (forall @t118 @t76)) % 150.60/150.90 (define @t120 () (forall @t118 @t75)) % 150.60/150.90 (define @t121 () (or @t120 @t74)) % 150.60/150.90 (define @t122 () (forall @t8 @t69)) % 150.60/150.90 (define @t123 () (not @t122)) % 150.60/150.90 (define @t124 () (not @t11)) % 150.60/150.90 (define @t125 () (or @t124 @t72)) % 150.60/150.90 (define @t126 () (and @t11 @t71)) % 150.60/150.90 (define @t127 () (forall @t13 (not @t126))) % 150.60/150.90 (define @t128 () (not @t127)) % 150.60/150.90 (define @t129 () (not @t4)) % 150.60/150.90 (define @t130 () (not @t6)) % 150.60/150.90 (define @t131 () (or @t130 @t129)) % 150.60/150.90 (define @t132 () (forall @t8 (not @t7))) % 150.60/150.90 (define @t133 () (not @t132)) % 150.60/150.90 (define @t134 () (forall @t8 @t129)) % 150.60/150.90 (define @t135 () (not @t134)) % 150.60/150.90 (define @t136 () (=> tptp.foundationAx @t117)) % 150.60/150.90 (define @t137 () (@quantifiers_skolemize @t50 0)) % 150.60/150.90 (define @t138 () (_ @t53 (_ @t52 @t51 @t137) tptp.emptyset)) % 150.60/150.90 (define @t139 () (not (_ @t49 @t54 @t138))) % 150.60/150.90 (define @t140 () (forall @t13 (or (not (_ @t49 @t57 @t138)) (not (forall @t8 (or @t56 @t139)))))) % 150.60/150.90 (define @t141 () (not @t140)) % 150.60/150.90 (define @t142 () (_ @t48 @t47 @t137)) % 150.60/150.90 (define @t143 () (_ @t49 @t142 @t138)) % 150.60/150.90 (define @t144 () (not @t143)) % 150.60/150.90 (define @t145 () (or @t144 @t141)) % 150.60/150.90 (define @t146 () (@list false false)) % 150.60/150.90 (define @t147 () (@quantifiers_skolemize @t140 0)) % 150.60/150.90 (define @t148 () (forall @t8 (or (not (_ @t49 @t54 @t147)) @t139))) % 150.60/150.90 (define @t149 () (not @t148)) % 150.60/150.90 (define @t150 () (_ @t49 (_ @t48 @t47 @t147) @t138)) % 150.60/150.90 (define @t151 () (not @t150)) % 150.60/150.90 (define @t152 () (or @t151 @t149)) % 150.60/150.90 (define @t153 () (@list true)) % 150.60/150.90 (define @t154 () (@list @t152)) % 150.60/150.90 (define @t155 () (not (_ @t49 @t142 @t147))) % 150.60/150.90 (define @t156 () (or @t155 @t144)) % 150.60/150.90 (define @t157 () (or @t151 (= @t147 @t137))) % 150.60/150.90 (define @t158 () (= @t137 @t147)) % 150.60/150.90 (define @t159 () (or @t151 @t158)) % 150.60/150.90 (define @t160 () (_ @t49 @t142 @t137)) % 150.60/150.90 (define @t161 () (not @t50)) % 150.60/150.90 (define @t162 () (not (not @t160))) % 150.60/150.90 (assume @p1 @t19) % 150.60/150.90 (assume @p2 @t25) % 150.60/150.90 (assume @p3 @t30) % 150.60/150.90 (assume @p4 @t38) % 150.60/150.90 (assume @p5 @t46) % 150.60/150.90 (assume @p6 true) % 150.60/150.90 (step @p7 :rule evaluate :args ((= true false))) % 150.60/150.90 ; WARNING: add trust step for TRUST % 150.60/150.90 ; trust TRUST PREPROCESS_HO_ELIM % 150.60/150.90 (step @p8 :rule trust :premises () :args ((= (not (=> @t77 (=> @t67 (=> @t64 @t61)))) (not (=> (forall @t59 (or (not (_ @t49 (_ @t48 @t47 @t58) @t1)) (not (forall @t13 (or (not (_ @t49 @t57 @t1)) (not (forall @t8 (or @t56 (not (_ @t49 @t54 @t1)))))))))) (=> (forall @t23 (_ @t49 @t54 (_ @t53 (_ @t52 @t51 @t2) @t20))) (=> @t55 @t50))))))) % 150.60/150.90 (step @p9 :rule bool-impl-true2 :args (@t61)) % 150.60/150.90 (step @p10 :rule refl :args (@t64)) % 150.60/150.90 (step @p11 :rule cong :premises (@p10 @p9) :args (@t78)) % 150.60/150.90 (step @p12 :rule refl :args (@t67)) % 150.60/150.90 (step @p13 :rule cong :premises (@p12 @p11) :args (@t79)) % 150.60/150.90 (step @p14 :rule refl :args (@t77)) % 150.60/150.90 (step @p15 :rule cong :premises (@p14 @p13) :args (@t80)) % 150.60/150.90 (step @p16 :rule cong :premises (@p15) :args ((not @t80))) % 150.60/150.90 (step @p17 :rule refl :args (@t61)) % 150.60/150.90 (step @p18 :rule bool-eq-true :args (tptp.in__Cong)) % 150.60/150.90 (step @p19 :rule symm :premises (@p18)) % 150.60/150.90 (step @p20 :rule quant-unused-vars :args ((= (forall @t82 true) true))) % 150.60/150.90 (step @p21 :rule evaluate :args ((or false true))) % 150.60/150.90 (step @p22 :rule eq-refl :args (@t83)) % 150.60/150.90 (step @p23 :rule evaluate :args ((not true))) % 150.60/150.90 (step @p24 :rule eq-refl :args (@t5)) % 150.60/150.90 (step @p25 :rule cong :premises (@p24) :args (@t84)) % 150.60/150.90 (step @p26 :rule trans :premises (@p25 @p23)) % 150.60/150.90 (step @p27 :rule nary_cong :premises (@p26 @p22) :args (@t85)) % 150.60/150.90 (step @p28 :rule trans :premises (@p27 @p21)) % 150.60/150.90 (step @p29 :rule cong :premises (@p28) :args ((forall @t82 @t85))) % 150.60/150.90 (step @p30 :rule trans :premises (@p29 @p20)) % 150.60/150.90 (step @p31 :rule quant-var-elim-eq :args ((= (forall @t17 @t88) @t85))) % 150.60/150.90 (step @p32 :rule aci_norm :args ((= @t89 @t88))) % 150.60/150.90 (step @p33 :rule cong :premises (@p32) :args (@t90)) % 150.60/150.90 (step @p34 :rule trans :premises (@p33 @p31)) % 150.60/150.90 (step @p35 :rule cong :premises (@p34) :args (@t91)) % 150.60/150.90 (step @p36 :rule quant-merge-prenex :args ((= @t91 @t92))) % 150.60/150.90 (step @p37 :rule symm :premises (@p36)) % 150.60/150.90 (step @p38 :rule quant_var_reordering :args ((= @t93 @t92))) % 150.60/150.90 (step @p39 :rule trans :premises (@p38 @p37 @p35)) % 150.60/150.90 (step @p40 :rule trans :premises (@p39 @p30)) % 150.60/150.90 (step @p41 :rule quant-merge-prenex :args ((= (forall @t36 @t95) @t93))) % 150.60/150.90 (step @p42 :rule alpha_equiv :args (@t96 (@list @t81) (@list @t20))) % 150.60/150.90 (step @p43 :rule refl :args (@t87)) % 150.60/150.90 (step @p44 :rule nary_cong :premises (@p43 @p42) :args (@t97)) % 150.60/150.90 (step @p45 :rule quant-miniscope-or :args ((= @t95 @t97))) % 150.60/150.90 (step @p46 :rule trans :premises (@p45 @p44)) % 150.60/150.90 (step @p47 :rule symm :premises (@p46)) % 150.60/150.90 (step @p48 :rule cong :premises (@p47) :args ((forall @t36 (or @t87 @t102)))) % 150.60/150.90 (step @p49 :rule trans :premises (@p48 @p41)) % 150.60/150.90 (step @p50 :rule trans :premises (@p49 @p40)) % 150.60/150.90 (step @p51 :rule bool-impl-elim :args (@t34 @t102)) % 150.60/150.90 (step @p52 :rule cong :premises (@p51) :args ((forall @t36 (=> @t34 @t102)))) % 150.60/150.90 (step @p53 :rule trans :premises (@p52 @p50)) % 150.60/150.90 (step @p54 :rule aci_norm :args ((= (or false @t100) @t100))) % 150.60/150.90 (step @p55 :rule eq-symm :args (@t98 @t99)) % 150.60/150.90 (step @p56 :rule eq-refl :args (@t20)) % 150.60/150.90 (step @p57 :rule cong :premises (@p56) :args (@t103)) % 150.60/150.90 (step @p58 :rule trans :premises (@p57 @p23)) % 150.60/150.90 (step @p59 :rule nary_cong :premises (@p58 @p55) :args (@t104)) % 150.60/150.90 (step @p60 :rule trans :premises (@p59 @p54)) % 150.60/150.90 (step @p61 :rule cong :premises (@p60) :args ((forall @t101 @t104))) % 150.60/150.90 (step @p62 :rule quant-var-elim-eq :args ((= (forall @t8 @t107) @t104))) % 150.60/150.90 (step @p63 :rule aci_norm :args ((= @t108 @t107))) % 150.60/150.90 (step @p64 :rule cong :premises (@p63) :args (@t109)) % 150.60/150.90 (step @p65 :rule trans :premises (@p64 @p62)) % 150.60/150.90 (step @p66 :rule cong :premises (@p65) :args (@t110)) % 150.60/150.90 (step @p67 :rule quant-merge-prenex :args ((= @t110 @t111))) % 150.60/150.90 (step @p68 :rule symm :premises (@p67)) % 150.60/150.90 (step @p69 :rule quant_var_reordering :args ((= (forall @t23 @t108) @t111))) % 150.60/150.90 (step @p70 :rule trans :premises (@p69 @p68 @p66)) % 150.60/150.90 (step @p71 :rule trans :premises (@p70 @p61)) % 150.60/150.90 (step @p72 :rule refl :args (@t99)) % 150.60/150.90 (step @p73 :rule refl :args (@t31)) % 150.60/150.90 (step @p74 :rule cong :premises (@p73 @p72) :args ((= @t31 @t99))) % 150.60/150.90 (step @p75 :rule symm :premises (@p74)) % 150.60/150.90 (step @p76 :rule eq_resolve :premises (@p73 @p75)) % 150.60/150.90 (step @p77 :rule refl :args (@t68)) % 150.60/150.90 (step @p78 :rule refl :args (@t4)) % 150.60/150.90 (step @p79 :rule cong :premises (@p78 @p77) :args ((= @t4 @t68))) % 150.60/150.90 (step @p80 :rule symm :premises (@p79)) % 150.60/150.90 (step @p81 :rule eq_resolve :premises (@p78 @p80)) % 150.60/150.90 (step @p82 :rule cong :premises (@p81 @p76) :args (@t32)) % 150.60/150.90 (step @p83 :rule refl :args (@t106)) % 150.60/150.90 (step @p84 :rule nary_cong :premises (@p83 @p82) :args (@t112)) % 150.60/150.90 (step @p85 :rule cong :premises (@p84) :args ((forall @t23 @t112))) % 150.60/150.90 (step @p86 :rule trans :premises (@p85 @p71)) % 150.60/150.90 (step @p87 :rule bool-impl-elim :args (@t26 @t32)) % 150.60/150.90 (step @p88 :rule cong :premises (@p87) :args (@t33)) % 150.60/150.90 (step @p89 :rule trans :premises (@p88 @p86)) % 150.60/150.90 (step @p90 :rule refl :args (@t34)) % 150.60/150.90 (step @p91 :rule cong :premises (@p90 @p89) :args (@t35)) % 150.60/150.90 (step @p92 :rule cong :premises (@p91) :args (@t37)) % 150.60/150.90 (step @p93 :rule trans :premises (@p92 @p53)) % 150.60/150.90 (step @p94 :rule refl :args (tptp.in__Cong)) % 150.60/150.90 (step @p95 :rule cong :premises (@p94 @p93) :args (@t38)) % 150.60/150.90 (step @p96 :rule trans :premises (@p95 @p18)) % 150.60/150.90 (step @p97 :rule eq_resolve :premises (@p4 @p96)) % 150.60/150.90 (step @p98 :rule eq_resolve :premises (@p97 @p19)) % 150.60/150.90 (step @p99 :rule cong :premises (@p98 @p17) :args (@t113)) % 150.60/150.90 (step @p100 :rule refl :args (@t26)) % 150.60/150.90 (step @p101 :rule refl :args ((tptp.in @t2 @t27))) % 150.60/150.90 (step @p102 :rule refl :args (@t62)) % 150.60/150.90 (step @p103 :rule refl :args (@t2)) % 150.60/150.90 (step @p104 :rule cong :premises (@p103 @p102) :args (@t63)) % 150.60/150.90 (step @p105 :rule trans :premises (@p104 @p101)) % 150.60/150.90 (step @p106 :rule refl :args (@t3)) % 150.60/150.90 (step @p107 :rule ho_cong :premises (@p106 @p102)) % 150.60/150.90 (step @p108 :rule cong :premises (@p107 @p105) :args ((= (_ @t3 @t62) @t63))) % 150.60/150.90 (step @p109 :rule symm :premises (@p108)) % 150.60/150.90 (step @p110 :rule refl :args (@t28)) % 150.60/150.90 (step @p111 :rule eq_resolve :premises (@p110 @p109)) % 150.60/150.90 (step @p112 :rule refl :args (@t27)) % 150.60/150.90 (step @p113 :rule cong :premises (@p112 @p102) :args ((= @t27 @t62))) % 150.60/150.90 (step @p114 :rule symm :premises (@p113)) % 150.60/150.90 (step @p115 :rule eq_resolve :premises (@p112 @p114)) % 150.60/150.90 (step @p116 :rule ho_cong :premises (@p106 @p115)) % 150.60/150.90 (step @p117 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trans :premises (@p130 @p128)) % 150.60/150.90 (step @p132 :rule ho_cong :premises (@p106 @p129)) % 150.60/150.90 (step @p133 :rule cong :premises (@p132 @p131) :args ((= (_ @t3 @t65) @t66))) % 150.60/150.90 (step @p134 :rule symm :premises (@p133)) % 150.60/150.90 (step @p135 :rule refl :args (@t22)) % 150.60/150.90 (step @p136 :rule eq_resolve :premises (@p135 @p134)) % 150.60/150.90 (step @p137 :rule refl :args (@t21)) % 150.60/150.90 (step @p138 :rule cong :premises (@p137 @p129) :args ((= @t21 @t65))) % 150.60/150.90 (step @p139 :rule symm :premises (@p138)) % 150.60/150.90 (step @p140 :rule eq_resolve :premises (@p137 @p139)) % 150.60/150.90 (step @p141 :rule ho_cong :premises (@p106 @p140)) % 150.60/150.90 (step @p142 :rule trans :premises (@p141 @p136)) % 150.60/150.90 (step @p143 :rule cong :premises (@p142) :args (@t24)) % 150.60/150.90 (step @p144 :rule refl :args (tptp.setadjoinIL)) % 150.60/150.90 (step @p145 :rule cong :premises (@p144 @p143) :args (@t25)) % 150.60/150.90 (step @p146 :rule eq_resolve :premises (@p2 @p145)) % 150.60/150.90 (step @p147 :rule cong :premises (@p146 @p127) :args (@t117)) % 150.60/150.90 (step @p148 :rule quant-merge-prenex :args ((= (forall @t17 @t119) @t77))) % 150.60/150.90 (step @p149 :rule refl :args (@t74)) % 150.60/150.90 (step @p150 :rule alpha_equiv :args (@t120 (@list @t58) (@list @t2))) % 150.60/150.90 (step @p151 :rule nary_cong :premises (@p150 @p149) :args (@t121)) % 150.60/150.90 (step @p152 :rule quant-miniscope-or :args ((= @t119 @t121))) % 150.60/150.90 (step @p153 :rule trans :premises (@p152 @p151)) % 150.60/150.90 (step @p154 :rule symm :premises (@p153)) % 150.60/150.90 (step @p155 :rule cong :premises (@p154) :args ((forall @t17 (or @t122 @t74)))) % 150.60/150.90 (step @p156 :rule trans :premises (@p155 @p148)) % 150.60/150.90 (step @p157 :rule bool-double-not-elim :args (@t122)) % 150.60/150.90 (step @p158 :rule nary_cong :premises (@p157 @p149) :args ((or (not @t123) @t74))) % 150.60/150.90 (step @p159 :rule bool-impl-elim :args (@t123 @t74)) % 150.60/150.90 (step @p160 :rule trans :premises (@p159 @p158)) % 150.60/150.90 (step @p161 :rule cong :premises (@p160) :args ((forall @t17 (=> @t123 @t74)))) % 150.60/150.90 (step @p162 :rule trans :premises (@p161 @p156)) % 150.60/150.90 (step @p163 :rule refl :args (@t72)) % 150.60/150.90 (step @p164 :rule refl :args (@t73)) % 150.60/150.90 (step @p165 :rule refl :args (@t11)) % 150.60/150.90 (step @p166 :rule cong :premises (@p165 @p164) :args ((= @t11 @t73))) % 150.60/150.90 (step @p167 :rule symm :premises (@p166)) % 150.60/150.90 (step @p168 :rule eq_resolve :premises (@p165 @p167)) % 150.60/150.90 (step @p169 :rule cong :premises (@p168) :args (@t124)) % 150.60/150.90 (step @p170 :rule nary_cong :premises (@p169 @p163) :args (@t125)) % 150.60/150.90 (step @p171 :rule cong :premises (@p170) :args ((forall @t13 @t125))) % 150.60/150.90 (step @p172 :rule bool-and-de-morgan :args (@t11 @t71 true)) % 150.60/150.90 (step @p173 :rule cong :premises (@p172) :args (@t127)) % 150.60/150.90 (step @p174 :rule trans :premises (@p173 @p171)) % 150.60/150.90 (step @p175 :rule cong :premises (@p174) :args (@t128)) % 150.60/150.90 (step @p176 :rule exists-elim :args ((= (exists @t13 @t126) @t128))) % 150.60/150.90 (step @p177 :rule trans :premises (@p176 @p175)) % 150.60/150.90 (step @p178 :rule bool-double-not-elim :args (@t71)) % 150.60/150.90 (step @p179 :rule cong :premises (@p81) :args (@t129)) % 150.60/150.90 (step @p180 :rule refl :args (@t70)) % 150.60/150.90 (step @p181 :rule refl :args (@t6)) % 150.60/150.90 (step @p182 :rule cong :premises (@p181 @p180) :args ((= @t6 @t70))) % 150.60/150.90 (step @p183 :rule symm :premises (@p182)) % 150.60/150.90 (step @p184 :rule eq_resolve :premises (@p181 @p183)) % 150.60/150.90 (step @p185 :rule cong :premises (@p184) :args (@t130)) % 150.60/150.90 (step @p186 :rule nary_cong :premises (@p185 @p179) :args (@t131)) % 150.60/150.90 (step @p187 :rule cong :premises (@p186) :args ((forall @t8 @t131))) % 150.60/150.90 (step @p188 :rule bool-and-de-morgan :args (@t6 @t4 true)) % 150.60/150.90 (step @p189 :rule cong :premises (@p188) :args (@t132)) % 150.60/150.90 (step @p190 :rule trans :premises (@p189 @p187)) % 150.60/150.90 (step @p191 :rule cong :premises (@p190) :args (@t133)) % 150.60/150.90 (step @p192 :rule exists-elim :args ((= @t9 @t133))) % 150.60/150.90 (step @p193 :rule trans :premises (@p192 @p191)) % 150.60/150.90 (step @p194 :rule cong :premises (@p193) :args (@t10)) % 150.60/150.90 (step @p195 :rule trans :premises (@p194 @p178)) % 150.60/150.90 (step @p196 :rule refl :args (@t11)) % 150.60/150.90 (step @p197 :rule nary_cong :premises (@p196 @p195) :args (@t12)) % 150.60/150.90 (step @p198 :rule cong :premises (@p197) :args (@t14)) % 150.60/150.90 (step @p199 :rule trans :premises (@p198 @p177)) % 150.60/150.90 (step @p200 :rule cong :premises (@p179) :args (@t134)) % 150.60/150.90 (step @p201 :rule cong :premises (@p200) :args (@t135)) % 150.60/150.90 (step @p202 :rule exists-elim :args ((= @t15 @t135))) % 150.60/150.90 (step @p203 :rule trans :premises (@p202 @p201)) % 150.60/150.90 (step @p204 :rule cong :premises (@p203 @p199) :args (@t16)) % 150.60/150.90 (step @p205 :rule cong :premises (@p204) :args (@t18)) % 150.60/150.90 (step @p206 :rule trans :premises (@p205 @p162)) % 150.60/150.90 (step @p207 :rule refl :args (tptp.foundationAx)) % 150.60/150.90 (step @p208 :rule cong :premises (@p207 @p206) :args (@t19)) % 150.60/150.90 (step @p209 :rule eq_resolve :premises (@p1 @p208)) % 150.60/150.90 (step @p210 :rule cong :premises (@p209 @p147) :args (@t136)) % 150.60/150.90 (step @p211 :rule cong :premises (@p210) :args ((not @t136))) % 150.60/150.90 (step @p212 :rule trans :premises (@p211 @p16)) % 150.60/150.90 (step @p213 :rule refl :args (@t60)) % 150.60/150.90 (step @p214 :rule refl :args (@t39)) % 150.60/150.90 (step @p215 :rule cong :premises (@p214 @p213) :args ((= @t39 @t60))) % 150.60/150.90 (step @p216 :rule symm :premises (@p215)) % 150.60/150.90 (step @p217 :rule eq_resolve :premises (@p214 @p216)) % 150.60/150.90 (step @p218 :rule cong :premises (@p217) :args (@t40)) % 150.60/150.90 (step @p219 :rule cong :premises (@p218) :args (@t41)) % 150.60/150.90 (step @p220 :rule cong :premises (@p94 @p219) :args (@t42)) % 150.60/150.90 (step @p221 :rule cong :premises (@p124 @p220) :args (@t43)) % 150.60/150.90 (step @p222 :rule cong :premises (@p144 @p221) :args (@t44)) % 150.60/150.90 (step @p223 :rule cong :premises (@p207 @p222) :args (@t45)) % 150.60/150.90 (step @p224 :rule cong :premises (@p223) :args (@t46)) % 150.60/150.90 (step @p225 :rule trans :premises (@p224 @p212 @p8)) % 150.60/150.90 (step @p226 :rule eq_resolve :premises (@p5 @p225)) % 150.60/150.90 (step @p227 :rule not_implies_elim1 :premises (@p226)) % 150.60/150.90 (step @p228 :rule instantiate :premises (@p227) :args ((@list @t138 @t137))) % 150.60/150.90 (step @p229 :rule not_implies_elim2 :premises (@p226)) % 150.60/150.90 (step @p230 :rule not_implies_elim1 :premises (@p229)) % 150.60/150.90 (step @p231 :rule instantiate :premises (@p230) :args ((@list @t137 tptp.emptyset))) % 150.60/150.90 (step @p232 :rule cnf_or_pos :args (@t145)) % 150.60/150.90 (step @p233 :rule reordering :premises (@p232) :args ((or @t144 @t141 (not @t145)))) % 150.60/150.90 (step @p234 :rule chain_m_resolution :premises (@p233 @p231 @p228) :args (@t141 @t146 (@list @t143 @t145))) % 150.60/150.90 (step @p235 :rule skolemize :premises (@p234)) % 150.60/150.90 (step @p236 :rule bool-double-not-elim :args (@t148)) % 150.60/150.90 (step @p237 :rule refl :args (@t152)) % 150.60/150.90 (step @p238 :rule nary_cong :premises (@p237 @p236) :args ((or @t152 (not @t149)))) % 150.60/150.90 (step @p239 :rule cnf_or_neg :args (@t152 1)) % 150.60/150.91 (step @p240 :rule eq_resolve :premises (@p239 @p238)) % 150.60/150.91 (step @p241 :rule reordering :premises (@p240) :args ((or @t148 @t152))) % 150.60/150.91 (step @p242 :rule chain_m_resolution :premises (@p241 @p235) :args (@t148 @t153 @t154)) % 150.60/150.91 (step @p243 :rule instantiate :premises (@p242) :args ((@list @t137))) % 150.60/150.91 (step @p244 :rule cnf_or_pos :args (@t156)) % 150.60/150.91 (step @p245 :rule reordering :premises (@p244) :args ((or @t144 @t155 (not @t156)))) % 150.60/150.91 (step @p246 :rule chain_m_resolution :premises (@p245 @p231 @p243) :args (@t155 @t146 (@list @t143 @t156))) % 150.60/150.91 (step @p247 :rule false_intro :premises (@p246)) % 150.60/150.91 (step @p248 :rule not_implies_elim2 :premises (@p229)) % 150.60/150.91 (step @p249 :rule not_implies_elim1 :premises (@p248)) % 150.60/150.91 (step @p250 :rule eq-symm :args (@t147 @t137)) % 150.60/150.91 (step @p251 :rule refl :args (@t151)) % 150.60/150.91 (step @p252 :rule nary_cong :premises (@p251 @p250) :args (@t157)) % 150.60/150.91 (step @p253 :rule refl :args (@t55)) % 150.60/150.91 (step @p254 :rule cong :premises (@p253 @p252) :args ((=> @t55 @t157))) % 150.60/150.91 (assume-push @p292 @t55) % 150.60/150.91 (step @p256 :rule instantiate :premises (@p249) :args ((@list @t147 @t137))) % 150.60/150.91 (step-pop @p293 :rule scope :premises (@p256)) % 150.60/150.91 (step @p257 :rule process_scope :premises (@p293) :args (@t157)) % 150.60/150.91 (step @p259 :rule eq_resolve :premises (@p257 @p254)) % 150.60/150.91 (step @p260 :rule implies_elim :premises (@p259)) % 150.60/150.91 (step @p261 :rule chain_m_resolution :premises (@p260 @p249) :args (@t159 (@list false) (@list @t55))) % 150.60/150.91 (step @p262 :rule bool-double-not-elim :args (@t150)) % 150.60/150.91 (step @p263 :rule nary_cong :premises (@p237 @p262) :args ((or @t152 (not @t151)))) % 150.60/150.91 (step @p264 :rule cnf_or_neg :args (@t152 0)) % 150.60/150.91 (step @p265 :rule eq_resolve :premises (@p264 @p263)) % 150.60/150.91 (step @p266 :rule reordering :premises (@p265) :args ((or @t150 @t152))) % 150.60/150.91 (step @p267 :rule chain_m_resolution :premises (@p266 @p235) :args (@t150 @t153 @t154)) % 150.60/150.91 (step @p268 :rule cnf_or_pos :args (@t159)) % 150.60/150.91 (step @p269 :rule reordering :premises (@p268) :args ((or @t151 @t158 (not @t159)))) % 150.60/150.91 (step @p270 :rule chain_m_resolution :premises (@p269 @p267 @p261) :args (@t158 @t146 (@list @t150 @t159))) % 150.60/150.91 (step @p271 :rule refl :args (@t142)) % 150.60/150.91 (step @p272 :rule cong :premises (@p271 @p270) :args (@t160)) % 150.60/150.91 (step @p273 :rule not_implies_elim2 :premises (@p248)) % 150.60/150.91 (step @p274 :rule refl :args (@t160)) % 150.60/150.91 (step @p275 :rule bool-double-not-elim :args (@t50)) % 150.60/150.91 (step @p276 :rule nary_cong :premises (@p275 @p274) :args ((or (not @t161) @t160))) % 150.60/150.91 (step @p277 :rule bool-double-not-elim :args (@t160)) % 150.60/150.91 (step @p278 :rule refl :args (@t161)) % 150.60/150.91 (step @p279 :rule cong :premises (@p278 @p277) :args ((=> @t161 @t162))) % 150.60/150.91 (assume-push @p294 @t161) % 150.60/150.91 (step @p281 :rule skolemize :premises (@p273)) % 150.60/150.91 (step-pop @p295 :rule scope :premises (@p281)) % 150.60/150.91 (step @p282 :rule process_scope :premises (@p295) :args (@t162)) % 150.60/150.91 (step @p284 :rule eq_resolve :premises (@p282 @p279)) % 150.60/150.91 (step @p285 :rule implies_elim :premises (@p284)) % 150.60/150.91 (step @p286 :rule eq_resolve :premises (@p285 @p276)) % 150.60/150.91 (step @p287 :rule chain_m_resolution :premises (@p286 @p273) :args (@t160 @t153 (@list @t50))) % 150.60/150.91 (step @p288 :rule true_intro :premises (@p287)) % 150.60/150.91 (step @p289 :rule symm :premises (@p288)) % 150.60/150.91 (step @p290 :rule trans :premises (@p289 @p272 @p247)) % 150.60/150.91 (step @p291 false :rule eq_resolve :premises (@p290 @p7)) % 150.60/150.91 ) % 150.60/150.91 % SZS output end Proof % 150.60/150.91 % cvc5 exiting %------------------------------------------------------------------------------