%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET597^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n022.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 08:48:09 AM UTC 2026 % Result : Theorem 1.24s 1.44s % Output : Proof 1.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET597^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n022.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 16:04:08 EDT 2026 % 0.17/0.35 % CPUTime : % 0.29/0.50 %----Proving TH0 % 1.24/1.44 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 1.24/1.44 % SZS status Theorem % 1.24/1.44 % SZS output start Proof % 1.24/1.44 ( % 1.24/1.44 (declare-sort tptp.a 0) % 1.24/1.44 (define @t1 () (@var "Xx" tptp.a)) % 1.24/1.44 (define @t2 () (@var "V" (-> tptp.a Bool))) % 1.24/1.44 (define @t3 () (_ @t2 @t1)) % 1.24/1.44 (define @t4 () (@var "X" (-> tptp.a Bool))) % 1.24/1.44 (define @t5 () (_ @t4 @t1)) % 1.24/1.44 (define @t6 () (@list @t1)) % 1.24/1.44 (define @t7 () (forall @t6 (=> @t5 @t3))) % 1.24/1.44 (define @t8 () (@var "Z" (-> tptp.a Bool))) % 1.24/1.44 (define @t9 () (_ @t8 @t1)) % 1.24/1.44 (define @t10 () (forall @t6 (=> @t9 @t3))) % 1.24/1.44 (define @t11 () (@var "Y" (-> tptp.a Bool))) % 1.24/1.44 (define @t12 () (_ @t11 @t1)) % 1.24/1.44 (define @t13 () (forall @t6 (=> @t12 @t3))) % 1.24/1.44 (define @t14 () (and @t13 @t10)) % 1.24/1.44 (define @t15 () (=> @t14 @t7)) % 1.24/1.44 (define @t16 () (@list @t2)) % 1.24/1.44 (define @t17 () (forall @t16 @t15)) % 1.24/1.44 (define @t18 () (forall @t6 (=> @t9 @t5))) % 1.24/1.44 (define @t19 () (forall @t6 (=> @t12 @t5))) % 1.24/1.44 (define @t20 () (and @t19 @t18 @t17)) % 1.24/1.44 (define @t21 () (@var "Xz" tptp.a)) % 1.24/1.44 (define @t22 () (_ @t8 @t21)) % 1.24/1.44 (define @t23 () (_ @t11 @t21)) % 1.24/1.44 (define @t24 () (or @t23 @t22)) % 1.24/1.44 (define @t25 () (@list @t21)) % 1.24/1.44 (define @t26 () (lambda @t25 @t24)) % 1.24/1.44 (define @t27 () (= @t4 @t26)) % 1.24/1.44 (define @t28 () (= @t27 @t20)) % 1.24/1.44 (define @t29 () (@list @t4 @t11 @t8)) % 1.24/1.44 (define @t30 () (forall @t29 @t28)) % 1.24/1.44 (define @t31 () (not @t30)) % 1.24/1.44 (define @t32 () (_ @t8 @t21)) % 1.24/1.44 (define @t33 () (_ @t11 @t21)) % 1.24/1.44 (define @t34 () (= @t4 (lambda @t25 (or @t33 @t32)))) % 1.24/1.44 (define @t35 () (@var "BOUND_VARIABLE_7483" tptp.a)) % 1.24/1.44 (define @t36 () (_ @t2 @t35)) % 1.24/1.44 (define @t37 () (not (_ @t4 @t35))) % 1.24/1.44 (define @t38 () (_ @t2 @t1)) % 1.24/1.44 (define @t39 () (_ @t8 @t1)) % 1.24/1.44 (define @t40 () (not @t39)) % 1.24/1.44 (define @t41 () (forall @t6 (or @t40 @t38))) % 1.24/1.44 (define @t42 () (not @t41)) % 1.24/1.44 (define @t43 () (_ @t11 @t1)) % 1.24/1.44 (define @t44 () (not @t43)) % 1.24/1.44 (define @t45 () (forall @t6 (or @t44 @t38))) % 1.24/1.44 (define @t46 () (not @t45)) % 1.24/1.44 (define @t47 () (or @t46 @t42 @t37 @t36)) % 1.24/1.44 (define @t48 () (@list @t2 @t35)) % 1.24/1.44 (define @t49 () (_ @t4 @t1)) % 1.24/1.44 (define @t50 () (and (forall @t6 (or @t44 @t49)) (forall @t6 (or @t40 @t49)) (forall @t48 @t47))) % 1.24/1.44 (define @t51 () (= @t27 @t50)) % 1.24/1.44 (define @t52 () (or @t37 @t36)) % 1.24/1.44 (define @t53 () (or @t46 @t42 @t52)) % 1.24/1.44 (define @t54 () (forall @t48 @t53)) % 1.24/1.44 (define @t55 () (@list @t35)) % 1.24/1.44 (define @t56 () (forall @t55 @t53)) % 1.24/1.44 (define @t57 () (forall @t55 @t52)) % 1.24/1.44 (define @t58 () (or @t46 @t42 @t57)) % 1.24/1.44 (define @t59 () (forall @t6 (or (not @t49) @t38))) % 1.24/1.44 (define @t60 () (or @t46 @t42 @t59)) % 1.24/1.44 (define @t61 () (and @t45 @t41)) % 1.24/1.44 (define @t62 () (not @t5)) % 1.24/1.44 (define @t63 () (or @t62 @t3)) % 1.24/1.44 (define @t64 () (not @t9)) % 1.24/1.44 (define @t65 () (or @t64 @t3)) % 1.24/1.44 (define @t66 () (not @t12)) % 1.24/1.44 (define @t67 () (or @t66 @t3)) % 1.24/1.44 (define @t68 () (or @t64 @t5)) % 1.24/1.44 (define @t69 () (or @t66 @t5)) % 1.24/1.44 (define @t70 () (forall @t29 (= @t50 @t34))) % 1.24/1.44 (define @t71 () (@quantifiers_skolemize @t70 2)) % 1.24/1.44 (define @t72 () (@quantifiers_skolemize @t70 1)) % 1.24/1.44 (define @t73 () (or (_ @t72 @t21) (_ @t71 @t21))) % 1.24/1.44 (define @t74 () (lambda @t25 @t73)) % 1.24/1.44 (define @t75 () (@purify @t74)) % 1.24/1.44 (define @t76 () (@quantifiers_skolemize @t70 0)) % 1.24/1.44 (define @t77 () (= @t76 @t75)) % 1.24/1.44 (define @t78 () (not (_ @t71 @t1))) % 1.24/1.44 (define @t79 () (not (_ @t72 @t1))) % 1.24/1.44 (define @t80 () (forall @t48 (or (not (forall @t6 (or @t79 @t38))) (not (forall @t6 (or @t78 @t38))) (not (_ @t76 @t35)) @t36))) % 1.24/1.44 (define @t81 () (_ @t76 @t1)) % 1.24/1.44 (define @t82 () (forall @t6 (or @t78 @t81))) % 1.24/1.44 (define @t83 () (forall @t6 (or @t79 @t81))) % 1.24/1.44 (define @t84 () (and @t83 @t82 @t80)) % 1.24/1.44 (define @t85 () (= @t84 @t77)) % 1.24/1.44 (define @t86 () (not @t85)) % 1.24/1.44 (define @t87 () (not @t70)) % 1.24/1.44 (define @t88 () (= @t76 @t74)) % 1.24/1.44 (define @t89 () (= @t84 @t88)) % 1.24/1.44 (define @t90 () (not @t89)) % 1.24/1.44 (define @t91 () (@list true)) % 1.24/1.44 (define @t92 () (not @t84)) % 1.24/1.44 (define @t93 () (@quantifiers_skolemize @t80 1)) % 1.24/1.44 (define @t94 () (@quantifiers_skolemize @t80 0)) % 1.24/1.44 (define @t95 () (_ @t94 @t93)) % 1.24/1.44 (define @t96 () (_ @t76 @t93)) % 1.24/1.44 (define @t97 () (not @t96)) % 1.24/1.44 (define @t98 () (_ @t94 @t1)) % 1.24/1.44 (define @t99 () (forall @t6 (or @t78 @t98))) % 1.24/1.44 (define @t100 () (not @t99)) % 1.24/1.44 (define @t101 () (forall @t6 (or @t79 @t98))) % 1.24/1.44 (define @t102 () (not @t101)) % 1.24/1.44 (define @t103 () (or @t102 @t100 @t97 @t95)) % 1.24/1.44 (define @t104 () (not @t103)) % 1.24/1.44 (define @t105 () (not @t80)) % 1.24/1.44 (define @t106 () (_ @t71 @t93)) % 1.24/1.44 (define @t107 () (_ @t72 @t93)) % 1.24/1.44 (define @t108 () (or @t107 @t106)) % 1.24/1.44 (define @t109 () (_ @t76 @t93)) % 1.24/1.44 (define @t110 () (= @t109 @t108)) % 1.24/1.44 (define @t111 () (=> @t77 @t110)) % 1.24/1.44 (define @t112 () (@list @t93)) % 1.24/1.44 (define @t113 () (not @t107)) % 1.24/1.44 (define @t114 () (or @t113 @t95)) % 1.24/1.44 (define @t115 () (= @t96 @t108)) % 1.24/1.44 (define @t116 () (not @t106)) % 1.24/1.44 (define @t117 () (or @t116 @t95)) % 1.24/1.44 (define @t118 () (@quantifiers_skolemize @t82 0)) % 1.24/1.44 (define @t119 () (_ @t76 @t118)) % 1.24/1.44 (define @t120 () (_ @t71 @t118)) % 1.24/1.44 (define @t121 () (not @t120)) % 1.24/1.44 (define @t122 () (or @t121 @t119)) % 1.24/1.44 (define @t123 () (not @t122)) % 1.24/1.44 (define @t124 () (not @t82)) % 1.24/1.44 (define @t125 () (or (_ @t72 @t118) @t120)) % 1.24/1.44 (define @t126 () (_ @t75 @t21)) % 1.24/1.44 (define @t127 () (_ @t74 @t21)) % 1.24/1.44 (define @t128 () (= @t126 @t127)) % 1.24/1.44 (define @t129 () (forall @t25 @t128)) % 1.24/1.44 (define @t130 () (_ @t75 @t118)) % 1.24/1.44 (define @t131 () (= @t125 @t130)) % 1.24/1.44 (define @t132 () (not @t130)) % 1.24/1.44 (define @t133 () (not @t77)) % 1.24/1.44 (define @t134 () (not @t119)) % 1.24/1.44 (define @t135 () (and @t77 @t134)) % 1.24/1.44 (define @t136 () (@const 0 tptp.a)) % 1.24/1.44 (define @t137 () (@list @t136)) % 1.24/1.44 (define @t138 () (_ @t76 @t136)) % 1.24/1.44 (define @t139 () (_ @t71 @t136)) % 1.24/1.44 (define @t140 () (not @t139)) % 1.24/1.44 (define @t141 () (or @t140 @t138)) % 1.24/1.44 (define @t142 () (_ @t72 @t136)) % 1.24/1.44 (define @t143 () (not @t142)) % 1.24/1.44 (define @t144 () (or @t143 @t138)) % 1.24/1.44 (define @t145 () (not @t138)) % 1.24/1.44 (define @t146 () (or @t142 @t139 @t145)) % 1.24/1.44 (define @t147 () (not (= @t136 @t136))) % 1.24/1.44 (define @t148 () (@var "BOUND_VARIABLE_30340" tptp.a)) % 1.24/1.44 (define @t149 () (lambda (@list @t148) (not (= @t136 @t148)))) % 1.24/1.44 (define @t150 () (_ @t149 @t136)) % 1.24/1.44 (define @t151 () (or @t140 @t147)) % 1.24/1.44 (define @t152 () (not (= @t1 @t136))) % 1.24/1.44 (define @t153 () (or @t152 @t78 @t152)) % 1.24/1.44 (define @t154 () (or @t78 @t152)) % 1.24/1.44 (define @t155 () (not (= @t136 @t1))) % 1.24/1.44 (define @t156 () (_ @t149 @t1)) % 1.24/1.44 (define @t157 () (or @t78 @t156)) % 1.24/1.44 (define @t158 () (forall @t6 @t157)) % 1.24/1.44 (define @t159 () (not @t158)) % 1.24/1.44 (define @t160 () (or @t143 @t147)) % 1.24/1.44 (define @t161 () (or @t152 @t79 @t152)) % 1.24/1.44 (define @t162 () (or @t79 @t152)) % 1.24/1.44 (define @t163 () (or @t79 @t156)) % 1.24/1.44 (define @t164 () (forall @t6 @t163)) % 1.24/1.44 (define @t165 () (not @t164)) % 1.24/1.44 (define @t166 () (or @t165 @t159 @t145 @t150)) % 1.24/1.44 (define @t167 () (or @t142 @t139)) % 1.24/1.44 (define @t168 () (_ @t74 @t136)) % 1.24/1.44 (define @t169 () (_ @t75 @t136)) % 1.24/1.44 (define @t170 () (= @t138 @t169)) % 1.24/1.44 (define @t171 () (not @t170)) % 1.24/1.44 (define @t172 () (or @t77 @t171)) % 1.24/1.44 (define @t173 () (= @t138 @t167)) % 1.24/1.44 (define @t174 () (not @t146)) % 1.24/1.44 (define @t175 () (not @t83)) % 1.24/1.44 (define @t176 () (@list false false)) % 1.24/1.44 (define @t177 () (@list @t83)) % 1.24/1.44 (define @t178 () (@quantifiers_skolemize @t83 0)) % 1.24/1.44 (define @t179 () (_ @t76 @t178)) % 1.24/1.44 (define @t180 () (_ @t72 @t178)) % 1.24/1.44 (define @t181 () (not @t180)) % 1.24/1.44 (define @t182 () (or @t181 @t179)) % 1.24/1.44 (define @t183 () (not @t182)) % 1.24/1.44 (define @t184 () (not @t179)) % 1.24/1.44 (define @t185 () (@list @t182)) % 1.24/1.44 (define @t186 () (or @t180 (_ @t71 @t178))) % 1.24/1.44 (define @t187 () (_ @t75 @t178)) % 1.24/1.44 (define @t188 () (= @t186 @t187)) % 1.24/1.44 (define @t189 () (not @t187)) % 1.24/1.44 (define @t190 () (and @t187 @t77 @t184)) % 1.24/1.44 (assume @p1 @t31) % 1.24/1.44 (assume @p2 true) % 1.24/1.44 (step @p3 :rule eq-symm :args (@t34 @t50)) % 1.24/1.44 (step @p4 :rule cong :premises (@p3) :args ((forall @t29 (= @t34 @t50)))) % 1.24/1.44 (step @p5 :rule refl :args (@t50)) % 1.24/1.44 (step @p6 :rule refl :args (@t32)) % 1.24/1.44 (step @p7 :rule refl :args (@t22)) % 1.24/1.44 (step @p8 :rule cong :premises (@p7 @p6) :args ((= @t22 @t32))) % 1.24/1.44 (step @p9 :rule symm :premises (@p8)) % 1.24/1.44 (step @p10 :rule eq_resolve :premises (@p7 @p9)) % 1.24/1.44 (step @p11 :rule refl :args (@t33)) % 1.24/1.44 (step @p12 :rule refl :args (@t23)) % 1.24/1.44 (step @p13 :rule cong :premises (@p12 @p11) :args ((= @t23 @t33))) % 1.24/1.44 (step @p14 :rule symm :premises (@p13)) % 1.24/1.44 (step @p15 :rule eq_resolve :premises (@p12 @p14)) % 1.24/1.44 (step @p16 :rule nary_cong :premises (@p15 @p10) :args (@t24)) % 1.24/1.44 (step @p17 :rule cong :premises (@p16) :args (@t26)) % 1.24/1.44 (step @p18 :rule refl :args (@t4)) % 1.24/1.44 (step @p19 :rule cong :premises (@p18 @p17) :args (@t27)) % 1.24/1.44 (step @p20 :rule cong :premises (@p19 @p5) :args (@t51)) % 1.24/1.44 (step @p21 :rule cong :premises (@p20) :args ((forall @t29 @t51))) % 1.24/1.44 (step @p22 :rule trans :premises (@p21 @p4)) % 1.24/1.44 (step @p23 :rule aci_norm :args ((= @t53 @t47))) % 1.24/1.44 (step @p24 :rule cong :premises (@p23) :args (@t54)) % 1.24/1.44 (step @p25 :rule quant-merge-prenex :args ((= (forall @t16 @t56) @t54))) % 1.24/1.44 (step @p26 :rule alpha_equiv :args (@t57 (@list @t35) (@list @t1))) % 1.24/1.44 (step @p27 :rule refl :args (@t42)) % 1.24/1.44 (step @p28 :rule refl :args (@t46)) % 1.24/1.44 (step @p29 :rule nary_cong :premises (@p28 @p27 @p26) :args (@t58)) % 1.24/1.44 (step @p30 :rule quant-miniscope-or :args ((= @t56 @t58))) % 1.24/1.44 (step @p31 :rule trans :premises (@p30 @p29)) % 1.24/1.44 (step @p32 :rule symm :premises (@p31)) % 1.24/1.44 (step @p33 :rule cong :premises (@p32) :args ((forall @t16 @t60))) % 1.24/1.44 (step @p34 :rule trans :premises (@p33 @p25)) % 1.24/1.44 (step @p35 :rule trans :premises (@p34 @p24)) % 1.24/1.44 (step @p36 :rule aci_norm :args ((= (or (or @t46 @t42) @t59) @t60))) % 1.24/1.44 (step @p37 :rule refl :args (@t59)) % 1.24/1.44 (step @p38 :rule bool-and-de-morgan :args (@t45 @t41 true)) % 1.24/1.44 (step @p39 :rule nary_cong :premises (@p38 @p37) :args ((or (not @t61) @t59))) % 1.24/1.44 (step @p40 :rule trans :premises (@p39 @p36)) % 1.24/1.44 (step @p41 :rule bool-impl-elim :args (@t61 @t59)) % 1.24/1.44 (step @p42 :rule trans :premises (@p41 @p40)) % 1.24/1.44 (step @p43 :rule cong :premises (@p42) :args ((forall @t16 (=> @t61 @t59)))) % 1.24/1.44 (step @p44 :rule trans :premises (@p43 @p35)) % 1.24/1.44 (step @p45 :rule refl :args (@t38)) % 1.24/1.44 (step @p46 :rule refl :args (@t3)) % 1.24/1.44 (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t3 @t38))) % 1.24/1.44 (step @p48 :rule symm :premises (@p47)) % 1.24/1.44 (step @p49 :rule eq_resolve :premises (@p46 @p48)) % 1.24/1.44 (step @p50 :rule refl :args (@t49)) % 1.24/1.44 (step @p51 :rule refl :args (@t5)) % 1.24/1.44 (step @p52 :rule cong :premises (@p51 @p50) :args ((= @t5 @t49))) % 1.24/1.44 (step @p53 :rule symm :premises (@p52)) % 1.24/1.44 (step @p54 :rule eq_resolve :premises (@p51 @p53)) % 1.24/1.44 (step @p55 :rule cong :premises (@p54) :args (@t62)) % 1.24/1.44 (step @p56 :rule nary_cong :premises (@p55 @p49) :args (@t63)) % 1.24/1.44 (step @p57 :rule cong :premises (@p56) :args ((forall @t6 @t63))) % 1.24/1.44 (step @p58 :rule bool-impl-elim :args (@t5 @t3)) % 1.24/1.44 (step @p59 :rule cong :premises (@p58) :args (@t7)) % 1.24/1.44 (step @p60 :rule trans :premises (@p59 @p57)) % 1.24/1.44 (step @p61 :rule refl :args (@t39)) % 1.24/1.44 (step @p62 :rule refl :args (@t9)) % 1.24/1.44 (step @p63 :rule cong :premises (@p62 @p61) :args ((= @t9 @t39))) % 1.24/1.44 (step @p64 :rule symm :premises (@p63)) % 1.24/1.44 (step @p65 :rule eq_resolve :premises (@p62 @p64)) % 1.24/1.44 (step @p66 :rule cong :premises (@p65) :args (@t64)) % 1.24/1.44 (step @p67 :rule nary_cong :premises (@p66 @p49) :args (@t65)) % 1.24/1.44 (step @p68 :rule cong :premises (@p67) :args ((forall @t6 @t65))) % 1.24/1.44 (step @p69 :rule bool-impl-elim :args (@t9 @t3)) % 1.24/1.44 (step @p70 :rule cong :premises (@p69) :args (@t10)) % 1.24/1.44 (step @p71 :rule trans :premises (@p70 @p68)) % 1.24/1.44 (step @p72 :rule refl :args (@t43)) % 1.24/1.44 (step @p73 :rule refl :args (@t12)) % 1.24/1.44 (step @p74 :rule cong :premises (@p73 @p72) :args ((= @t12 @t43))) % 1.24/1.44 (step @p75 :rule symm :premises (@p74)) % 1.24/1.44 (step @p76 :rule eq_resolve :premises (@p73 @p75)) % 1.24/1.44 (step @p77 :rule cong :premises (@p76) :args (@t66)) % 1.24/1.44 (step @p78 :rule nary_cong :premises (@p77 @p49) :args (@t67)) % 1.24/1.44 (step @p79 :rule cong :premises (@p78) :args ((forall @t6 @t67))) % 1.24/1.44 (step @p80 :rule bool-impl-elim :args (@t12 @t3)) % 1.24/1.44 (step @p81 :rule cong :premises (@p80) :args (@t13)) % 1.24/1.44 (step @p82 :rule trans :premises (@p81 @p79)) % 1.24/1.44 (step @p83 :rule nary_cong :premises (@p82 @p71) :args (@t14)) % 1.24/1.44 (step @p84 :rule cong :premises (@p83 @p60) :args (@t15)) % 1.24/1.44 (step @p85 :rule cong :premises (@p84) :args (@t17)) % 1.24/1.44 (step @p86 :rule trans :premises (@p85 @p44)) % 1.24/1.44 (step @p87 :rule nary_cong :premises (@p66 @p54) :args (@t68)) % 1.24/1.44 (step @p88 :rule cong :premises (@p87) :args ((forall @t6 @t68))) % 1.24/1.44 (step @p89 :rule bool-impl-elim :args (@t9 @t5)) % 1.24/1.44 (step @p90 :rule cong :premises (@p89) :args (@t18)) % 1.24/1.44 (step @p91 :rule trans :premises (@p90 @p88)) % 1.24/1.44 (step @p92 :rule nary_cong :premises (@p77 @p54) :args (@t69)) % 1.24/1.44 (step @p93 :rule cong :premises (@p92) :args ((forall @t6 @t69))) % 1.24/1.44 (step @p94 :rule bool-impl-elim :args (@t12 @t5)) % 1.24/1.44 (step @p95 :rule cong :premises (@p94) :args (@t19)) % 1.24/1.44 (step @p96 :rule trans :premises (@p95 @p93)) % 1.24/1.44 (step 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aci_norm :args ((= @t162 @t161))) % 1.24/1.44 (step @p303 :rule cong :premises (@p302) :args ((forall @t6 @t162))) % 1.24/1.44 (step @p304 :rule trans :premises (@p303 @p301)) % 1.24/1.44 (step @p305 :rule trans :premises (@p304 @p300)) % 1.24/1.44 (step @p306 :rule refl :args (@t79)) % 1.24/1.44 (step @p307 :rule nary_cong :premises (@p306 @p289) :args (@t163)) % 1.24/1.44 (step @p308 :rule cong :premises (@p307) :args (@t164)) % 1.24/1.44 (step @p309 :rule trans :premises (@p308 @p305)) % 1.24/1.44 (step @p310 :rule cong :premises (@p309) :args (@t165)) % 1.24/1.44 (step @p311 :rule trans :premises (@p310 @p296)) % 1.24/1.44 (step @p312 :rule nary_cong :premises (@p311 @p295 @p275 @p274) :args (@t166)) % 1.24/1.44 (step @p313 :rule trans :premises (@p312 @p268)) % 1.24/1.44 (step @p314 :rule refl :args (@t80)) % 1.24/1.44 (step @p315 :rule cong :premises (@p314 @p313) :args ((=> @t80 @t166))) % 1.24/1.44 (assume-push @p440 @t80) % 1.24/1.44 (step @p317 :rule instantiate :premises (@p440) :args ((@list @t149 @t136))) % 1.24/1.44 (step-pop @p441 :rule scope :premises (@p317)) % 1.24/1.44 (step @p318 :rule process_scope :premises (@p441) :args (@t166)) % 1.24/1.44 (step @p320 :rule eq_resolve :premises (@p318 @p315)) % 1.24/1.44 (step @p321 :rule implies_elim :premises (@p320)) % 1.24/1.44 (step @p322 :rule cnf_equiv_neg2 :args (@t85)) % 1.24/1.44 (step @p323 :rule eq-refl :args (@t167)) % 1.24/1.44 (step @p324 :rule beta-reduce :args ((= @t168 @t167))) % 1.24/1.44 (step @p325 :rule refl :args (@t167)) % 1.24/1.44 (step @p326 :rule cong :premises (@p325 @p324) :args ((= @t167 @t168))) % 1.24/1.44 (step @p327 :rule trans :premises (@p326 @p323)) % 1.24/1.44 (step @p328 :rule eq-symm :args (@t168 @t167)) % 1.24/1.44 (step @p329 :rule trans :premises (@p328 @p327)) % 1.24/1.44 (step @p330 :rule refl :args (@t136)) % 1.24/1.44 (step @p331 :rule ho_cong :premises (@p108 @p330)) % 1.24/1.44 (step @p332 :rule cong :premises (@p331 @p325) :args ((= @t169 @t167))) % 1.24/1.44 (step @p333 :rule trans :premises (@p332 @p329)) % 1.24/1.44 (step @p334 :rule true_elim :premises (@p333)) % 1.24/1.44 (step @p335 :rule refl :args (@t138)) % 1.24/1.44 (step @p336 :rule cong :premises (@p335 @p334) :args (@t170)) % 1.24/1.44 (step @p337 :rule cong :premises (@p336) :args (@t171)) % 1.24/1.44 (step @p338 :rule nary_cong :premises (@p165 @p337) :args (@t172)) % 1.24/1.44 ; trust TRUST THEORY_LEMMA % 1.24/1.44 (step @p339 :rule trust :premises () :args (@t172)) % 1.24/1.44 (step @p340 :rule eq_resolve :premises (@p339 @p338)) % 1.24/1.44 (step @p341 :rule cnf_equiv_neg2 :args (@t173)) % 1.24/1.44 (step @p342 :rule cnf_or_neg :args (@t167 0)) % 1.24/1.44 (step @p343 :rule cnf_or_neg :args (@t167 1)) % 1.24/1.44 (step @p344 :rule cnf_or_pos :args (@t146)) % 1.24/1.44 (step @p345 :rule reordering :premises (@p344) :args ((or @t142 @t139 @t145 @t174))) % 1.24/1.44 (step @p346 :rule chain_m_resolution :premises (@p345 @p343 @p342 @p341) :args ((or @t173 @t145 @t174) (@list true true true) (@list @t139 @t142 @t167))) % 1.24/1.44 (step @p347 :rule cnf_equiv_neg1 :args (@t173)) % 1.24/1.44 (step @p348 :rule reordering :premises (@p347) :args ((or @t138 @t167 @t173))) % 1.24/1.44 (step @p349 :rule cnf_or_pos :args (@t144)) % 1.24/1.44 (step @p350 :rule reordering :premises (@p349) :args ((or @t138 @t143 (not @t144)))) % 1.24/1.44 (step @p351 :rule cnf_or_pos :args (@t141)) % 1.24/1.44 (step @p352 :rule reordering :premises (@p351) :args ((or @t138 @t140 (not @t141)))) % 1.24/1.44 (step @p353 :rule cnf_or_pos :args (@t167)) % 1.24/1.44 (step @p354 :rule reordering :premises (@p353) :args ((or @t142 @t139 (not @t167)))) % 1.24/1.44 (step @p355 :rule chain_m_resolution :premises (@p354 @p352 @p350 @p348 @p346 @p340 @p322 @p127 @p321 @p267 @p266 @p261) :args ((or @t175 @t124 @t105) (@list true true false true true true true false false false false) (@list @t139 @t142 @t167 @t138 @t173 @t77 @t85 @t146 @t84 @t144 @t141))) % 1.24/1.44 (step @p356 :rule chain_m_resolution :premises (@p355 @p256 @p188) :args (@t175 @t176 (@list @t82 @t80))) % 1.24/1.44 (step @p357 :rule cnf_and_pos :args (@t84 0)) % 1.24/1.44 (step @p358 :rule reordering :premises (@p357) :args ((or @t83 @t92))) % 1.24/1.44 (step @p359 :rule chain_m_resolution :premises (@p358 @p356) :args (@t92 @t91 @t177)) % 1.24/1.44 (step @p360 :rule chain_m_resolution :premises (@p140 @p359 @p127) :args (@t77 (@list true true) (@list @t84 @t85))) % 1.24/1.44 (step @p361 :rule refl :args (@t183)) % 1.24/1.44 (step @p362 :rule bool-double-not-elim :args (@t83)) % 1.24/1.44 (step @p363 :rule nary_cong :premises (@p362 @p361) :args ((or (not @t175) @t183))) % 1.24/1.44 (assume-push @p442 @t175) % 1.24/1.44 (step @p365 :rule skolemize :premises (@p442)) % 1.24/1.44 (step-pop @p443 :rule scope :premises (@p365)) % 1.24/1.44 (step @p366 :rule process_scope :premises (@p443) :args (@t183)) % 1.24/1.44 (step @p368 :rule implies_elim :premises (@p366)) % 1.24/1.44 (step @p369 :rule eq_resolve :premises (@p368 @p363)) % 1.24/1.44 (step @p370 :rule chain_m_resolution :premises (@p369 @p356) :args (@t183 @t91 @t177)) % 1.24/1.44 (step @p371 :rule cnf_or_neg :args (@t182 1)) % 1.24/1.44 (step @p372 :rule chain_m_resolution :premises (@p371 @p370) :args (@t184 @t91 @t185)) % 1.24/1.44 (step @p373 :rule instantiate :premises (@p226) :args ((@list @t178))) % 1.24/1.44 (step @p374 :rule bool-double-not-elim :args (@t180)) % 1.24/1.44 (step @p375 :rule refl :args (@t182)) % 1.24/1.44 (step @p376 :rule nary_cong :premises (@p375 @p374) :args ((or @t182 (not @t181)))) % 1.24/1.44 (step @p377 :rule cnf_or_neg :args (@t182 0)) % 1.24/1.44 (step @p378 :rule eq_resolve :premises (@p377 @p376)) % 1.24/1.44 (step @p379 :rule reordering :premises (@p378) :args ((or @t180 @t182))) % 1.24/1.44 (step @p380 :rule chain_m_resolution :premises (@p379 @p370) :args (@t180 @t91 @t185)) % 1.24/1.44 (step @p381 :rule cnf_or_neg :args (@t186 0)) % 1.24/1.44 (step @p382 :rule reordering :premises (@p381) :args ((or @t181 @t186))) % 1.24/1.44 (step @p383 :rule chain_m_resolution :premises (@p382 @p380) :args (@t186 (@list false) (@list @t180))) % 1.24/1.44 (step @p384 :rule cnf_equiv_pos1 :args (@t188)) % 1.24/1.44 (step @p385 :rule reordering :premises (@p384) :args ((or @t187 (not @t186) (not @t188)))) % 1.24/1.44 (step @p386 :rule chain_m_resolution :premises (@p385 @p383 @p373) :args (@t187 @t176 (@list @t186 @t188))) % 1.24/1.44 (step @p387 :rule refl :args (@t189)) % 1.24/1.44 (step @p388 :rule bool-double-not-elim :args (@t179)) % 1.24/1.44 (step @p389 :rule nary_cong :premises (@p232 @p388 @p387) :args ((or @t133 (not @t184) @t189))) % 1.24/1.44 (assume-push @p444 @t187) % 1.24/1.44 (assume-push @p445 @t77) % 1.24/1.44 (assume-push @p446 @t184) % 1.24/1.44 (step @p393 :rule evaluate :args ((= false true))) % 1.24/1.44 (step @p394 :rule true_intro :premises (@p444)) % 1.24/1.44 (step @p395 :rule refl :args (@t178)) % 1.24/1.44 (step @p396 :rule ho_cong :premises (@p445 @p395)) % 1.24/1.44 (step @p397 :rule false_intro :premises (@p446)) % 1.24/1.44 (step @p398 :rule symm :premises (@p397)) % 1.24/1.44 (step @p399 :rule trans :premises (@p398 @p396 @p394)) % 1.24/1.44 (step @p400 false :rule eq_resolve :premises (@p399 @p393)) % 1.24/1.44 (step-pop @p447 :rule scope :premises (@p400)) % 1.24/1.44 (step-pop @p448 :rule scope :premises (@p447)) % 1.24/1.44 (step-pop @p449 :rule scope :premises (@p448)) % 1.24/1.44 (step @p401 :rule process_scope :premises (@p449) :args (false)) % 1.24/1.44 (assume-push @p450 @t77) % 1.24/1.44 (assume-push @p451 @t184) % 1.24/1.44 (assume-push @p452 @t187) % 1.24/1.44 (step @p408 :rule and_intro :premises (@p452 @p450 @p451)) % 1.24/1.44 (step-pop @p453 :rule scope :premises (@p408)) % 1.24/1.44 (step-pop @p454 :rule scope :premises (@p453)) % 1.24/1.44 (step-pop @p455 :rule scope :premises (@p454)) % 1.24/1.44 (step @p409 :rule process_scope :premises (@p455) :args (@t190)) % 1.24/1.44 (step @p413 :rule implies_elim :premises (@p409)) % 1.24/1.44 (step @p414 :rule resolution :premises (@p413 @p401) :args (true @t190)) % 1.24/1.44 (step @p415 :rule not_and :premises (@p414)) % 1.24/1.44 (step @p416 :rule eq_resolve :premises (@p415 @p389)) % 1.24/1.44 (step @p417 false :rule chain_m_resolution :premises (@p416 @p386 @p372 @p360) :args (false (@list false true false) (@list @t187 @t179 @t77))) % 1.24/1.44 ) % 1.24/1.44 % SZS output end Proof % 1.24/1.44 % cvc5 exiting %------------------------------------------------------------------------------