%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : QUA006^1 : TPTP v9.2.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n018.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 08:44:40 AM UTC 2026 % Result : Theorem 224.53s 225.00s % Output : Proof 224.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : QUA006^1 : TPTP v9.2.1. Released v4.1.0. % 0.13/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n018.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 13:20:05 EDT 2026 % 0.18/0.35 % CPUTime : % 0.28/0.50 %----Proving TH0 % 224.53/225.00 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 224.53/225.00 --- 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... % 224.53/225.00 --- 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... % 224.53/225.00 --- Run --ho-elim --full-saturate-quant at 18s... % 224.53/225.00 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 224.53/225.00 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 12s... % 224.53/225.00 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 9s... % 224.53/225.00 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 6s... % 224.53/225.00 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 21s... % 224.53/225.00 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 18s... % 224.53/225.00 % SZS status Theorem % 224.53/225.00 % SZS output start Proof % 224.53/225.00 ( % 224.53/225.00 (declare-sort $$unsorted 0) % 224.53/225.00 (declare-const tptp.sup (-> (-> $$unsorted Bool) $$unsorted)) % 224.53/225.00 (declare-const tptp.multiplication (-> $$unsorted $$unsorted $$unsorted)) % 224.53/225.00 (declare-const tptp.one $$unsorted) % 224.53/225.00 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 224.53/225.00 (declare-const tptp.zero $$unsorted) % 224.53/225.00 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 224.53/225.00 (define tptp.union () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 224.53/225.00 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 224.53/225.00 (define tptp.supset () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "F" (-> (-> $$unsorted Bool) Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (and (_ _let_3 _let_2) (= (_ tptp.sup _let_2) _let_1)))))))) % 224.53/225.00 (define tptp.unionset () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "F" (-> (-> $$unsorted Bool) Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (and (_ _let_3 _let_2) (_ _let_2 _let_1)))))))) % 224.53/225.00 (define tptp.addition () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (lambda (@list _let_2 _let_1) (_ tptp.sup (_ (_ tptp.union (_ tptp.singleton _let_2)) (_ tptp.singleton _let_1))))))) % 224.53/225.00 (define tptp.crossmult () (let ((_let_1 (@var "Y1" $$unsorted))) (let ((_let_2 (@var "X1" $$unsorted))) (let ((_let_3 (@var "A" $$unsorted))) (let ((_let_4 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_5 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_5 _let_4 _let_3) (exists (@list _let_2 _let_1) (and (_ _let_5 _let_2) (_ _let_4 _let_1) (= _let_3 (_ (_ tptp.multiplication _let_2) _let_1))))))))))) % 224.53/225.00 (define @t1 () (= (_ tptp.sup tptp.emptyset) tptp.zero)) % 224.53/225.00 (define @t2 () (@var "X" $$unsorted)) % 224.53/225.00 (define @t3 () (_ tptp.singleton @t2)) % 224.53/225.00 (define @t4 () (= (_ tptp.sup @t3) @t2)) % 224.53/225.00 (define @t5 () (@list @t2)) % 224.53/225.00 (define @t6 () (forall @t5 @t4)) % 224.53/225.00 (define @t7 () (@var "X" (-> (-> $$unsorted Bool) Bool))) % 224.53/225.00 (define @t8 () (@var "X2" $$unsorted)) % 224.53/225.00 (define @t9 () (@var "X1" $$unsorted)) % 224.53/225.00 (define @t10 () (@var "Y" (-> $$unsorted Bool))) % 224.53/225.00 (define @t11 () (@var "X" (-> $$unsorted Bool))) % 224.53/225.00 (define @t12 () (_ tptp.sup @t10)) % 224.53/225.00 (define @t13 () (_ tptp.sup @t11)) % 224.53/225.00 (define @t14 () (_ (_ tptp.multiplication @t13) @t12)) % 224.53/225.00 (define @t15 () (= @t14 (_ tptp.sup (_ (_ tptp.crossmult @t11) @t10)))) % 224.53/225.00 (define @t16 () (@list @t11 @t10)) % 224.53/225.00 (define @t17 () (forall @t16 @t15)) % 224.53/225.00 (define @t18 () (_ (_ tptp.multiplication tptp.zero) @t9)) % 224.53/225.00 (define @t19 () (@list @t9)) % 224.53/225.00 (define @t20 () (forall @t19 (= @t18 tptp.zero))) % 224.53/225.00 (define @t21 () (not @t20)) % 224.53/225.00 (define @t22 () (lambda @t5 false)) % 224.53/225.00 (define @t23 () (@var "U" $$unsorted)) % 224.53/225.00 (define @t24 () (lambda (@list @t11 @t10 @t23) (or (_ @t11 @t23) (_ @t10 @t23)))) % 224.53/225.00 (define @t25 () (@list @t2 @t23)) % 224.53/225.00 (define @t26 () (lambda @t25 (= @t23 @t2))) % 224.53/225.00 (define @t27 () (@var "F" (-> (-> $$unsorted Bool) Bool))) % 224.53/225.00 (define @t28 () (_ @t27 @t10)) % 224.53/225.00 (define @t29 () (@list @t10)) % 224.53/225.00 (define @t30 () (@list @t27 @t2)) % 224.53/225.00 (define @t31 () (lambda @t30 (exists @t29 (and @t28 (= @t12 @t2))))) % 224.53/225.00 (define @t32 () (lambda @t30 (exists @t29 (and @t28 (_ @t10 @t2))))) % 224.53/225.00 (define @t33 () (@var "Y" $$unsorted)) % 224.53/225.00 (define @t34 () (lambda (@list @t2 @t33) (_ tptp.sup (_ (_ tptp.union @t3) (_ tptp.singleton @t33))))) % 224.53/225.00 (define @t35 () (@var "Y1" $$unsorted)) % 224.53/225.00 (define @t36 () (_ (_ tptp.multiplication @t9) @t35)) % 224.53/225.00 (define @t37 () (@var "A" $$unsorted)) % 224.53/225.00 (define @t38 () (= @t37 @t36)) % 224.53/225.00 (define @t39 () (_ @t10 @t35)) % 224.53/225.00 (define @t40 () (_ @t11 @t9)) % 224.53/225.00 (define @t41 () (and @t40 @t39 @t38)) % 224.53/225.00 (define @t42 () (@list @t9 @t35)) % 224.53/225.00 (define @t43 () (exists @t42 @t41)) % 224.53/225.00 (define @t44 () (@list @t11 @t10 @t37)) % 224.53/225.00 (define @t45 () (lambda @t44 @t43)) % 224.53/225.00 (define @t46 () (tptp.multiplication @t9 @t35)) % 224.53/225.00 (define @t47 () (= @t37 @t46)) % 224.53/225.00 (define @t48 () (not @t47)) % 224.53/225.00 (define @t49 () (@var "BOUND_VARIABLE_7928" $$unsorted)) % 224.53/225.00 (define @t50 () (lambda (@list @t49) false)) % 224.53/225.00 (define @t51 () (tptp.sup @t50)) % 224.53/225.00 (define @t52 () (forall @t19 (= @t51 (tptp.multiplication @t51 @t9)))) % 224.53/225.00 (define @t53 () (@quantifiers_skolemize @t52 0)) % 224.53/225.00 (define @t54 () (@list @t23)) % 224.53/225.00 (define @t55 () (lambda @t54 (= @t23 @t53))) % 224.53/225.00 (define @t56 () (@purify @t55)) % 224.53/225.00 (define @t57 () (not (_ @t56 @t35))) % 224.53/225.00 (define @t58 () (@purify @t50)) % 224.53/225.00 (define @t59 () (not (_ @t58 @t9))) % 224.53/225.00 (define @t60 () (or @t59 @t57 @t48)) % 224.53/225.00 (define @t61 () (forall @t42 @t60)) % 224.53/225.00 (define @t62 () (not @t61)) % 224.53/225.00 (define @t63 () (@list @t37)) % 224.53/225.00 (define @t64 () (lambda @t63 @t62)) % 224.53/225.00 (define @t65 () (@purify @t64)) % 224.53/225.00 (define @t66 () (_ @t65 @t37)) % 224.53/225.00 (define @t67 () (_ @t64 @t37)) % 224.53/225.00 (define @t68 () (= @t66 @t67)) % 224.53/225.00 (define @t69 () (forall @t63 @t68)) % 224.53/225.00 (define @t70 () (@const 0 $$unsorted)) % 224.53/225.00 (define @t71 () (not (= @t70 @t46))) % 224.53/225.00 (define @t72 () (or @t59 @t57 @t71)) % 224.53/225.00 (define @t73 () (forall @t42 @t72)) % 224.53/225.00 (define @t74 () (not @t73)) % 224.53/225.00 (define @t75 () (_ @t65 @t70)) % 224.53/225.00 (define @t76 () (forall @t63 (= @t62 @t66))) % 224.53/225.00 (define @t77 () (= @t74 @t75)) % 224.53/225.00 (define @t78 () (not (= @t46 @t70))) % 224.53/225.00 (define @t79 () (forall @t42 (or @t59 @t57 @t78))) % 224.53/225.00 (define @t80 () (not @t79)) % 224.53/225.00 (define @t81 () (= @t75 @t80)) % 224.53/225.00 (define @t82 () (@list false)) % 224.53/225.00 (define @t83 () (_ tptp.sup @t50)) % 224.53/225.00 (define @t84 () (tptp.multiplication @t83 @t9)) % 224.53/225.00 (define @t85 () (= @t83 @t84)) % 224.53/225.00 (define @t86 () (forall @t19 @t85)) % 224.53/225.00 (define @t87 () (@list @t49)) % 224.53/225.00 (define @t88 () (tptp.multiplication tptp.zero @t9)) % 224.53/225.00 (define @t89 () (= tptp.zero @t88)) % 224.53/225.00 (define @t90 () (forall @t19 @t89)) % 224.53/225.00 (define @t91 () (= tptp.zero @t18)) % 224.53/225.00 (define @t92 () (tptp.sup @t58)) % 224.53/225.00 (define @t93 () (= @t92 (tptp.multiplication @t92 @t53))) % 224.53/225.00 (define @t94 () (not @t93)) % 224.53/225.00 (define @t95 () (not @t52)) % 224.53/225.00 (define @t96 () (tptp.multiplication @t51 @t53)) % 224.53/225.00 (define @t97 () (= @t51 @t96)) % 224.53/225.00 (define @t98 () (not @t97)) % 224.53/225.00 (define @t99 () (@list true)) % 224.53/225.00 (define @t100 () (= @t2 @t23)) % 224.53/225.00 (define @t101 () (lambda @t54 @t100)) % 224.53/225.00 (define @t102 () (tptp.sup @t101)) % 224.53/225.00 (define @t103 () (_ tptp.sup @t101)) % 224.53/225.00 (define @t104 () (= @t2 @t103)) % 224.53/225.00 (define @t105 () (_ (lambda @t25 @t100) @t2)) % 224.53/225.00 (define @t106 () (= (_ tptp.sup @t105) @t2)) % 224.53/225.00 (define @t107 () (tptp.sup @t55)) % 224.53/225.00 (define @t108 () (= @t53 @t107)) % 224.53/225.00 (define @t109 () (forall @t5 (= @t2 @t102))) % 224.53/225.00 (define @t110 () (lambda @t54 (= @t53 @t23))) % 224.53/225.00 (define @t111 () (tptp.sup @t110)) % 224.53/225.00 (define @t112 () (= @t53 @t111)) % 224.53/225.00 (define @t113 () (tptp.sup @t56)) % 224.53/225.00 (define @t114 () (= @t53 @t113)) % 224.53/225.00 (define @t115 () (not @t38)) % 224.53/225.00 (define @t116 () (not @t39)) % 224.53/225.00 (define @t117 () (not @t40)) % 224.53/225.00 (define @t118 () (or @t117 @t116 @t115)) % 224.53/225.00 (define @t119 () (forall @t42 @t118)) % 224.53/225.00 (define @t120 () (lambda @t63 (not @t119))) % 224.53/225.00 (define @t121 () (_ @t10 @t35)) % 224.53/225.00 (define @t122 () (not @t121)) % 224.53/225.00 (define @t123 () (_ @t11 @t9)) % 224.53/225.00 (define @t124 () (not @t123)) % 224.53/225.00 (define @t125 () (or @t124 @t122 @t48)) % 224.53/225.00 (define @t126 () (forall @t42 @t125)) % 224.53/225.00 (define @t127 () (not @t126)) % 224.53/225.00 (define @t128 () (lambda @t63 @t127)) % 224.53/225.00 (define @t129 () (tptp.sup @t128)) % 224.53/225.00 (define @t130 () (_ tptp.sup @t128)) % 224.53/225.00 (define @t131 () (tptp.sup @t10)) % 224.53/225.00 (define @t132 () (tptp.sup @t11)) % 224.53/225.00 (define @t133 () (tptp.multiplication @t132 @t131)) % 224.53/225.00 (define @t134 () (= @t14 @t130)) % 224.53/225.00 (define @t135 () (lambda (@list @t10 @t37) @t127)) % 224.53/225.00 (define @t136 () (_ (lambda @t44 @t127) @t11)) % 224.53/225.00 (define @t137 () (= @t14 (_ tptp.sup (_ @t136 @t10)))) % 224.53/225.00 (define @t138 () (forall @t42 (not @t41))) % 224.53/225.00 (define @t139 () (not @t138)) % 224.53/225.00 (define @t140 () (_ @t55 @t35)) % 224.53/225.00 (define @t141 () (not @t140)) % 224.53/225.00 (define @t142 () (_ @t50 @t9)) % 224.53/225.00 (define @t143 () (not @t142)) % 224.53/225.00 (define @t144 () (or @t143 @t141 @t48)) % 224.53/225.00 (define @t145 () (forall @t42 @t144)) % 224.53/225.00 (define @t146 () (not @t145)) % 224.53/225.00 (define @t147 () (lambda @t63 @t146)) % 224.53/225.00 (define @t148 () (tptp.sup @t64)) % 224.53/225.00 (define @t149 () (tptp.multiplication @t92 @t113)) % 224.53/225.00 (define @t150 () (= @t149 @t148)) % 224.53/225.00 (define @t151 () (forall @t16 (= @t133 @t129))) % 224.53/225.00 (define @t152 () (= @t149 (tptp.sup @t65))) % 224.53/225.00 (define @t153 () (= @t58 @t65)) % 224.53/225.00 (define @t154 () (and @t114 @t152 @t153)) % 224.53/225.00 (define @t155 () (not @t153)) % 224.53/225.00 (define @t156 () (_ @t50 @t70)) % 224.53/225.00 (define @t157 () (_ @t58 @t70)) % 224.53/225.00 (define @t158 () (= @t157 @t75)) % 224.53/225.00 (define @t159 () (not @t158)) % 224.53/225.00 (define @t160 () (or @t153 @t159)) % 224.53/225.00 (define @t161 () (= @t35 @t53)) % 224.53/225.00 (define @t162 () (not @t161)) % 224.53/225.00 (define @t163 () (or @t143 @t141 @t71)) % 224.53/225.00 (define @t164 () (forall @t42 @t163)) % 224.53/225.00 (define @t165 () (not @t164)) % 224.53/225.00 (define @t166 () (_ @t147 @t70)) % 224.53/225.00 (define @t167 () (= @t156 @t166)) % 224.53/225.00 (define @t168 () (not @t167)) % 224.53/225.00 (define @t169 () (= @t50 @t147)) % 224.53/225.00 (define @t170 () (@quantifiers_skolemize @t79 1)) % 224.53/225.00 (define @t171 () (@quantifiers_skolemize @t79 0)) % 224.53/225.00 (define @t172 () (tptp.multiplication @t171 @t170)) % 224.53/225.00 (define @t173 () (not (= @t70 @t172))) % 224.53/225.00 (define @t174 () (= @t53 @t170)) % 224.53/225.00 (define @t175 () (_ @t55 @t170)) % 224.53/225.00 (define @t176 () (_ @t56 @t170)) % 224.53/225.00 (define @t177 () (not @t176)) % 224.53/225.00 (define @t178 () (_ @t50 @t171)) % 224.53/225.00 (define @t179 () (_ @t58 @t171)) % 224.53/225.00 (define @t180 () (not @t179)) % 224.53/225.00 (define @t181 () (or @t180 @t177 @t173)) % 224.53/225.00 (define @t182 () (not @t181)) % 224.53/225.00 (define @t183 () (not (= @t172 @t70))) % 224.53/225.00 (define @t184 () (or @t180 @t177 @t183)) % 224.53/225.00 (define @t185 () (not @t184)) % 224.53/225.00 (assume @p1 @t1) % 224.53/225.00 (assume @p2 @t6) % 224.53/225.00 (assume @p3 (forall (@list @t7) (= (_ tptp.sup (_ tptp.supset @t7)) (_ tptp.sup (_ tptp.unionset @t7))))) % 224.53/225.00 (assume @p4 (forall (@list @t9 @t8) (= (_ (_ tptp.leq @t9) @t8) (= (_ (_ tptp.addition @t9) @t8) @t8)))) % 224.53/225.00 (assume @p5 @t17) % 224.53/225.00 (assume @p6 (forall @t5 (= (_ (_ tptp.multiplication @t2) tptp.one) @t2))) % 224.53/225.00 (assume @p7 (forall @t5 (= (_ (_ tptp.multiplication tptp.one) @t2) @t2))) % 224.53/225.00 (assume @p8 @t21) % 224.53/225.00 (assume @p9 true) % 224.53/225.00 (step @p10 (= tptp.emptyset @t22) :rule refl :args (@t22)) % 224.53/225.00 (step @p11 (= tptp.union @t24) :rule refl :args (@t24)) % 224.53/225.00 (step @p12 (= tptp.singleton @t26) :rule refl :args (@t26)) % 224.53/225.00 (step @p13 (= tptp.supset @t31) :rule refl :args (@t31)) % 224.53/225.00 (step @p14 (= tptp.unionset @t32) :rule refl :args (@t32)) % 224.53/225.00 (step @p15 (= tptp.addition @t34) :rule refl :args (@t34)) % 224.53/225.00 (step @p16 (= tptp.crossmult @t45) :rule refl :args (@t45)) % 224.53/225.00 (step @p17 :rule eq-symm :args (@t66 @t62)) % 224.53/225.00 (step @p18 :rule beta-reduce :args ((= @t67 @t62))) % 224.53/225.00 (step @p19 :rule refl :args (@t66)) % 224.53/225.00 (step @p20 :rule cong :premises (@p19 @p18) :args (@t68)) % 224.53/225.00 (step @p21 :rule trans :premises (@p20 @p17)) % 224.53/225.00 (step @p22 :rule cong :premises (@p21) :args (@t69)) % 224.53/225.00 (step @p23 :rule quant-unused-vars :args ((= (forall @t63 true) true))) % 224.53/225.00 (step @p24 :rule eq-refl :args (@t67)) % 224.53/225.00 (step @p25 :rule cong :premises (@p24) :args ((forall @t63 (= @t67 @t67)))) % 224.53/225.00 (step @p26 :rule trans :premises (@p25 @p23)) % 224.53/225.00 (step @p27 :rule refl :args (@t67)) % 224.53/225.00 (step @p28 :rule refl :args (@t37)) % 224.53/225.00 (step @p29 :rule skolem_intro :args (@t65)) % 224.53/225.00 (step @p30 :rule ho_cong :premises (@p29 @p28)) % 224.53/225.00 (step @p31 :rule cong :premises (@p30 @p27) :args (@t68)) % 224.53/225.00 (step @p32 :rule cong :premises (@p31) :args (@t69)) % 224.53/225.00 (step @p33 :rule trans :premises (@p32 @p26)) % 224.53/225.00 (step @p34 :rule true_elim :premises (@p33)) % 224.53/225.00 (step @p35 :rule eq_resolve :premises (@p34 @p22)) % 224.53/225.00 (step @p36 :rule eq-symm :args (@t70 @t46)) % 224.53/225.00 (step @p37 :rule cong :premises (@p36) :args (@t71)) % 224.53/225.00 (step @p38 :rule refl :args (@t57)) % 224.53/225.00 (step @p39 :rule refl :args (@t59)) % 224.53/225.00 (step @p40 :rule nary_cong :premises (@p39 @p38 @p37) :args (@t72)) % 224.53/225.00 (step @p41 :rule cong :premises (@p40) :args (@t73)) % 224.53/225.00 (step @p42 :rule cong :premises (@p41) :args (@t74)) % 224.53/225.00 (step @p43 :rule refl :args (@t75)) % 224.53/225.00 (step @p44 :rule cong :premises (@p43 @p42) :args ((= @t75 @t74))) % 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224.53/225.00 (step @p278 :rule cong :premises (@p277) :args (@t57)) % 224.53/225.00 (step @p279 :rule ho_cong :premises (@p113 @p71)) % 224.53/225.00 (step @p280 :rule cong :premises (@p279) :args (@t59)) % 224.53/225.00 (step @p281 :rule nary_cong :premises (@p280 @p278 @p275) :args (@t60)) % 224.53/225.00 (step @p282 :rule cong :premises (@p281) :args (@t61)) % 224.53/225.00 (step @p283 :rule cong :premises (@p282) :args (@t62)) % 224.53/225.00 (step @p284 :rule cong :premises (@p283) :args (@t64)) % 224.53/225.00 (step @p285 :rule trans :premises (@p29 @p284)) % 224.53/225.00 (step @p286 :rule cong :premises (@p284 @p285) :args ((= @t64 @t65))) % 224.53/225.00 (step @p287 :rule trans :premises (@p286 @p274)) % 224.53/225.00 (step @p288 :rule true_elim :premises (@p287)) % 224.53/225.00 (step @p289 :rule cong :premises (@p288) :args (@t148)) % 224.53/225.00 (step @p290 :rule refl :args (@t149)) % 224.53/225.00 (step @p291 :rule cong :premises (@p290 @p289) :args (@t150)) % 224.53/225.00 (step @p292 :rule refl :args (@t151)) % 224.53/225.00 (step @p293 :rule cong :premises (@p292 @p291) :args ((=> @t151 @t150))) % 224.53/225.00 (assume-push @p453 @t151) % 224.53/225.00 (step @p295 :rule instantiate :premises (@p273) :args ((@list @t58 @t56))) % 224.53/225.00 (step-pop @p454 :rule scope :premises (@p295)) % 224.53/225.00 (step @p296 :rule process_scope :premises (@p454) :args (@t150)) % 224.53/225.00 (step @p298 :rule eq_resolve :premises (@p296 @p293)) % 224.53/225.00 (step @p299 :rule implies_elim :premises (@p298)) % 224.53/225.00 (step @p300 :rule chain_m_resolution :premises (@p299 @p273) :args (@t152 @t82 (@list @t151))) % 224.53/225.00 (assume-push @p455 @t114) % 224.53/225.00 (assume-push @p456 @t152) % 224.53/225.00 (assume-push @p457 @t153) % 224.53/225.00 (assume-push @p458 @t114) % 224.53/225.00 (assume-push @p459 @t152) % 224.53/225.00 (assume-push @p460 @t153) % 224.53/225.00 (step @p307 :rule symm :premises (@p178)) % 224.53/225.00 (step @p308 :rule refl :args (@t92)) % 224.53/225.00 (step @p309 :rule cong :premises (@p308 @p307) :args (@t149)) % 224.53/225.00 (step @p310 :rule symm :premises (@p300)) % 224.53/225.00 (step @p311 :rule cong :premises (@p457) :args (@t92)) % 224.53/225.00 (step @p312 :rule trans :premises (@p311 @p310 @p309)) % 224.53/225.00 (step-pop @p461 :rule scope :premises (@p312)) % 224.53/225.00 (step-pop @p462 :rule scope :premises (@p461)) % 224.53/225.00 (step-pop @p463 :rule scope :premises (@p462)) % 224.53/225.00 (step @p313 :rule process_scope :premises (@p463) :args (@t93)) % 224.53/225.00 (step @p317 :rule and_intro :premises (@p178 @p300 @p457)) % 224.53/225.00 (step @p318 :rule modus_ponens :premises (@p317 @p313)) % 224.53/225.00 (step-pop @p464 :rule scope :premises (@p318)) % 224.53/225.00 (step-pop @p465 :rule scope :premises (@p464)) % 224.53/225.00 (step-pop @p466 :rule scope :premises (@p465)) % 224.53/225.00 (step @p319 :rule process_scope :premises (@p466) :args (@t93)) % 224.53/225.00 (step @p323 :rule implies_elim :premises (@p319)) % 224.53/225.00 (step @p324 :rule cnf_and_neg :args (@t154)) % 224.53/225.00 (step @p325 :rule resolution :premises (@p324 @p323) :args (true @t154)) % 224.53/225.00 (step @p326 :rule reordering :premises (@p325) :args ((or @t93 (not @t114) (not @t152) @t155))) % 224.53/225.00 (step @p327 :rule chain_m_resolution :premises (@p326 @p300 @p178 @p130) :args (@t155 (@list false false true) (@list @t152 @t114 @t93))) % 224.53/225.00 (step @p328 :rule bool-double-not-elim :args (@t75)) % 224.53/225.00 (step @p329 :rule bool-eq-false :args (@t75)) % 224.53/225.00 (step @p330 :rule eq-symm :args (false @t75)) % 224.53/225.00 (step @p331 :rule trans :premises (@p330 @p329)) % 224.53/225.00 (step @p332 :rule evaluate :args ((not false))) % 224.53/225.00 (step @p333 :rule beta-reduce :args ((= @t156 false))) % 224.53/225.00 (step @p334 :rule cong :premises (@p333) :args ((not @t156))) % 224.53/225.00 (step @p335 :rule trans :premises (@p334 @p332)) % 224.53/225.00 (step @p336 :rule refl :args (@t70)) % 224.53/225.00 (step @p337 :rule ho_cong :premises (@p113 @p336)) % 224.53/225.00 (step @p338 :rule cong :premises (@p337) :args ((not @t157))) % 224.53/225.00 (step @p339 :rule bool-eq-false :args (@t157)) % 224.53/225.00 (step @p340 :rule trans :premises (@p339 @p338 @p335)) % 224.53/225.00 (step @p341 :rule true_elim :premises (@p340)) % 224.53/225.00 (step @p342 :rule cong :premises (@p341 @p43) :args (@t158)) % 224.53/225.00 (step @p343 :rule trans :premises (@p342 @p331)) % 224.53/225.00 (step @p344 :rule cong :premises (@p343) :args (@t159)) % 224.53/225.00 (step @p345 :rule trans :premises (@p344 @p328)) % 224.53/225.00 (step @p346 :rule refl :args (@t153)) % 224.53/225.00 (step @p347 :rule nary_cong :premises (@p346 @p345) :args (@t160)) % 224.53/225.00 (step @p348 :rule evaluate :args ((or true false))) % 224.53/225.00 (step @p349 :rule evaluate :args ((not true))) % 224.53/225.00 (step @p350 :rule evaluate :args ((= false false))) % 224.53/225.00 (step @p351 :rule quant-unused-vars :args ((= (forall @t42 true) true))) % 224.53/225.00 (step @p352 :rule absorb :args ((= (or true @t162 @t78) true))) % 224.53/225.00 (step @p353 :rule beta-reduce :args ((= @t140 @t161))) % 224.53/225.00 (step @p354 :rule cong :premises (@p353) :args (@t141)) % 224.53/225.00 (step @p355 :rule beta-reduce :args ((= @t142 false))) % 224.53/225.00 (step @p356 :rule cong :premises (@p355) :args (@t143)) % 224.53/225.00 (step @p357 :rule trans :premises (@p356 @p332)) % 224.53/225.00 (step @p358 :rule nary_cong :premises (@p357 @p354 @p37) :args (@t163)) % 224.53/225.00 (step @p359 :rule trans :premises (@p358 @p352)) % 224.53/225.00 (step @p360 :rule cong :premises (@p359) :args (@t164)) % 224.53/225.00 (step @p361 :rule trans :premises (@p360 @p351)) % 224.53/225.00 (step @p362 :rule cong :premises (@p361) :args (@t165)) % 224.53/225.00 (step @p363 :rule trans :premises (@p362 @p349)) % 224.53/225.00 (step @p364 :rule beta-reduce :args ((= @t166 @t165))) % 224.53/225.00 (step @p365 :rule trans :premises (@p364 @p363)) % 224.53/225.00 (step @p366 :rule cong :premises (@p333 @p365) :args (@t167)) % 224.53/225.00 (step @p367 :rule trans :premises (@p366 @p350)) % 224.53/225.00 (step @p368 :rule cong :premises (@p367) :args (@t168)) % 224.53/225.00 (step @p369 :rule trans :premises (@p368 @p349)) % 224.53/225.00 (step @p370 :rule alpha_equiv :args ((lambda @t63 false) (@list @t37) @t87)) % 224.53/225.00 (step @p371 :rule trans :premises (@p370 @p74)) % 224.53/225.00 (step @p372 :rule absorb :args ((= (or true @t162 @t48) true))) % 224.53/225.00 (step @p373 :rule nary_cong :premises (@p357 @p354 @p275) :args (@t144)) % 224.53/225.00 (step @p374 :rule trans :premises (@p373 @p372)) % 224.53/225.00 (step @p375 :rule cong :premises (@p374) :args (@t145)) % 224.53/225.00 (step @p376 :rule trans :premises (@p375 @p351)) % 224.53/225.00 (step @p377 :rule cong :premises (@p376) :args (@t146)) % 224.53/225.00 (step @p378 :rule trans :premises (@p377 @p349)) % 224.53/225.00 (step @p379 :rule cong :premises (@p378) :args (@t147)) % 224.53/225.00 (step @p380 :rule trans :premises (@p379 @p371)) % 224.53/225.00 (step @p381 :rule cong :premises (@p109 @p380) :args (@t169)) % 224.53/225.00 (step @p382 :rule trans :premises (@p381 @p108)) % 224.53/225.00 (step @p383 :rule nary_cong :premises (@p382 @p369) :args ((or @t169 @t168))) % 224.53/225.00 (step @p384 :rule trans :premises (@p383 @p348)) % 224.53/225.00 (step @p385 :rule ho_cong :premises (@p285 @p336)) % 224.53/225.00 (step @p386 :rule cong :premises (@p337 @p385) :args (@t158)) % 224.53/225.00 (step @p387 :rule cong :premises (@p386) :args (@t159)) % 224.53/225.00 (step @p388 :rule cong :premises (@p113 @p285) :args (@t153)) % 224.53/225.00 (step @p389 :rule nary_cong :premises (@p388 @p387) :args (@t160)) % 224.53/225.00 (step @p390 :rule trans :premises (@p389 @p384)) % 224.53/225.00 (step @p391 :rule true_elim :premises (@p390)) % 224.53/225.00 (step @p392 :rule eq_resolve :premises (@p391 @p347)) % 224.53/225.00 (step @p393 :rule chain_m_resolution :premises (@p392 @p327) :args (@t75 @t99 (@list @t153))) % 224.53/225.00 (step @p394 :rule cnf_equiv_pos1 :args (@t81)) % 224.53/225.00 (step @p395 :rule reordering :premises (@p394) :args ((or (not @t75) @t80 (not @t81)))) % 224.53/225.00 (step @p396 :rule chain_m_resolution :premises (@p395 @p393 @p55) :args (@t80 (@list false false) (@list @t75 @t81))) % 224.53/225.00 (step @p397 :rule bool-double-not-elim :args (@t79)) % 224.53/225.00 (step @p398 :rule bool-impl-false1 :args (@t80)) % 224.53/225.00 (step @p399 :rule trans :premises (@p398 @p397)) % 224.53/225.00 (step @p400 :rule absorb :args ((= (or true (not @t174) @t173) true))) % 224.53/225.00 (step @p401 :rule refl :args (@t173)) % 224.53/225.00 (step @p402 :rule eq-refl :args (@t174)) % 224.53/225.00 (step @p403 :rule refl :args (@t174)) % 224.53/225.00 (step @p404 :rule eq-symm :args (@t170 @t53)) % 224.53/225.00 (step @p405 :rule beta-reduce :args ((= @t175 (= @t170 @t53)))) % 224.53/225.00 (step @p406 :rule trans :premises (@p405 @p404)) % 224.53/225.00 (step @p407 :rule cong :premises (@p406 @p403) :args ((= @t175 @t174))) % 224.53/225.00 (step @p408 :rule trans :premises (@p407 @p402)) % 224.53/225.00 (step @p409 :rule refl :args (@t170)) % 224.53/225.00 (step @p410 :rule ho_cong :premises (@p157 @p409)) % 224.53/225.00 (step @p411 :rule cong :premises (@p410 @p403) :args ((= @t176 @t174))) % 224.53/225.00 (step @p412 :rule trans :premises (@p411 @p408)) % 224.53/225.00 (step @p413 :rule true_elim :premises (@p412)) % 224.53/225.00 (step @p414 :rule cong :premises (@p413) :args (@t177)) % 224.53/225.00 (step @p415 :rule beta-reduce :args ((= @t178 false))) % 224.53/225.00 (step @p416 :rule cong :premises (@p415) :args ((not @t178))) % 224.53/225.00 (step @p417 :rule trans :premises (@p416 @p332)) % 224.53/225.00 (step @p418 :rule refl :args (@t171)) % 224.53/225.00 (step @p419 :rule ho_cong :premises (@p113 @p418)) % 224.53/225.00 (step @p420 :rule cong :premises (@p419) :args (@t180)) % 224.53/225.00 (step @p421 :rule bool-eq-false :args (@t179)) % 224.53/225.00 (step @p422 :rule trans :premises (@p421 @p420 @p417)) % 224.53/225.00 (step @p423 :rule true_elim :premises (@p422)) % 224.53/225.00 (step @p424 :rule cong :premises (@p423) :args (@t180)) % 224.53/225.00 (step @p425 :rule trans :premises (@p424 @p332)) % 224.53/225.00 (step @p426 :rule nary_cong :premises (@p425 @p414 @p401) :args (@t181)) % 224.53/225.00 (step @p427 :rule trans :premises (@p426 @p400)) % 224.53/225.00 (step @p428 :rule cong :premises (@p427) :args (@t182)) % 224.53/225.00 (step @p429 :rule trans :premises (@p428 @p349)) % 224.53/225.00 (step @p430 :rule refl :args (@t80)) % 224.53/225.00 (step @p431 :rule cong :premises (@p430 @p429) :args ((=> @t80 @t182))) % 224.53/225.00 (step @p432 :rule trans :premises (@p431 @p399)) % 224.53/225.00 (step @p433 :rule eq-symm :args (@t172 @t70)) % 224.53/225.00 (step @p434 :rule cong :premises (@p433) :args (@t183)) % 224.53/225.00 (step @p435 :rule refl :args (@t177)) % 224.53/225.00 (step @p436 :rule refl :args (@t180)) % 224.53/225.00 (step @p437 :rule nary_cong :premises (@p436 @p435 @p434) :args (@t184)) % 224.53/225.00 (step @p438 :rule cong :premises (@p437) :args (@t185)) % 224.53/225.00 (step @p439 :rule cong :premises (@p430 @p438) :args ((=> @t80 @t185))) % 224.53/225.00 (step @p440 :rule trans :premises (@p439 @p432)) % 224.53/225.00 (assume-push @p467 @t80) % 224.53/225.00 (step @p442 :rule skolemize :premises (@p467)) % 224.53/225.00 (step-pop @p468 :rule scope :premises (@p442)) % 224.53/225.00 (step @p443 :rule process_scope :premises (@p468) :args (@t185)) % 224.53/225.00 (step @p445 :rule eq_resolve :premises (@p443 @p440)) % 224.53/225.00 (step @p446 false :rule chain_m_resolution :premises (@p445 @p396) :args (false @t99 (@list @t79))) % 224.53/225.00 ) % 224.53/225.00 % SZS output end Proof % 224.53/225.00 % cvc5 exiting %------------------------------------------------------------------------------