%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO932^8 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n011.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 09:13:49 AM UTC 2026 % Result : Theorem 0.37s 0.59s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SYO932^8 : TPTP v9.2.1. Released v3.6.0. % 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 : n011.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 : Wed Jun 3 01:09:50 EDT 2026 % 0.17/0.35 % CPUTime : % 0.29/0.51 %----Proving TH0 % 0.37/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.59 % SZS status Theorem % 0.37/0.59 % SZS output start Proof % 0.37/0.59 ( % 0.37/0.59 (declare-sort $$unsorted 0) % 0.37/0.59 (declare-sort tptp.individuals 0) % 0.37/0.59 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.37/0.59 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.37/0.59 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.37/0.59 (define tptp.mor () (let ((_let_1 (@var "U" $$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))))))) % 0.37/0.59 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.59 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "V" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.37/0.59 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.37/0.59 (define tptp.mbox () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.37/0.59 (define tptp.mdia () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.37/0.59 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.37/0.59 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.37/0.59 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.37/0.59 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.37/0.59 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.37/0.59 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.37/0.59 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 0.37/0.59 (define @t2 () (@var "X" tptp.individuals)) % 0.37/0.59 (define @t3 () (@var "A" (-> tptp.individuals $$unsorted Bool))) % 0.37/0.59 (define @t4 () (_ @t3 @t2)) % 0.37/0.59 (define @t5 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.37/0.59 (define @t6 () (_ tptp.mbox @t5)) % 0.37/0.59 (define @t7 () (@list @t2 @t1)) % 0.37/0.59 (define @t8 () (lambda @t7 (_ (_ @t6 @t4) @t1))) % 0.37/0.59 (define @t9 () (lambda @t7 (_ @t4 @t1))) % 0.37/0.59 (define @t10 () (@list @t5 @t3)) % 0.37/0.59 (define @t11 () (forall @t10 (_ tptp.mvalid (_ (_ tptp.mimpl (_ @t6 (_ tptp.mall @t9))) (_ tptp.mall @t8))))) % 0.37/0.59 (define @t12 () (not @t11)) % 0.37/0.59 (define @t13 () (@var "X" $$unsorted)) % 0.37/0.59 (define @t14 () (@list @t13)) % 0.37/0.59 (define @t15 () (lambda @t14 false)) % 0.37/0.59 (define @t16 () (lambda @t14 true)) % 0.37/0.59 (define @t17 () (@var "U" $$unsorted)) % 0.37/0.59 (define @t18 () (@var "X" (-> $$unsorted Bool))) % 0.37/0.59 (define @t19 () (_ @t18 @t17)) % 0.37/0.59 (define @t20 () (lambda (@list @t18 @t17) (not @t19))) % 0.37/0.59 (define @t21 () (@var "Y" (-> $$unsorted Bool))) % 0.37/0.59 (define @t22 () (_ @t21 @t17)) % 0.37/0.59 (define @t23 () (@list @t18 @t21 @t17)) % 0.37/0.59 (define @t24 () (lambda @t23 (or @t19 @t22))) % 0.37/0.59 (define @t25 () (lambda @t23 (and @t19 @t22))) % 0.37/0.59 (define @t26 () (@var "V" (-> $$unsorted Bool))) % 0.37/0.59 (define @t27 () (@var "U" (-> $$unsorted Bool))) % 0.37/0.59 (define @t28 () (@list @t27 @t26 @t1)) % 0.37/0.59 (define @t29 () (lambda @t28 (_ (_ (_ tptp.mor (_ tptp.mnot @t27)) @t26) @t1))) % 0.37/0.59 (define @t30 () (lambda @t28 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t27) @t26)) (_ (_ tptp.mimpl @t26) @t27)) @t1))) % 0.37/0.59 (define @t31 () (@var "Y" $$unsorted)) % 0.37/0.59 (define @t32 () (@var "P" (-> $$unsorted Bool))) % 0.37/0.59 (define @t33 () (_ @t32 @t31)) % 0.37/0.59 (define @t34 () (_ (_ @t5 @t13) @t31)) % 0.37/0.59 (define @t35 () (@list @t31)) % 0.37/0.59 (define @t36 () (forall @t35 (=> @t34 @t33))) % 0.37/0.59 (define @t37 () (@list @t5 @t32 @t13)) % 0.37/0.59 (define @t38 () (lambda @t37 @t36)) % 0.37/0.59 (define @t39 () (lambda @t37 (exists @t35 (and @t34 @t33)))) % 0.37/0.59 (define @t40 () (@var "W" $$unsorted)) % 0.37/0.59 (define @t41 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.37/0.59 (define @t42 () (_ (_ @t41 @t2) @t40)) % 0.37/0.59 (define @t43 () (@list @t2)) % 0.37/0.59 (define @t44 () (forall @t43 @t42)) % 0.37/0.59 (define @t45 () (@list @t41 @t40)) % 0.37/0.59 (define @t46 () (lambda @t45 @t44)) % 0.37/0.59 (define @t47 () (lambda @t45 (exists @t43 @t42))) % 0.37/0.59 (define @t48 () (_ @t32 @t40)) % 0.37/0.59 (define @t49 () (@list @t40)) % 0.37/0.59 (define @t50 () (forall @t49 @t48)) % 0.37/0.59 (define @t51 () (@list @t32)) % 0.37/0.59 (define @t52 () (lambda @t51 @t50)) % 0.37/0.59 (define @t53 () (lambda @t51 (exists @t49 @t48))) % 0.37/0.59 (define @t54 () (not @t48)) % 0.37/0.59 (define @t55 () (lambda @t51 (exists @t49 @t54))) % 0.37/0.59 (define @t56 () (lambda @t51 (forall @t49 @t54))) % 0.37/0.59 (define @t57 () (@var "BOUND_VARIABLE_7865" $$unsorted)) % 0.37/0.59 (define @t58 () (@var "BOUND_VARIABLE_7863" tptp.individuals)) % 0.37/0.59 (define @t59 () (_ @t3 @t58 @t57)) % 0.37/0.59 (define @t60 () (not (_ @t5 @t40 @t57))) % 0.37/0.59 (define @t61 () (@var "BOUND_VARIABLE_7800" tptp.individuals)) % 0.37/0.59 (define @t62 () (_ @t3 @t61 @t31)) % 0.37/0.59 (define @t63 () (not (_ @t5 @t40 @t31))) % 0.37/0.59 (define @t64 () (@list @t31 @t61)) % 0.37/0.59 (define @t65 () (not (forall @t64 (or @t63 @t62)))) % 0.37/0.59 (define @t66 () (or @t65 @t60 @t59)) % 0.37/0.59 (define @t67 () (forall (@list @t5 @t3 @t40 @t58 @t57) @t66)) % 0.37/0.59 (define @t68 () (@list @t40 @t58 @t57)) % 0.37/0.59 (define @t69 () (or @t60 @t59)) % 0.37/0.59 (define @t70 () (or @t65 @t69)) % 0.37/0.59 (define @t71 () (forall @t68 @t70)) % 0.37/0.59 (define @t72 () (@list @t58 @t57)) % 0.37/0.59 (define @t73 () (forall @t72 @t70)) % 0.37/0.59 (define @t74 () (forall @t72 @t69)) % 0.37/0.59 (define @t75 () (or @t65 @t74)) % 0.37/0.59 (define @t76 () (_ @t3 @t2 @t31)) % 0.37/0.59 (define @t77 () (or @t63 @t76)) % 0.37/0.59 (define @t78 () (@list @t2 @t31)) % 0.37/0.59 (define @t79 () (forall @t78 @t77)) % 0.37/0.59 (define @t80 () (or @t65 @t79)) % 0.37/0.59 (define @t81 () (not (_ @t5 @t1 @t31))) % 0.37/0.59 (define @t82 () (or @t81 @t76)) % 0.37/0.59 (define @t83 () (forall @t78 @t82)) % 0.37/0.59 (define @t84 () (forall @t64 (or @t81 @t62))) % 0.37/0.59 (define @t85 () (not @t84)) % 0.37/0.59 (define @t86 () (@list @t1)) % 0.37/0.59 (define @t87 () (lambda @t86 (or @t85 @t83))) % 0.37/0.59 (define @t88 () (_ @t87 @t40)) % 0.37/0.59 (define @t89 () (forall @t49 @t88)) % 0.37/0.59 (define @t90 () (_ @t32 @t40)) % 0.37/0.59 (define @t91 () (lambda @t51 (forall @t49 @t90))) % 0.37/0.59 (define @t92 () (lambda @t49 @t79)) % 0.37/0.59 (define @t93 () (_ @t92 @t1)) % 0.37/0.59 (define @t94 () (or @t85 @t93)) % 0.37/0.59 (define @t95 () (lambda @t86 @t94)) % 0.37/0.59 (define @t96 () (_ @t26 @t1)) % 0.37/0.59 (define @t97 () (@list @t26 @t1)) % 0.37/0.59 (define @t98 () (forall @t35 @t77)) % 0.37/0.59 (define @t99 () (forall @t35 @t82)) % 0.37/0.59 (define @t100 () (lambda @t7 @t99)) % 0.37/0.59 (define @t101 () (_ @t100 @t2 @t40)) % 0.37/0.59 (define @t102 () (forall @t43 @t101)) % 0.37/0.59 (define @t103 () (lambda @t49 @t102)) % 0.37/0.59 (define @t104 () (_ @t41 @t2 @t40)) % 0.37/0.59 (define @t105 () (lambda @t45 (forall @t43 @t104))) % 0.37/0.59 (define @t106 () (_ @t5 @t13 @t31)) % 0.37/0.59 (define @t107 () (not @t106)) % 0.37/0.59 (define @t108 () (_ @t4 @t31)) % 0.37/0.59 (define @t109 () (or @t107 @t108)) % 0.37/0.59 (define @t110 () (_ @t4 @t31)) % 0.37/0.59 (define @t111 () (or @t107 @t110)) % 0.37/0.59 (define @t112 () (forall @t35 @t111)) % 0.37/0.59 (define @t113 () (lambda @t14 @t112)) % 0.37/0.59 (define @t114 () (_ @t32 @t31)) % 0.37/0.59 (define @t115 () (forall @t35 (or @t107 @t114))) % 0.37/0.59 (define @t116 () (lambda (@list @t32 @t13) @t115)) % 0.37/0.59 (define @t117 () (_ (lambda @t37 @t115) @t5)) % 0.37/0.59 (define @t118 () (lambda @t7 (_ (_ @t117 @t4) @t1))) % 0.37/0.59 (define @t119 () (or @t107 @t62)) % 0.37/0.59 (define @t120 () (forall @t64 @t119)) % 0.37/0.59 (define @t121 () (lambda @t14 @t120)) % 0.37/0.59 (define @t122 () (_ @t121 @t1)) % 0.37/0.59 (define @t123 () (not @t122)) % 0.37/0.59 (define @t124 () (or @t123 @t96)) % 0.37/0.59 (define @t125 () (lambda @t97 @t124)) % 0.37/0.59 (define @t126 () (or (not (_ @t27 @t1)) @t96)) % 0.37/0.59 (define @t127 () (lambda @t28 @t126)) % 0.37/0.59 (define @t128 () (@list @t61)) % 0.37/0.59 (define @t129 () (forall @t128 @t119)) % 0.37/0.59 (define @t130 () (forall @t128 @t62)) % 0.37/0.59 (define @t131 () (or @t107 @t130)) % 0.37/0.59 (define @t132 () (forall @t43 @t76)) % 0.37/0.59 (define @t133 () (_ @t3 @t2 @t40)) % 0.37/0.59 (define @t134 () (lambda @t49 (forall @t43 @t133))) % 0.37/0.59 (define @t135 () (_ @t134 @t31)) % 0.37/0.59 (define @t136 () (or @t107 @t135)) % 0.37/0.59 (define @t137 () (forall @t35 @t136)) % 0.37/0.59 (define @t138 () (lambda @t14 @t137)) % 0.37/0.59 (define @t139 () (_ @t4 @t40)) % 0.37/0.59 (define @t140 () (_ @t9 @t2 @t40)) % 0.37/0.59 (define @t141 () (forall @t43 @t140)) % 0.37/0.59 (define @t142 () (lambda @t49 @t141)) % 0.37/0.59 (define @t143 () (_ @t105 @t9)) % 0.37/0.59 (define @t144 () (forall @t10 (_ @t91 (_ (_ @t127 (_ @t117 @t143)) (_ @t105 @t118))))) % 0.37/0.59 (define @t145 () (not @t34)) % 0.37/0.59 (define @t146 () (or @t145 @t33)) % 0.37/0.59 (define @t147 () (not (_ @t27 @t17))) % 0.37/0.59 (define @t148 () (@list @t17)) % 0.37/0.59 (define @t149 () (lambda @t148 (or @t147 (_ @t26 @t17)))) % 0.37/0.59 (define @t150 () (@list @t21 @t17)) % 0.37/0.59 (define @t151 () (lambda @t148 @t147)) % 0.37/0.59 (define @t152 () (_ @t151 @t17)) % 0.37/0.59 (define @t153 () (or @t152 @t22)) % 0.37/0.59 (define @t154 () (lambda @t150 @t153)) % 0.37/0.59 (define @t155 () (@quantifiers_skolemize @t67 1)) % 0.37/0.59 (define @t156 () (@quantifiers_skolemize @t67 2)) % 0.37/0.59 (define @t157 () (@quantifiers_skolemize @t67 0)) % 0.37/0.59 (define @t158 () (forall @t64 (or (not (_ @t157 @t156 @t31)) (_ @t155 @t61 @t31)))) % 0.37/0.59 (define @t159 () (@quantifiers_skolemize @t67 4)) % 0.37/0.59 (define @t160 () (@quantifiers_skolemize @t67 3)) % 0.37/0.59 (define @t161 () (_ @t155 @t160 @t159)) % 0.37/0.59 (define @t162 () (_ @t157 @t156 @t159)) % 0.37/0.59 (define @t163 () (not @t162)) % 0.37/0.59 (define @t164 () (not @t158)) % 0.37/0.59 (define @t165 () (or @t164 @t163 @t161)) % 0.37/0.59 (define @t166 () (@list true)) % 0.37/0.59 (define @t167 () (@list @t165)) % 0.37/0.59 (define @t168 () (or @t163 @t161)) % 0.37/0.59 (define @t169 () (not @t168)) % 0.37/0.59 (assume @p1 @t12) % 0.37/0.59 (assume @p2 true) % 0.37/0.59 (step @p3 (= tptp.mfalse @t15) :rule refl :args (@t15)) % 0.37/0.59 (step @p4 (= tptp.mtrue @t16) :rule refl :args (@t16)) % 0.37/0.59 (step @p5 (= tptp.mnot @t20) :rule refl :args (@t20)) % 0.37/0.59 (step @p6 (= tptp.mor @t24) :rule refl :args (@t24)) % 0.37/0.59 (step @p7 (= tptp.mand @t25) :rule refl :args (@t25)) % 0.37/0.59 (step @p8 (= tptp.mimpl @t29) :rule refl :args (@t29)) % 0.37/0.59 (step @p9 (= tptp.miff @t30) :rule refl :args (@t30)) % 0.37/0.59 (step @p10 (= tptp.mbox @t38) :rule refl :args (@t38)) % 0.37/0.59 (step @p11 (= tptp.mdia @t39) :rule refl :args (@t39)) % 0.37/0.59 (step @p12 (= tptp.mall @t46) :rule refl :args (@t46)) % 0.37/0.59 (step @p13 (= tptp.mexists @t47) :rule refl :args (@t47)) % 0.37/0.59 (step @p14 (= tptp.mvalid @t52) :rule refl :args (@t52)) % 0.37/0.59 (step @p15 (= tptp.msatisfiable @t53) :rule refl :args (@t53)) % 0.37/0.59 (step @p16 (= tptp.mcountersatisfiable @t55) :rule refl :args (@t55)) % 0.37/0.59 (step @p17 (= tptp.minvalid @t56) :rule refl :args (@t56)) % 0.37/0.59 (step @p18 :rule quant-merge-prenex :args ((= (forall @t10 (forall @t68 @t66)) @t67))) % 0.37/0.59 (step @p19 :rule aci_norm :args ((= @t70 @t66))) % 0.37/0.59 (step @p20 :rule cong :premises (@p19) :args (@t71)) % 0.37/0.59 (step @p21 :rule quant-merge-prenex :args ((= (forall @t49 @t73) @t71))) % 0.37/0.59 (step @p22 :rule alpha_equiv :args (@t74 (@list @t58 @t57) (@list @t2 @t31))) % 0.37/0.59 (step @p23 :rule refl :args (@t65)) % 0.37/0.59 (step @p24 :rule nary_cong :premises (@p23 @p22) :args (@t75)) % 0.37/0.59 (step @p25 :rule quant-miniscope-or :args ((= @t73 @t75))) % 0.37/0.59 (step @p26 :rule trans :premises (@p25 @p24)) % 0.37/0.59 (step @p27 :rule symm :premises (@p26)) % 0.37/0.59 (step @p28 :rule cong :premises (@p27) :args ((forall @t49 @t80))) % 0.37/0.59 (step @p29 :rule trans :premises (@p28 @p21)) % 0.37/0.59 (step @p30 :rule trans :premises (@p29 @p20)) % 0.37/0.59 (step @p31 :rule beta-reduce :args ((= @t88 @t80))) % 0.37/0.59 (step @p32 :rule cong :premises (@p31) :args (@t89)) % 0.37/0.59 (step @p33 :rule trans :premises (@p32 @p30)) % 0.37/0.59 (step @p34 :rule beta-reduce :args ((= (_ @t91 @t87) @t89))) % 0.37/0.59 (step @p35 :rule trans :premises (@p34 @p33)) % 0.37/0.59 (step @p36 :rule beta-reduce :args ((= @t93 @t83))) % 0.37/0.59 (step @p37 :rule refl :args (@t85)) % 0.37/0.59 (step @p38 :rule nary_cong :premises (@p37 @p36) :args (@t94)) % 0.37/0.59 (step @p39 :rule cong :premises (@p38) :args (@t95)) % 0.37/0.59 (step @p40 :rule beta-reduce :args ((= (_ (lambda @t97 (or @t85 @t96)) @t92) @t95))) % 0.37/0.59 (step @p41 :rule trans :premises (@p40 @p39)) % 0.37/0.59 (step @p42 :rule quant-merge-prenex :args ((= 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0.37/0.59 (step @p58 :rule cong :premises (@p57) :args ((forall @t35 @t109))) % 0.37/0.59 (step @p59 :rule refl :args (@t110)) % 0.37/0.59 (step @p60 :rule refl :args (@t107)) % 0.37/0.59 (step @p61 :rule nary_cong :premises (@p60 @p59) :args (@t111)) % 0.37/0.59 (step @p62 :rule cong :premises (@p61) :args (@t112)) % 0.37/0.59 (step @p63 :rule trans :premises (@p62 @p58)) % 0.37/0.59 (step @p64 :rule cong :premises (@p63) :args (@t113)) % 0.37/0.59 (step @p65 :rule beta-reduce :args ((= (_ @t116 @t4) @t113))) % 0.37/0.59 (step @p66 :rule trans :premises (@p65 @p64)) % 0.37/0.59 (step @p67 :rule refl :args (@t4)) % 0.37/0.59 (step @p68 :rule beta-reduce :args ((= @t117 @t116))) % 0.37/0.59 (step @p69 :rule ho_cong :premises (@p68 @p67)) % 0.37/0.59 (step @p70 :rule trans :premises (@p69 @p66)) % 0.37/0.59 (step @p71 :rule ho_cong :premises (@p70 @p50)) % 0.37/0.59 (step @p72 :rule trans :premises (@p71 @p49)) % 0.37/0.59 (step @p73 :rule cong :premises (@p72) :args (@t118)) % 0.37/0.59 (step @p74 :rule refl :args (@t105)) % 0.37/0.59 (step @p75 :rule ho_cong :premises (@p74 @p73)) % 0.37/0.59 (step @p76 :rule trans :premises (@p75 @p48)) % 0.37/0.59 (step @p77 :rule refl :args (@t96)) % 0.37/0.59 (step @p78 :rule beta-reduce :args ((= @t122 @t84))) % 0.37/0.59 (step @p79 :rule cong :premises (@p78) :args (@t123)) % 0.37/0.59 (step @p80 :rule nary_cong :premises (@p79 @p77) :args (@t124)) % 0.37/0.59 (step @p81 :rule cong :premises (@p80) :args (@t125)) % 0.37/0.59 (step @p82 :rule beta-reduce :args ((= (_ @t127 @t121) @t125))) % 0.37/0.59 (step @p83 :rule trans :premises (@p82 @p81)) % 0.37/0.59 (step @p84 :rule quant-merge-prenex :args ((= (forall @t35 @t129) @t120))) % 0.37/0.59 (step @p85 :rule alpha_equiv :args (@t130 (@list @t61) (@list @t2))) % 0.37/0.59 (step @p86 :rule nary_cong :premises (@p56 @p85) :args (@t131)) % 0.37/0.59 (step @p87 :rule quant-miniscope-or :args ((= @t129 @t131))) % 0.37/0.59 (step @p88 :rule trans :premises (@p87 @p86)) % 0.37/0.59 (step @p89 :rule symm :premises (@p88)) % 0.37/0.59 (step @p90 :rule cong :premises (@p89) :args ((forall @t35 (or @t107 @t132)))) % 0.37/0.59 (step @p91 :rule trans :premises (@p90 @p84)) % 0.37/0.59 (step @p92 :rule beta-reduce :args ((= @t135 @t132))) % 0.37/0.59 (step @p93 :rule nary_cong :premises (@p60 @p92) :args (@t136)) % 0.37/0.59 (step @p94 :rule cong :premises (@p93) :args (@t137)) % 0.37/0.59 (step @p95 :rule trans :premises (@p94 @p91)) % 0.37/0.59 (step @p96 :rule cong :premises (@p95) :args (@t138)) % 0.37/0.59 (step @p97 :rule beta-reduce :args ((= (_ @t116 @t134) @t138))) % 0.37/0.59 (step @p98 :rule trans :premises (@p97 @p96)) % 0.37/0.59 (step @p99 :rule refl :args (@t133)) % 0.37/0.59 (step @p100 :rule refl :args (@t139)) % 0.37/0.59 (step @p101 :rule cong :premises (@p100 @p99) :args ((= @t139 @t133))) % 0.37/0.59 (step @p102 :rule symm :premises (@p101)) % 0.37/0.59 (step @p103 :rule eq_resolve :premises (@p100 @p102)) % 0.37/0.59 (step @p104 :rule cong 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trans :premises (@p119 @p35)) % 0.37/0.59 (step @p121 :rule cong :premises (@p120) :args (@t144)) % 0.37/0.59 (step @p122 :rule trans :premises (@p121 @p18)) % 0.37/0.59 (step @p123 :rule cong :premises (@p122) :args ((not @t144))) % 0.37/0.59 (step @p124 :rule refl :args (@t5)) % 0.37/0.59 (step @p125 :rule refl :args (@t114)) % 0.37/0.59 (step @p126 :rule refl :args (@t33)) % 0.37/0.59 (step @p127 :rule cong :premises (@p126 @p125) :args ((= @t33 @t114))) % 0.37/0.59 (step @p128 :rule symm :premises (@p127)) % 0.37/0.59 (step @p129 :rule eq_resolve :premises (@p126 @p128)) % 0.37/0.59 (step @p130 :rule refl :args (@t106)) % 0.37/0.59 (step @p131 :rule refl :args (@t34)) % 0.37/0.59 (step @p132 :rule cong :premises (@p131 @p130) :args ((= @t34 @t106))) % 0.37/0.59 (step @p133 :rule symm :premises (@p132)) % 0.37/0.59 (step @p134 :rule eq_resolve :premises (@p131 @p133)) % 0.37/0.59 (step @p135 :rule cong :premises (@p134) :args (@t145)) % 0.37/0.59 (step @p136 :rule nary_cong :premises (@p135 @p129) :args (@t146)) % 0.37/0.59 (step @p137 :rule cong :premises (@p136) :args ((forall @t35 @t146))) % 0.37/0.59 (step @p138 :rule bool-impl-elim :args (@t34 @t33)) % 0.37/0.59 (step @p139 :rule cong :premises (@p138) :args (@t36)) % 0.37/0.59 (step @p140 :rule trans :premises (@p139 @p137)) % 0.37/0.59 (step @p141 :rule cong :premises (@p140) :args (@t38)) % 0.37/0.59 (step @p142 :rule trans :premises (@p10 @p141)) % 0.37/0.59 (step @p143 :rule ho_cong :premises (@p142 @p124)) % 0.37/0.59 (step @p144 :rule ho_cong :premises (@p143 @p67)) % 0.37/0.59 (step @p145 :rule ho_cong :premises (@p144 @p50)) % 0.37/0.59 (step @p146 :rule cong :premises (@p145) :args (@t8)) % 0.37/0.59 (step @p147 :rule refl :args (@t104)) % 0.37/0.59 (step @p148 :rule refl :args (@t42)) % 0.37/0.59 (step @p149 :rule cong :premises (@p148 @p147) :args ((= @t42 @t104))) % 0.37/0.59 (step @p150 :rule symm :premises (@p149)) % 0.37/0.59 (step @p151 :rule eq_resolve :premises (@p148 @p150)) % 0.37/0.59 (step @p152 :rule cong :premises (@p151) :args (@t44)) % 0.37/0.59 (step @p153 :rule cong :premises (@p152) :args (@t46)) % 0.37/0.59 (step @p154 :rule trans :premises (@p12 @p153)) % 0.37/0.59 (step @p155 :rule ho_cong :premises (@p154 @p146)) % 0.37/0.59 (step @p156 :rule refl :args (@t9)) % 0.37/0.59 (step @p157 :rule ho_cong :premises (@p154 @p156)) % 0.37/0.59 (step @p158 :rule ho_cong :premises (@p143 @p157)) % 0.37/0.59 (step @p159 :rule beta-reduce :args ((= (_ @t149 @t1) @t126))) % 0.37/0.59 (step @p160 :rule beta-reduce :args ((= (_ (lambda @t150 (or @t147 @t22)) @t26) @t149))) % 0.37/0.59 (step @p161 :rule refl :args (@t26)) % 0.37/0.59 (step @p162 :rule refl :args (@t22)) % 0.37/0.59 (step @p163 :rule beta-reduce :args ((= @t152 @t147))) % 0.37/0.59 (step @p164 :rule nary_cong :premises (@p163 @p162) :args (@t153)) % 0.37/0.59 (step @p165 :rule cong :premises (@p164) :args (@t154)) % 0.37/0.59 (step @p166 :rule beta-reduce :args ((= (_ @t24 @t151) @t154))) % 0.37/0.59 (step @p167 :rule trans :premises (@p166 @p165)) % 0.37/0.59 (step @p168 :rule beta-reduce :args ((= (_ @t20 @t27) @t151))) % 0.37/0.59 (step @p169 :rule refl :args (@t24)) % 0.37/0.59 (step @p170 :rule ho_cong :premises (@p169 @p168)) % 0.37/0.59 (step @p171 :rule trans :premises (@p170 @p167)) % 0.37/0.59 (step @p172 :rule ho_cong :premises (@p171 @p161)) % 0.37/0.59 (step @p173 :rule trans :premises (@p172 @p160)) % 0.37/0.59 (step @p174 :rule ho_cong :premises (@p173 @p50)) % 0.37/0.59 (step @p175 :rule trans :premises (@p174 @p159)) % 0.37/0.59 (step @p176 :rule refl :args (@t27)) % 0.37/0.59 (step @p177 :rule ho_cong :premises (@p5 @p176)) % 0.37/0.59 (step @p178 :rule ho_cong :premises (@p6 @p177)) % 0.37/0.59 (step @p179 :rule ho_cong :premises (@p178 @p161)) % 0.37/0.59 (step @p180 :rule ho_cong :premises (@p179 @p50)) % 0.37/0.59 (step @p181 :rule trans :premises (@p180 @p175)) % 0.37/0.59 (step @p182 :rule cong :premises (@p181) :args (@t29)) % 0.37/0.59 (step @p183 :rule trans :premises (@p8 @p182)) % 0.37/0.59 (step @p184 :rule ho_cong :premises (@p183 @p158)) % 0.37/0.59 (step @p185 :rule ho_cong :premises (@p184 @p155)) % 0.37/0.59 (step @p186 :rule refl :args (@t90)) % 0.37/0.59 (step @p187 :rule refl :args (@t48)) % 0.37/0.59 (step @p188 :rule cong :premises (@p187 @p186) :args ((= @t48 @t90))) % 0.37/0.59 (step @p189 :rule symm :premises (@p188)) % 0.37/0.59 (step @p190 :rule eq_resolve :premises (@p187 @p189)) % 0.37/0.59 (step @p191 :rule cong :premises (@p190) :args (@t50)) % 0.37/0.59 (step @p192 :rule cong :premises (@p191) :args (@t52)) % 0.37/0.59 (step @p193 :rule trans :premises (@p14 @p192)) % 0.37/0.59 (step @p194 :rule ho_cong :premises (@p193 @p185)) % 0.37/0.59 (step @p195 :rule cong :premises (@p194) :args (@t11)) % 0.37/0.59 (step @p196 :rule cong :premises (@p195) :args (@t12)) % 0.37/0.59 (step @p197 :rule trans :premises (@p196 @p123)) % 0.37/0.59 (step @p198 :rule eq_resolve :premises (@p1 @p197)) % 0.37/0.59 (step @p199 :rule skolemize :premises (@p198)) % 0.37/0.59 (step @p200 :rule bool-double-not-elim :args (@t158)) % 0.37/0.59 (step @p201 :rule refl :args (@t165)) % 0.37/0.59 (step @p202 :rule nary_cong :premises (@p201 @p200) :args ((or @t165 (not @t164)))) % 0.37/0.59 (step @p203 :rule cnf_or_neg :args (@t165 0)) % 0.37/0.59 (step @p204 :rule eq_resolve :premises (@p203 @p202)) % 0.37/0.59 (step @p205 :rule reordering :premises (@p204) :args ((or @t158 @t165))) % 0.37/0.59 (step @p206 :rule chain_m_resolution :premises (@p205 @p199) :args (@t158 @t166 @t167)) % 0.37/0.59 (step @p207 :rule cnf_or_neg :args (@t165 2)) % 0.37/0.59 (step @p208 :rule chain_m_resolution :premises (@p207 @p199) :args ((not @t161) @t166 @t167)) % 0.37/0.59 (step @p209 :rule bool-double-not-elim :args (@t162)) % 0.37/0.59 (step @p210 :rule nary_cong :premises (@p201 @p209) :args ((or @t165 (not @t163)))) % 0.37/0.59 (step @p211 :rule cnf_or_neg :args (@t165 1)) % 0.37/0.59 (step @p212 :rule eq_resolve :premises (@p211 @p210)) % 0.37/0.59 (step @p213 :rule reordering :premises (@p212) :args ((or @t162 @t165))) % 0.37/0.59 (step @p214 :rule chain_m_resolution :premises (@p213 @p199) :args (@t162 @t166 @t167)) % 0.37/0.59 (step @p215 :rule cnf_or_pos :args (@t168)) % 0.37/0.59 (step @p216 :rule reordering :premises (@p215) :args ((or @t163 @t161 @t169))) % 0.37/0.59 (step @p217 :rule chain_m_resolution :premises (@p216 @p214 @p208) :args (@t169 (@list false true) (@list @t162 @t161))) % 0.37/0.59 (assume-push @p224 @t158) % 0.37/0.59 (step @p219 :rule instantiate :premises (@p206) :args ((@list @t159 @t160))) % 0.37/0.59 (step-pop @p225 :rule scope :premises (@p219)) % 0.37/0.59 (step @p220 :rule process_scope :premises (@p225) :args (@t168)) % 0.37/0.59 (step @p222 :rule implies_elim :premises (@p220)) % 0.37/0.59 (step @p223 false :rule chain_m_resolution :premises (@p222 @p217 @p206) :args (false (@list true false) (@list @t168 @t158))) % 0.37/0.59 ) % 0.37/0.59 % SZS output end Proof % 0.37/0.59 % cvc5 exiting %------------------------------------------------------------------------------