%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUN067+2 : TPTP v9.2.1. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n010.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 08:42:53 AM UTC 2026 % Result : Theorem 0.38s 0.58s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUN067+2 : TPTP v9.2.1. Released v7.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n010.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 12:38:40 EDT 2026 % 0.18/0.34 % CPUTime : % 0.31/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.58 % SZS status Theorem % 0.38/0.58 % SZS output start Proof % 0.38/0.58 ( % 0.38/0.58 (declare-sort $$unsorted 0) % 0.38/0.58 (declare-const tptp.r4 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.58 (declare-const tptp.r3 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.58 (declare-const tptp.r2 (-> $$unsorted $$unsorted Bool)) % 0.38/0.58 (declare-const tptp.r1 (-> $$unsorted Bool)) % 0.38/0.58 (define @t1 () (@var "Y24" $$unsorted)) % 0.38/0.58 (define @t2 () (@var "X19" $$unsorted)) % 0.38/0.58 (define @t3 () (= @t2 @t1)) % 0.38/0.58 (define @t4 () (tptp.r1 @t2)) % 0.38/0.58 (define @t5 () (@list @t1)) % 0.38/0.58 (define @t6 () (@var "Y21" $$unsorted)) % 0.38/0.58 (define @t7 () (@var "X12" $$unsorted)) % 0.38/0.58 (define @t8 () (= @t7 @t6)) % 0.38/0.58 (define @t9 () (@var "X11" $$unsorted)) % 0.38/0.58 (define @t10 () (tptp.r2 @t9 @t7)) % 0.38/0.58 (define @t11 () (@var "Y22" $$unsorted)) % 0.38/0.58 (define @t12 () (@var "X15" $$unsorted)) % 0.38/0.58 (define @t13 () (= @t12 @t11)) % 0.38/0.58 (define @t14 () (@var "X14" $$unsorted)) % 0.38/0.58 (define @t15 () (@var "X13" $$unsorted)) % 0.38/0.58 (define @t16 () (tptp.r3 @t15 @t14 @t12)) % 0.38/0.58 (define @t17 () (@var "Y23" $$unsorted)) % 0.38/0.58 (define @t18 () (@var "X18" $$unsorted)) % 0.38/0.58 (define @t19 () (= @t18 @t17)) % 0.38/0.58 (define @t20 () (@var "X17" $$unsorted)) % 0.38/0.58 (define @t21 () (@var "X16" $$unsorted)) % 0.38/0.58 (define @t22 () (tptp.r4 @t21 @t20 @t18)) % 0.38/0.58 (define @t23 () (@var "Y7" $$unsorted)) % 0.38/0.58 (define @t24 () (@var "X8" $$unsorted)) % 0.38/0.58 (define @t25 () (@var "X1" $$unsorted)) % 0.38/0.58 (define @t26 () (@var "Y4" $$unsorted)) % 0.38/0.58 (define @t27 () (@var "Y5" $$unsorted)) % 0.38/0.58 (define @t28 () (@var "Y15" $$unsorted)) % 0.38/0.58 (define @t29 () (@var "Y6" $$unsorted)) % 0.38/0.58 (define @t30 () (@var "X9" $$unsorted)) % 0.38/0.58 (define @t31 () (@var "X2" $$unsorted)) % 0.38/0.58 (define @t32 () (tptp.r4 @t31 @t30 @t29)) % 0.38/0.58 (define @t33 () (@var "Y2" $$unsorted)) % 0.38/0.58 (define @t34 () (tptp.r3 @t29 @t31 @t33)) % 0.38/0.58 (define @t35 () (and @t34 @t32)) % 0.38/0.58 (define @t36 () (@list @t29)) % 0.38/0.58 (define @t37 () (exists @t36 @t35)) % 0.38/0.58 (define @t38 () (@var "Y3" $$unsorted)) % 0.38/0.58 (define @t39 () (= @t38 @t33)) % 0.38/0.58 (define @t40 () (@var "Y14" $$unsorted)) % 0.38/0.58 (define @t41 () (tptp.r4 @t31 @t40 @t38)) % 0.38/0.58 (define @t42 () (tptp.r2 @t30 @t40)) % 0.38/0.58 (define @t43 () (and @t42 @t41)) % 0.38/0.58 (define @t44 () (@list @t40)) % 0.38/0.58 (define @t45 () (exists @t44 @t43)) % 0.38/0.58 (define @t46 () (and @t45 @t39)) % 0.38/0.58 (define @t47 () (@list @t38)) % 0.38/0.58 (define @t48 () (exists @t47 @t46)) % 0.38/0.58 (define @t49 () (and @t48 @t37)) % 0.38/0.58 (define @t50 () (@list @t33)) % 0.38/0.58 (define @t51 () (exists @t50 @t49)) % 0.38/0.58 (define @t52 () (forall (@list @t31 @t30) @t51)) % 0.38/0.58 (define @t53 () (@var "X10" $$unsorted)) % 0.38/0.58 (define @t54 () (@var "X3" $$unsorted)) % 0.38/0.58 (define @t55 () (@var "Y12" $$unsorted)) % 0.38/0.58 (define @t56 () (@var "Y13" $$unsorted)) % 0.38/0.58 (define @t57 () (@var "X4" $$unsorted)) % 0.38/0.58 (define @t58 () (@var "Y9" $$unsorted)) % 0.38/0.58 (define @t59 () (@var "Y16" $$unsorted)) % 0.38/0.58 (define @t60 () (@var "Y18" $$unsorted)) % 0.38/0.58 (define @t61 () (@var "Y8" $$unsorted)) % 0.38/0.58 (define @t62 () (@var "Y17" $$unsorted)) % 0.38/0.58 (define @t63 () (@var "X5" $$unsorted)) % 0.38/0.58 (define @t64 () (@var "Y11" $$unsorted)) % 0.38/0.58 (define @t65 () (@var "X6" $$unsorted)) % 0.38/0.58 (define @t66 () (@var "Y1" $$unsorted)) % 0.38/0.58 (define @t67 () (@var "Y19" $$unsorted)) % 0.38/0.58 (define @t68 () (@var "Y10" $$unsorted)) % 0.38/0.58 (define @t69 () (@var "X7" $$unsorted)) % 0.38/0.58 (define @t70 () (not (tptp.r2 @t69 @t68))) % 0.38/0.58 (define @t71 () (@var "Y20" $$unsorted)) % 0.38/0.58 (define @t72 () (not (= @t71 @t68))) % 0.38/0.58 (define @t73 () (not (tptp.r1 @t71))) % 0.38/0.58 (define @t74 () (or @t73 @t72)) % 0.38/0.58 (define @t75 () (@list @t71)) % 0.38/0.58 (define @t76 () (forall @t75 @t74)) % 0.38/0.58 (define @t77 () (or @t76 @t70)) % 0.38/0.58 (define @t78 () (forall (@list @t69 @t68) @t77)) % 0.38/0.58 (define @t79 () (not (= @t66 @t33))) % 0.38/0.58 (define @t80 () (not (tptp.r1 @t33))) % 0.38/0.58 (define @t81 () (or @t80 @t79)) % 0.38/0.58 (define @t82 () (forall @t50 @t81)) % 0.38/0.58 (define @t83 () (@list @t66)) % 0.38/0.58 (define @t84 () (exists @t83 @t82)) % 0.38/0.58 (define @t85 () (not @t84)) % 0.38/0.58 (define @t86 () (tptp.r1 @t66)) % 0.38/0.58 (define @t87 () (forall @t83 @t86)) % 0.38/0.58 (define @t88 () (not @t86)) % 0.38/0.58 (define @t89 () (forall @t83 (not @t88))) % 0.38/0.58 (define @t90 () (not @t89)) % 0.38/0.58 (define @t91 () (not (= @t66 @t66))) % 0.38/0.58 (define @t92 () (or @t88 @t91)) % 0.38/0.58 (define @t93 () (not (= @t33 @t66))) % 0.38/0.58 (define @t94 () (or @t93 @t80 @t93)) % 0.38/0.58 (define @t95 () (or @t80 @t93)) % 0.38/0.58 (define @t96 () (not (tptp.r1 @t68))) % 0.38/0.58 (define @t97 () (not (= @t68 @t68))) % 0.38/0.58 (define @t98 () (or @t96 @t97)) % 0.38/0.58 (define @t99 () (not (= @t68 @t71))) % 0.38/0.58 (define @t100 () (or @t99 @t73 @t99)) % 0.38/0.58 (define @t101 () (or @t73 @t99)) % 0.38/0.58 (define @t102 () (@var "BOUND_VARIABLE_7951" $$unsorted)) % 0.38/0.58 (define @t103 () (@var "BOUND_VARIABLE_7631" $$unsorted)) % 0.38/0.58 (define @t104 () (tptp.r1 @t103)) % 0.38/0.58 (define @t105 () (@quantifiers_skolemize (forall @t5 (or (not (forall (@list @t103) (or (not @t104) (and @t104 (= @t1 @t103))))) (not (tptp.r1 @t1)))) 0)) % 0.38/0.58 (define @t106 () (@var "BOUND_VARIABLE_7944" $$unsorted)) % 0.38/0.58 (define @t107 () (@list @t33 @t106 @t102)) % 0.38/0.58 (define @t108 () (forall @t107 (or (not (tptp.r2 @t105 @t106)) (not (tptp.r4 @t105 @t106 @t33)) (not (tptp.r3 @t102 @t105 @t33)) (not (tptp.r4 @t105 @t105 @t102))))) % 0.38/0.58 (define @t109 () (@quantifiers_skolemize @t108 1)) % 0.38/0.58 (define @t110 () (not (tptp.r4 @t31 @t30 @t102))) % 0.38/0.58 (define @t111 () (not (tptp.r3 @t102 @t31 @t33))) % 0.38/0.58 (define @t112 () (not (tptp.r4 @t31 @t106 @t33))) % 0.38/0.58 (define @t113 () (not (tptp.r2 @t30 @t106))) % 0.38/0.58 (define @t114 () (or @t111 @t110)) % 0.38/0.58 (define @t115 () (or @t113 @t112)) % 0.38/0.58 (define @t116 () (or @t115 @t114)) % 0.38/0.58 (define @t117 () (forall @t107 @t116)) % 0.38/0.58 (define @t118 () (forall (@list @t106 @t102) @t116)) % 0.38/0.58 (define @t119 () (forall (@list @t102) @t114)) % 0.38/0.58 (define @t120 () (forall (@list @t106) @t115)) % 0.38/0.58 (define @t121 () (@var "BOUND_VARIABLE_7906" $$unsorted)) % 0.38/0.58 (define @t122 () (@list @t121)) % 0.38/0.58 (define @t123 () (or @t120 @t119)) % 0.38/0.58 (define @t124 () (forall @t36 (or (not @t34) (not @t32)))) % 0.38/0.58 (define @t125 () (not (tptp.r4 @t31 @t121 @t33))) % 0.38/0.58 (define @t126 () (not (tptp.r2 @t30 @t121))) % 0.38/0.58 (define @t127 () (or @t126 @t125)) % 0.38/0.58 (define @t128 () (@list @t121)) % 0.38/0.58 (define @t129 () (forall @t128 @t127)) % 0.38/0.58 (define @t130 () (not @t124)) % 0.38/0.58 (define @t131 () (not @t129)) % 0.38/0.58 (define @t132 () (and @t131 @t130)) % 0.38/0.58 (define @t133 () (forall @t50 (not @t132))) % 0.38/0.58 (define @t134 () (not @t133)) % 0.38/0.58 (define @t135 () (forall @t36 (not @t35))) % 0.38/0.58 (define @t136 () (not @t135)) % 0.38/0.58 (define @t137 () (not (= @t33 @t33))) % 0.38/0.58 (define @t138 () (or @t137 @t126 @t125)) % 0.38/0.58 (define @t139 () (not (tptp.r4 @t31 @t121 @t38))) % 0.38/0.58 (define @t140 () (= @t33 @t38)) % 0.38/0.58 (define @t141 () (not @t140)) % 0.38/0.58 (define @t142 () (or @t141 @t141 @t126 @t139)) % 0.38/0.58 (define @t143 () (or @t141 @t126 @t139)) % 0.38/0.58 (define @t144 () (forall @t47 @t143)) % 0.38/0.58 (define @t145 () (forall @t128 @t144)) % 0.38/0.58 (define @t146 () (forall (@list @t121 @t38) @t143)) % 0.38/0.58 (define @t147 () (@list @t38 @t121)) % 0.38/0.58 (define @t148 () (or @t126 @t139)) % 0.38/0.58 (define @t149 () (or @t148 @t141)) % 0.38/0.58 (define @t150 () (forall @t147 @t149)) % 0.38/0.58 (define @t151 () (forall @t128 @t149)) % 0.38/0.58 (define @t152 () (forall @t128 @t148)) % 0.38/0.58 (define @t153 () (or @t152 @t141)) % 0.38/0.58 (define @t154 () (forall @t44 (or (not @t42) (not @t41)))) % 0.38/0.58 (define @t155 () (not @t154)) % 0.38/0.58 (define @t156 () (and @t155 @t140)) % 0.38/0.58 (define @t157 () (forall @t47 (not @t156))) % 0.38/0.58 (define @t158 () (not @t157)) % 0.38/0.58 (define @t159 () (forall @t44 (not @t43))) % 0.38/0.58 (define @t160 () (not @t159)) % 0.38/0.58 (define @t161 () (tptp.r2 @t105 @t109)) % 0.38/0.58 (define @t162 () (@quantifiers_skolemize @t108 2)) % 0.38/0.58 (define @t163 () (@quantifiers_skolemize @t108 0)) % 0.38/0.58 (define @t164 () (not @t161)) % 0.38/0.58 (define @t165 () (or @t164 (not (tptp.r4 @t105 @t109 @t163)) (not (tptp.r3 @t162 @t105 @t163)) (not (tptp.r4 @t105 @t105 @t162)))) % 0.38/0.58 (define @t166 () (tptp.r1 @t109)) % 0.38/0.58 (define @t167 () (not @t166)) % 0.38/0.58 (define @t168 () (or @t167 @t164)) % 0.38/0.58 (assume @p1 (exists @t5 (forall (@list @t2) (or (and (not @t4) (not @t3)) (and @t4 @t3))))) % 0.38/0.58 (assume @p2 (forall (@list @t9) (exists (@list @t6) (forall (@list @t7) (or (and (not @t10) (not @t8)) (and @t10 @t8)))))) % 0.38/0.58 (assume @p3 (forall (@list @t15 @t14) (exists (@list @t11) (forall (@list @t12) (or (and (not @t16) (not @t13)) (and @t16 @t13)))))) % 0.38/0.58 (assume @p4 (forall (@list @t21 @t20) (exists (@list @t17) (forall (@list @t18) (or (and (not @t22) (not @t19)) (and @t22 @t19)))))) % 0.38/0.58 (assume @p5 (forall (@list @t25 @t24) (exists (@list @t26) (and (exists (@list @t27) (and (exists (@list @t28) (and (tptp.r2 @t24 @t28) (tptp.r3 @t25 @t28 @t27))) (= @t27 @t26))) (exists (@list @t23) (and (tptp.r2 @t23 @t26) (tptp.r3 @t25 @t24 @t23))))))) % 0.38/0.58 (assume @p6 @t52) % 0.38/0.58 (assume @p7 (forall (@list @t54 @t53) (or (forall (@list @t55) (or (forall (@list @t56) (or (not (tptp.r2 @t54 @t56)) (not (= @t56 @t55)))) (not (tptp.r2 @t53 @t55)))) (= @t54 @t53)))) % 0.38/0.58 (assume @p8 (forall (@list @t57) (exists (@list @t58) (and (exists (@list @t59) (and (tptp.r1 @t59) (tptp.r3 @t57 @t59 @t58))) (= @t58 @t57))))) % 0.38/0.58 (assume @p9 (forall (@list @t63) (exists (@list @t61) (and (exists (@list @t62) (and (tptp.r1 @t62) (tptp.r4 @t63 @t62 @t61))) (exists (@list @t60) (and (tptp.r1 @t60) (= @t61 @t60))))))) % 0.38/0.58 (assume @p10 (forall (@list @t65) (or (exists (@list @t67) (and (tptp.r1 @t67) (= @t65 @t67))) (exists (@list @t66 @t64) (and (tptp.r2 @t66 @t64) (= @t65 @t64)))))) % 0.38/0.58 (assume @p11 @t78) % 0.38/0.58 (assume @p12 @t85) % 0.38/0.58 (assume @p13 true) % 0.38/0.58 (step @p14 :rule bool-double-not-elim :args (@t87)) % 0.38/0.58 (step @p15 :rule bool-double-not-elim :args (@t86)) % 0.38/0.58 (step @p16 :rule cong :premises (@p15) :args (@t89)) % 0.38/0.58 (step @p17 :rule cong :premises (@p16) :args (@t90)) % 0.38/0.58 (step @p18 :rule exists-elim :args ((= (exists @t83 @t88) @t90))) % 0.38/0.58 (step @p19 :rule trans :premises (@p18 @p17)) % 0.38/0.58 (step @p20 :rule aci_norm :args ((= (or @t88 false) @t88))) % 0.38/0.58 (step @p21 :rule evaluate :args ((not true))) % 0.38/0.58 (step @p22 :rule eq-refl :args (@t66)) % 0.38/0.58 (step @p23 :rule cong :premises (@p22) :args (@t91)) % 0.38/0.58 (step @p24 :rule trans :premises (@p23 @p21)) % 0.38/0.58 (step @p25 :rule refl :args (@t88)) % 0.38/0.58 (step @p26 :rule nary_cong :premises (@p25 @p24) :args (@t92)) % 0.38/0.58 (step @p27 :rule trans :premises (@p26 @p20)) % 0.38/0.58 (step @p28 :rule quant-var-elim-eq :args ((= (forall @t50 @t94) @t92))) % 0.38/0.58 (step @p29 :rule aci_norm :args ((= @t95 @t94))) % 0.38/0.58 (step @p30 :rule cong :premises (@p29) :args ((forall @t50 @t95))) % 0.38/0.58 (step @p31 :rule trans :premises (@p30 @p28)) % 0.38/0.58 (step @p32 :rule trans :premises (@p31 @p27)) % 0.38/0.58 (step @p33 :rule eq-symm :args (@t66 @t33)) % 0.38/0.58 (step @p34 :rule cong :premises (@p33) :args (@t79)) % 0.38/0.58 (step @p35 :rule refl :args (@t80)) % 0.38/0.58 (step @p36 :rule nary_cong :premises (@p35 @p34) :args (@t81)) % 0.38/0.58 (step @p37 :rule cong :premises (@p36) :args (@t82)) % 0.38/0.58 (step @p38 :rule trans :premises (@p37 @p32)) % 0.38/0.58 (step @p39 :rule cong :premises (@p38) :args (@t84)) % 0.38/0.58 (step @p40 :rule trans :premises (@p39 @p19)) % 0.38/0.58 (step @p41 :rule cong :premises (@p40) :args (@t85)) % 0.38/0.58 (step @p42 :rule trans :premises (@p41 @p14)) % 0.38/0.58 (step @p43 :rule eq_resolve :premises (@p12 @p42)) % 0.38/0.58 (step @p44 :rule refl :args (@t70)) % 0.38/0.58 (step @p45 :rule aci_norm :args ((= (or @t96 false) @t96))) % 0.38/0.58 (step @p46 :rule eq-refl :args (@t68)) % 0.38/0.58 (step @p47 :rule cong :premises (@p46) :args (@t97)) % 0.38/0.58 (step @p48 :rule trans :premises (@p47 @p21)) % 0.38/0.58 (step @p49 :rule refl :args (@t96)) % 0.38/0.58 (step @p50 :rule nary_cong :premises (@p49 @p48) :args (@t98)) % 0.38/0.58 (step @p51 :rule trans :premises (@p50 @p45)) % 0.38/0.58 (step @p52 :rule quant-var-elim-eq :args ((= (forall @t75 (or @t72 @t73 @t99)) @t98))) % 0.38/0.58 (step @p53 :rule refl :args (@t99)) % 0.38/0.58 (step @p54 :rule refl :args (@t73)) % 0.38/0.58 (step @p55 :rule eq-symm :args (@t68 @t71)) % 0.38/0.58 (step @p56 :rule cong :premises (@p55) :args (@t99)) % 0.38/0.58 (step @p57 :rule nary_cong :premises (@p56 @p54 @p53) :args (@t100)) % 0.38/0.58 (step @p58 :rule aci_norm :args ((= @t101 @t100))) % 0.38/0.58 (step @p59 :rule trans :premises (@p58 @p57)) % 0.38/0.58 (step @p60 :rule cong :premises (@p59) :args ((forall @t75 @t101))) % 0.38/0.58 (step @p61 :rule trans :premises (@p60 @p52)) % 0.38/0.58 (step @p62 :rule trans :premises (@p61 @p51)) % 0.38/0.58 (step @p63 :rule eq-symm :args (@t71 @t68)) % 0.38/0.58 (step @p64 :rule cong :premises (@p63) :args (@t72)) % 0.38/0.58 (step @p65 :rule refl :args (@t73)) % 0.38/0.58 (step @p66 :rule nary_cong :premises (@p65 @p64) :args (@t74)) % 0.38/0.58 (step @p67 :rule cong :premises (@p66) :args (@t76)) % 0.38/0.58 (step @p68 :rule trans :premises (@p67 @p62)) % 0.38/0.58 (step @p69 :rule nary_cong :premises (@p68 @p44) :args (@t77)) % 0.38/0.58 (step @p70 :rule cong :premises (@p69) :args (@t78)) % 0.38/0.58 (step @p71 :rule eq_resolve :premises (@p11 @p70)) % 0.38/0.58 (step @p72 :rule instantiate :premises (@p71) :args ((@list @t105 @t109))) % 0.38/0.58 (step @p73 :rule aci_norm :args ((= @t116 (or @t113 @t112 @t111 @t110)))) % 0.38/0.58 (step @p74 :rule cong :premises (@p73) :args (@t117)) % 0.38/0.58 (step @p75 :rule quant-merge-prenex :args ((= (forall @t50 @t118) @t117))) % 0.38/0.58 (step @p76 :rule alpha_equiv :args (@t119 (@list @t102) (@list @t29))) % 0.38/0.58 (step @p77 :rule alpha_equiv :args (@t120 (@list @t106) @t122)) % 0.38/0.58 (step @p78 :rule nary_cong :premises (@p77 @p76) :args (@t123)) % 0.38/0.58 (step @p79 :rule quant-miniscope-or :args ((= @t118 @t123))) % 0.38/0.58 (step @p80 :rule trans :premises (@p79 @p78)) % 0.38/0.58 (step @p81 :rule symm :premises (@p80)) % 0.38/0.58 (step @p82 :rule cong :premises (@p81) :args ((forall @t50 (or @t129 @t124)))) % 0.38/0.58 (step @p83 :rule trans :premises (@p82 @p75)) % 0.38/0.58 (step @p84 :rule trans :premises (@p83 @p74)) % 0.38/0.58 (step @p85 :rule bool-double-not-elim :args (@t124)) % 0.38/0.58 (step @p86 :rule bool-double-not-elim :args (@t129)) % 0.38/0.58 (step @p87 :rule nary_cong :premises (@p86 @p85) :args ((or (not @t131) (not @t130)))) % 0.38/0.58 (step @p88 :rule bool-and-de-morgan :args (@t131 @t130 true)) % 0.38/0.58 (step @p89 :rule trans :premises (@p88 @p87)) % 0.38/0.58 (step @p90 :rule cong :premises (@p89) :args (@t133)) % 0.38/0.58 (step @p91 :rule trans :premises (@p90 @p84)) % 0.38/0.58 (step @p92 :rule cong :premises (@p91) :args (@t134)) % 0.38/0.58 (step @p93 :rule exists-elim :args ((= (exists @t50 @t132) @t134))) % 0.38/0.58 (step @p94 :rule trans :premises (@p93 @p92)) % 0.38/0.58 (step @p95 :rule bool-and-de-morgan :args (@t34 @t32 true)) % 0.38/0.58 (step @p96 :rule cong :premises (@p95) :args (@t135)) % 0.38/0.58 (step @p97 :rule cong :premises (@p96) :args (@t136)) % 0.38/0.58 (step @p98 :rule exists-elim :args ((= @t37 @t136))) % 0.38/0.58 (step @p99 :rule trans :premises (@p98 @p97)) % 0.38/0.58 (step @p100 :rule aci_norm :args ((= (or false @t126 @t125) @t127))) % 0.38/0.58 (step @p101 :rule refl :args (@t125)) % 0.38/0.58 (step @p102 :rule refl :args (@t126)) % 0.38/0.58 (step @p103 :rule eq-refl :args (@t33)) % 0.38/0.58 (step @p104 :rule cong :premises (@p103) :args (@t137)) % 0.38/0.58 (step @p105 :rule trans :premises (@p104 @p21)) % 0.38/0.58 (step @p106 :rule nary_cong :premises (@p105 @p102 @p101) :args (@t138)) % 0.38/0.58 (step @p107 :rule trans :premises (@p106 @p100)) % 0.38/0.58 (step @p108 :rule cong :premises (@p107) :args ((forall @t128 @t138))) % 0.38/0.58 (step @p109 :rule quant-var-elim-eq :args ((= (forall @t47 (or (not @t39) @t141 @t126 @t139)) @t138))) % 0.38/0.58 (step @p110 :rule refl :args (@t139)) % 0.38/0.58 (step @p111 :rule refl :args (@t126)) % 0.38/0.58 (step @p112 :rule refl :args (@t141)) % 0.38/0.58 (step @p113 :rule eq-symm :args (@t33 @t38)) % 0.38/0.58 (step @p114 :rule cong :premises (@p113) :args (@t141)) % 0.38/0.58 (step @p115 :rule nary_cong :premises (@p114 @p112 @p111 @p110) :args (@t142)) % 0.38/0.58 (step @p116 :rule aci_norm :args ((= @t143 @t142))) % 0.38/0.58 (step @p117 :rule trans :premises (@p116 @p115)) % 0.38/0.58 (step @p118 :rule cong :premises (@p117) :args (@t144)) % 0.38/0.58 (step @p119 :rule trans :premises (@p118 @p109)) % 0.38/0.58 (step @p120 :rule cong :premises (@p119) :args (@t145)) % 0.38/0.58 (step @p121 :rule quant-merge-prenex :args ((= @t145 @t146))) % 0.38/0.58 (step @p122 :rule symm :premises (@p121)) % 0.38/0.58 (step @p123 :rule quant_var_reordering :args ((= (forall @t147 @t143) @t146))) % 0.38/0.58 (step @p124 :rule trans :premises (@p123 @p122 @p120)) % 0.38/0.58 (step @p125 :rule trans :premises (@p124 @p108)) % 0.38/0.58 (step @p126 :rule aci_norm :args ((= @t149 @t143))) % 0.38/0.58 (step @p127 :rule cong :premises (@p126) :args (@t150)) % 0.38/0.58 (step @p128 :rule trans :premises (@p127 @p125)) % 0.38/0.58 (step @p129 :rule quant-merge-prenex :args ((= (forall @t47 @t151) @t150))) % 0.38/0.58 (step @p130 :rule alpha_equiv :args (@t152 @t122 (@list @t40))) % 0.38/0.58 (step @p131 :rule nary_cong :premises (@p130 @p112) :args (@t153)) % 0.38/0.58 (step @p132 :rule quant-miniscope-or :args ((= @t151 @t153))) % 0.38/0.58 (step @p133 :rule trans :premises (@p132 @p131)) % 0.38/0.58 (step @p134 :rule symm :premises (@p133)) % 0.38/0.58 (step @p135 :rule cong :premises (@p134) :args ((forall @t47 (or @t154 @t141)))) % 0.38/0.58 (step @p136 :rule trans :premises (@p135 @p129)) % 0.38/0.58 (step @p137 :rule trans :premises (@p136 @p128)) % 0.38/0.58 (step @p138 :rule bool-double-not-elim :args (@t154)) % 0.38/0.58 (step @p139 :rule nary_cong :premises (@p138 @p112) :args ((or (not @t155) @t141))) % 0.38/0.58 (step @p140 :rule bool-and-de-morgan :args (@t155 @t140 true)) % 0.38/0.58 (step @p141 :rule trans :premises (@p140 @p139)) % 0.38/0.58 (step @p142 :rule cong :premises (@p141) :args (@t157)) % 0.38/0.58 (step @p143 :rule trans :premises (@p142 @p137)) % 0.38/0.58 (step @p144 :rule cong :premises (@p143) :args (@t158)) % 0.38/0.58 (step @p145 :rule exists-elim :args ((= (exists @t47 @t156) @t158))) % 0.38/0.58 (step @p146 :rule trans :premises (@p145 @p144)) % 0.38/0.58 (step @p147 :rule eq-symm :args (@t38 @t33)) % 0.38/0.58 (step @p148 :rule bool-and-de-morgan :args (@t42 @t41 true)) % 0.38/0.58 (step @p149 :rule cong :premises (@p148) :args (@t159)) % 0.38/0.58 (step @p150 :rule cong :premises (@p149) :args (@t160)) % 0.38/0.58 (step @p151 :rule exists-elim :args ((= @t45 @t160))) % 0.38/0.58 (step @p152 :rule trans :premises (@p151 @p150)) % 0.38/0.58 (step @p153 :rule nary_cong :premises (@p152 @p147) :args (@t46)) % 0.38/0.58 (step @p154 :rule cong :premises (@p153) :args (@t48)) % 0.38/0.58 (step @p155 :rule trans :premises (@p154 @p146)) % 0.38/0.58 (step @p156 :rule nary_cong :premises (@p155 @p99) :args (@t49)) % 0.38/0.58 (step @p157 :rule cong :premises (@p156) :args (@t51)) % 0.38/0.58 (step @p158 :rule trans :premises (@p157 @p94)) % 0.38/0.58 (step @p159 :rule cong :premises (@p158) :args (@t52)) % 0.38/0.58 (step @p160 :rule eq_resolve :premises (@p6 @p159)) % 0.38/0.58 (step @p161 :rule instantiate :premises (@p160) :args ((@list @t105 @t105))) % 0.38/0.58 (step @p162 :rule skolemize :premises (@p161)) % 0.38/0.58 (step @p163 :rule bool-double-not-elim :args (@t161)) % 0.38/0.58 (step @p164 :rule refl :args (@t165)) % 0.38/0.58 (step @p165 :rule nary_cong :premises (@p164 @p163) :args ((or @t165 (not @t164)))) % 0.38/0.58 (step @p166 :rule cnf_or_neg :args (@t165 0)) % 0.38/0.58 (step @p167 :rule eq_resolve :premises (@p166 @p165)) % 0.38/0.58 (step @p168 :rule reordering :premises (@p167) :args ((or @t161 @t165))) % 0.38/0.58 (step @p169 :rule chain_m_resolution :premises (@p168 @p162) :args (@t161 (@list true) (@list @t165))) % 0.38/0.58 (step @p170 :rule cnf_or_pos :args (@t168)) % 0.38/0.58 (step @p171 :rule reordering :premises (@p170) :args ((or @t164 @t167 (not @t168)))) % 0.38/0.58 (step @p172 :rule chain_m_resolution :premises (@p171 @p169 @p72) :args (@t167 (@list false false) (@list @t161 @t168))) % 0.38/0.58 (assume-push @p179 @t87) % 0.38/0.58 (step @p174 :rule instantiate :premises (@p43) :args ((@list @t109))) % 0.38/0.58 (step-pop @p180 :rule scope :premises (@p174)) % 0.38/0.58 (step @p175 :rule process_scope :premises (@p180) :args (@t166)) % 0.38/0.58 (step @p177 :rule implies_elim :premises (@p175)) % 0.38/0.58 (step @p178 false :rule chain_m_resolution :premises (@p177 @p172 @p43) :args (false (@list true false) (@list @t166 @t87))) % 0.38/0.58 ) % 0.38/0.58 % SZS output end Proof % 0.38/0.58 % cvc5 exiting %------------------------------------------------------------------------------