%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV095^5 : 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 : n024.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:55:26 AM UTC 2026 % Result : Theorem 0.82s 1.07s % Output : Proof 0.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SEV095^5 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.06/0.25 % Computer : n024.cluster.edu % 0.06/0.25 % Model : x86_64 x86_64 % 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.06/0.25 % Memory : 8042.1875MB % 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.06/0.25 % CPULimit : 300 % 0.06/0.25 % WCLimit : 300 % 0.06/0.25 % DateTime : Tue Jun 2 13:12:30 EDT 2026 % 0.06/0.25 % CPUTime : % 0.15/0.32 %----Proving TH0 % 0.82/1.07 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.82/1.07 % SZS status Theorem % 0.82/1.07 % SZS output start Proof % 0.82/1.07 ( % 0.82/1.07 (declare-sort $$unsorted 0) % 0.82/1.07 (define @t1 () (@var "Xw_2" $$unsorted)) % 0.82/1.07 (define @t2 () (@var "Xz" (-> $$unsorted Bool))) % 0.82/1.07 (define @t3 () (@var "Xx" (-> $$unsorted Bool))) % 0.82/1.07 (define @t4 () (@var "Xr_28" (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool))) % 0.82/1.07 (define @t5 () (_ @t4 @t3)) % 0.82/1.07 (define @t6 () (_ (_ @t5 @t2) @t1)) % 0.82/1.07 (define @t7 () (@var "Xr_27" (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool))) % 0.82/1.07 (define @t8 () (_ @t7 @t3)) % 0.82/1.07 (define @t9 () (_ (_ @t8 @t2) @t1)) % 0.82/1.07 (define @t10 () (or @t9 @t6)) % 0.82/1.07 (define @t11 () (@list @t1)) % 0.82/1.07 (define @t12 () (forall @t11 @t10)) % 0.82/1.07 (define @t13 () (@var "Xy" (-> $$unsorted Bool))) % 0.82/1.07 (define @t14 () (_ (_ (_ @t4 @t13) @t2) @t1)) % 0.82/1.07 (define @t15 () (_ (_ (_ @t7 @t13) @t2) @t1)) % 0.82/1.07 (define @t16 () (or @t15 @t14)) % 0.82/1.07 (define @t17 () (forall @t11 @t16)) % 0.82/1.07 (define @t18 () (_ (_ @t5 @t13) @t1)) % 0.82/1.07 (define @t19 () (_ (_ @t8 @t13) @t1)) % 0.82/1.07 (define @t20 () (or @t19 @t18)) % 0.82/1.07 (define @t21 () (forall @t11 @t20)) % 0.82/1.07 (define @t22 () (and @t21 @t17)) % 0.82/1.07 (define @t23 () (=> @t22 @t12)) % 0.82/1.07 (define @t24 () (@list @t3 @t13 @t2)) % 0.82/1.07 (define @t25 () (forall @t24 @t23)) % 0.82/1.07 (define @t26 () (_ (_ @t5 @t3) @t1)) % 0.82/1.07 (define @t27 () (_ (_ @t8 @t3) @t1)) % 0.82/1.07 (define @t28 () (or @t27 @t26)) % 0.82/1.07 (define @t29 () (@list @t3 @t1)) % 0.82/1.07 (define @t30 () (forall @t29 @t28)) % 0.82/1.07 (define @t31 () (@var "Xz" $$unsorted)) % 0.82/1.07 (define @t32 () (@var "Xv" (-> $$unsorted Bool))) % 0.82/1.07 (define @t33 () (_ @t32 @t31)) % 0.82/1.07 (define @t34 () (@var "Xu" (-> $$unsorted Bool))) % 0.82/1.07 (define @t35 () (_ @t34 @t31)) % 0.82/1.07 (define @t36 () (@list @t31)) % 0.82/1.07 (define @t37 () (forall @t36 (=> @t35 @t33))) % 0.82/1.07 (define @t38 () (_ (_ (_ @t4 @t34) @t32) @t1)) % 0.82/1.07 (define @t39 () (_ (_ (_ @t7 @t34) @t32) @t1)) % 0.82/1.07 (define @t40 () (or @t39 @t38)) % 0.82/1.07 (define @t41 () (forall @t11 @t40)) % 0.82/1.07 (define @t42 () (=> @t41 @t37)) % 0.82/1.07 (define @t43 () (@list @t34 @t32)) % 0.82/1.07 (define @t44 () (forall @t43 @t42)) % 0.82/1.07 (define @t45 () (and @t44 @t30 @t25)) % 0.82/1.07 (define @t46 () (@list @t4 @t7)) % 0.82/1.07 (define @t47 () (exists @t46 @t45)) % 0.82/1.07 (define @t48 () (not @t47)) % 0.82/1.07 (define @t49 () (@var "BOUND_VARIABLE_7525" $$unsorted)) % 0.82/1.07 (define @t50 () (_ @t4 @t3 @t2 @t49)) % 0.82/1.07 (define @t51 () (_ @t7 @t3 @t2 @t49)) % 0.82/1.07 (define @t52 () (_ @t4 @t13 @t2 @t1)) % 0.82/1.07 (define @t53 () (_ @t7 @t13 @t2 @t1)) % 0.82/1.07 (define @t54 () (forall @t11 (or @t53 @t52))) % 0.82/1.07 (define @t55 () (not @t54)) % 0.82/1.07 (define @t56 () (_ @t4 @t3 @t13 @t1)) % 0.82/1.07 (define @t57 () (_ @t7 @t3 @t13 @t1)) % 0.82/1.07 (define @t58 () (forall @t11 (or @t57 @t56))) % 0.82/1.07 (define @t59 () (not @t58)) % 0.82/1.07 (define @t60 () (or @t59 @t55 @t51 @t50)) % 0.82/1.07 (define @t61 () (@list @t3 @t13 @t2 @t49)) % 0.82/1.07 (define @t62 () (forall @t61 @t60)) % 0.82/1.07 (define @t63 () (not @t62)) % 0.82/1.07 (define @t64 () (_ @t4 @t3 @t3 @t1)) % 0.82/1.07 (define @t65 () (_ @t7 @t3 @t3 @t1)) % 0.82/1.07 (define @t66 () (forall @t29 (or @t65 @t64))) % 0.82/1.07 (define @t67 () (not @t66)) % 0.82/1.07 (define @t68 () (@var "BOUND_VARIABLE_7489" $$unsorted)) % 0.82/1.07 (define @t69 () (_ @t32 @t68)) % 0.82/1.07 (define @t70 () (not (_ @t34 @t68))) % 0.82/1.07 (define @t71 () (_ @t4 @t34 @t32 @t1)) % 0.82/1.07 (define @t72 () (_ @t7 @t34 @t32 @t1)) % 0.82/1.07 (define @t73 () (forall @t11 (or @t72 @t71))) % 0.82/1.07 (define @t74 () (not @t73)) % 0.82/1.07 (define @t75 () (or @t74 @t70 @t69)) % 0.82/1.07 (define @t76 () (@list @t34 @t32 @t68)) % 0.82/1.07 (define @t77 () (forall @t76 @t75)) % 0.82/1.07 (define @t78 () (not @t77)) % 0.82/1.07 (define @t79 () (or @t78 @t67 @t63)) % 0.82/1.07 (define @t80 () (forall @t46 @t79)) % 0.82/1.07 (define @t81 () (and @t77 @t66 @t62)) % 0.82/1.07 (define @t82 () (forall @t46 (not @t81))) % 0.82/1.07 (define @t83 () (not @t82)) % 0.82/1.07 (define @t84 () (or @t51 @t50)) % 0.82/1.07 (define @t85 () (or @t59 @t55 @t84)) % 0.82/1.07 (define @t86 () (forall @t61 @t85)) % 0.82/1.07 (define @t87 () (@list @t49)) % 0.82/1.07 (define @t88 () (forall @t87 @t85)) % 0.82/1.07 (define @t89 () (forall @t87 @t84)) % 0.82/1.07 (define @t90 () (or @t59 @t55 @t89)) % 0.82/1.07 (define @t91 () (_ @t4 @t3 @t2 @t1)) % 0.82/1.07 (define @t92 () (_ @t7 @t3 @t2 @t1)) % 0.82/1.07 (define @t93 () (forall @t11 (or @t92 @t91))) % 0.82/1.07 (define @t94 () (or @t59 @t55 @t93)) % 0.82/1.07 (define @t95 () (and @t58 @t54)) % 0.82/1.07 (define @t96 () (or @t70 @t69)) % 0.82/1.07 (define @t97 () (or @t74 @t96)) % 0.82/1.07 (define @t98 () (forall @t76 @t97)) % 0.82/1.07 (define @t99 () (@list @t68)) % 0.82/1.07 (define @t100 () (forall @t99 @t97)) % 0.82/1.07 (define @t101 () (forall @t99 @t96)) % 0.82/1.07 (define @t102 () (or @t74 @t101)) % 0.82/1.07 (define @t103 () (_ @t32 @t31)) % 0.82/1.07 (define @t104 () (_ @t34 @t31)) % 0.82/1.07 (define @t105 () (forall @t36 (or (not @t104) @t103))) % 0.82/1.07 (define @t106 () (not @t35)) % 0.82/1.07 (define @t107 () (or @t106 @t33)) % 0.82/1.07 (define @t108 () (@list @t13 @t2)) % 0.82/1.07 (define @t109 () (= @t13 @t2)) % 0.82/1.07 (define @t110 () (not @t109)) % 0.82/1.07 (define @t111 () (or @t110 @t109)) % 0.82/1.07 (define @t112 () (not (= @t13 @t13))) % 0.82/1.07 (define @t113 () (or @t112 @t110 @t109)) % 0.82/1.07 (define @t114 () (= @t3 @t2)) % 0.82/1.07 (define @t115 () (= @t3 @t13)) % 0.82/1.07 (define @t116 () (not @t115)) % 0.82/1.07 (define @t117 () (or @t116 @t116 @t110 @t114)) % 0.82/1.07 (define @t118 () (@list @t3)) % 0.82/1.07 (define @t119 () (or @t116 @t110 @t114)) % 0.82/1.07 (define @t120 () (forall @t118 @t119)) % 0.82/1.07 (define @t121 () (forall @t108 @t120)) % 0.82/1.07 (define @t122 () (forall (@list @t13 @t2 @t3) @t119)) % 0.82/1.07 (define @t123 () (forall @t24 @t119)) % 0.82/1.07 (define @t124 () (@var "BOUND_VARIABLE_74674" (-> $$unsorted Bool))) % 0.82/1.07 (define @t125 () (@var "BOUND_VARIABLE_74673" (-> $$unsorted Bool))) % 0.82/1.07 (define @t126 () (lambda (@list @t125 @t124 (@var "BOUND_VARIABLE_74675" $$unsorted)) (= @t125 @t124))) % 0.82/1.07 (define @t127 () (_ @t126 @t3 @t2 @t49)) % 0.82/1.07 (define @t128 () (lambda (@list (@var "BOUND_VARIABLE_74892" (-> $$unsorted Bool)) (@var "BOUND_VARIABLE_74893" (-> $$unsorted Bool)) (@var "BOUND_VARIABLE_74894" $$unsorted)) false)) % 0.82/1.07 (define @t129 () (_ @t128 @t3 @t2 @t49)) % 0.82/1.07 (define @t130 () (_ @t126 @t13 @t2 @t1)) % 0.82/1.07 (define @t131 () (_ @t128 @t13 @t2 @t1)) % 0.82/1.07 (define @t132 () (or @t131 @t130)) % 0.82/1.07 (define @t133 () (forall @t11 @t132)) % 0.82/1.07 (define @t134 () (not @t133)) % 0.82/1.07 (define @t135 () (_ @t126 @t3 @t13 @t1)) % 0.82/1.07 (define @t136 () (_ @t128 @t3 @t13 @t1)) % 0.82/1.07 (define @t137 () (or @t136 @t135)) % 0.82/1.07 (define @t138 () (forall @t11 @t137)) % 0.82/1.07 (define @t139 () (not @t138)) % 0.82/1.07 (define @t140 () (or @t139 @t134 @t129 @t127)) % 0.82/1.07 (define @t141 () (forall @t61 @t140)) % 0.82/1.07 (define @t142 () (not @t141)) % 0.82/1.07 (define @t143 () (_ @t126 @t3 @t3 @t1)) % 0.82/1.07 (define @t144 () (_ @t128 @t3 @t3 @t1)) % 0.82/1.07 (define @t145 () (or @t144 @t143)) % 0.82/1.07 (define @t146 () (forall @t29 @t145)) % 0.82/1.07 (define @t147 () (not @t146)) % 0.82/1.07 (define @t148 () (@list @t32 @t68)) % 0.82/1.07 (define @t149 () (not @t69)) % 0.82/1.07 (define @t150 () (or @t149 @t69)) % 0.82/1.07 (define @t151 () (not (= @t32 @t32))) % 0.82/1.07 (define @t152 () (or @t151 @t149 @t69)) % 0.82/1.07 (define @t153 () (= @t34 @t32)) % 0.82/1.07 (define @t154 () (not @t153)) % 0.82/1.07 (define @t155 () (or @t154 @t154 @t70 @t69)) % 0.82/1.07 (define @t156 () (@list @t34)) % 0.82/1.07 (define @t157 () (or @t154 @t70 @t69)) % 0.82/1.07 (define @t158 () (forall @t156 @t157)) % 0.82/1.07 (define @t159 () (forall @t148 @t158)) % 0.82/1.07 (define @t160 () (forall (@list @t32 @t68 @t34) @t157)) % 0.82/1.07 (define @t161 () (_ @t126 @t34 @t32 @t1)) % 0.82/1.07 (define @t162 () (_ @t128 @t34 @t32 @t1)) % 0.82/1.07 (define @t163 () (or @t162 @t161)) % 0.82/1.07 (define @t164 () (forall @t11 @t163)) % 0.82/1.07 (define @t165 () (not @t164)) % 0.82/1.07 (define @t166 () (or @t165 @t70 @t69)) % 0.82/1.07 (define @t167 () (forall @t76 @t166)) % 0.82/1.07 (define @t168 () (not @t167)) % 0.82/1.07 (define @t169 () (or @t168 @t147 @t142)) % 0.82/1.07 (assume @p1 @t48) % 0.82/1.07 (assume @p2 true) % 0.82/1.07 (step @p3 :rule bool-double-not-elim :args (@t80)) % 0.82/1.07 (step @p4 :rule aci_norm :args ((= (or @t78 (or @t67 @t63)) @t79))) % 0.82/1.07 (step @p5 :rule bool-and-de-morgan :args (@t66 @t62 true)) % 0.82/1.07 (step @p6 :rule refl :args (@t78)) % 0.82/1.07 (step @p7 :rule nary_cong :premises (@p6 @p5) :args ((or @t78 (not (and @t66 @t62))))) % 0.82/1.07 (step @p8 :rule bool-and-de-morgan :args (@t77 @t66 (and @t62))) % 0.82/1.07 (step @p9 :rule trans :premises (@p8 @p7)) % 0.82/1.07 (step @p10 :rule trans :premises (@p9 @p4)) % 0.82/1.07 (step @p11 :rule cong :premises (@p10) :args (@t82)) % 0.82/1.07 (step @p12 :rule cong :premises (@p11) :args (@t83)) % 0.82/1.07 (step @p13 :rule exists-elim :args ((= (exists @t46 @t81) @t83))) % 0.82/1.07 (step @p14 :rule trans :premises (@p13 @p12)) % 0.82/1.07 (step @p15 :rule aci_norm :args ((= @t85 @t60))) % 0.82/1.07 (step @p16 :rule cong :premises (@p15) :args (@t86)) % 0.82/1.07 (step @p17 :rule quant-merge-prenex :args ((= (forall @t24 @t88) @t86))) % 0.82/1.07 (step @p18 :rule alpha_equiv :args (@t89 (@list @t49) (@list @t1))) % 0.82/1.07 (step @p19 :rule refl :args (@t55)) % 0.82/1.07 (step @p20 :rule refl :args (@t59)) % 0.82/1.07 (step @p21 :rule nary_cong :premises (@p20 @p19 @p18) :args (@t90)) % 0.82/1.07 (step @p22 :rule quant-miniscope-or :args ((= @t88 @t90))) % 0.82/1.07 (step @p23 :rule trans :premises (@p22 @p21)) % 0.82/1.07 (step @p24 :rule symm :premises (@p23)) % 0.82/1.07 (step @p25 :rule cong :premises (@p24) :args ((forall @t24 @t94))) % 0.82/1.07 (step @p26 :rule trans :premises (@p25 @p17)) % 0.82/1.07 (step @p27 :rule trans :premises (@p26 @p16)) % 0.82/1.07 (step @p28 :rule aci_norm :args ((= (or (or @t59 @t55) @t93) @t94))) % 0.82/1.07 (step @p29 :rule refl :args (@t93)) % 0.82/1.07 (step @p30 :rule bool-and-de-morgan :args (@t58 @t54 true)) % 0.82/1.07 (step @p31 :rule nary_cong :premises (@p30 @p29) :args ((or (not @t95) @t93))) % 0.82/1.07 (step @p32 :rule trans :premises (@p31 @p28)) % 0.82/1.07 (step @p33 :rule bool-impl-elim :args (@t95 @t93)) % 0.82/1.07 (step @p34 :rule trans :premises (@p33 @p32)) % 0.82/1.07 (step @p35 :rule cong :premises (@p34) :args ((forall @t24 (=> @t95 @t93)))) % 0.82/1.07 (step @p36 :rule trans :premises (@p35 @p27)) % 0.82/1.07 (step @p37 :rule refl :args (@t91)) % 0.82/1.07 (step @p38 :rule refl :args (@t6)) % 0.82/1.07 (step @p39 :rule cong :premises (@p38 @p37) :args ((= @t6 @t91))) % 0.82/1.07 (step @p40 :rule symm :premises (@p39)) % 0.82/1.07 (step @p41 :rule eq_resolve :premises (@p38 @p40)) % 0.82/1.07 (step @p42 :rule refl :args (@t92)) % 0.82/1.07 (step @p43 :rule refl :args (@t9)) % 0.82/1.07 (step @p44 :rule cong :premises (@p43 @p42) :args ((= @t9 @t92))) % 0.82/1.07 (step @p45 :rule symm :premises (@p44)) % 0.82/1.07 (step @p46 :rule eq_resolve :premises (@p43 @p45)) % 0.82/1.07 (step @p47 :rule nary_cong :premises (@p46 @p41) :args (@t10)) % 0.82/1.07 (step @p48 :rule cong :premises (@p47) :args (@t12)) % 0.82/1.07 (step @p49 :rule refl :args (@t52)) % 0.82/1.07 (step @p50 :rule refl :args (@t14)) % 0.82/1.07 (step @p51 :rule cong :premises (@p50 @p49) :args ((= @t14 @t52))) % 0.82/1.07 (step @p52 :rule symm :premises (@p51)) % 0.82/1.07 (step @p53 :rule eq_resolve :premises (@p50 @p52)) % 0.82/1.07 (step @p54 :rule refl :args (@t53)) % 0.82/1.07 (step @p55 :rule refl :args (@t15)) % 0.82/1.07 (step @p56 :rule cong :premises (@p55 @p54) :args ((= @t15 @t53))) % 0.82/1.07 (step @p57 :rule symm :premises (@p56)) % 0.82/1.07 (step @p58 :rule eq_resolve :premises (@p55 @p57)) % 0.82/1.07 (step @p59 :rule nary_cong :premises (@p58 @p53) :args (@t16)) % 0.82/1.07 (step @p60 :rule cong :premises (@p59) :args (@t17)) % 0.82/1.07 (step @p61 :rule refl :args (@t56)) % 0.82/1.07 (step @p62 :rule refl :args (@t18)) % 0.82/1.07 (step @p63 :rule cong :premises (@p62 @p61) :args ((= @t18 @t56))) % 0.82/1.07 (step @p64 :rule symm :premises (@p63)) % 0.82/1.07 (step @p65 :rule eq_resolve :premises (@p62 @p64)) % 0.82/1.07 (step @p66 :rule refl :args (@t57)) % 0.82/1.07 (step @p67 :rule refl :args (@t19)) % 0.82/1.07 (step @p68 :rule cong :premises (@p67 @p66) :args ((= @t19 @t57))) % 0.82/1.07 (step @p69 :rule symm :premises (@p68)) % 0.82/1.07 (step @p70 :rule eq_resolve :premises (@p67 @p69)) % 0.82/1.07 (step @p71 :rule nary_cong :premises (@p70 @p65) :args (@t20)) % 0.82/1.07 (step @p72 :rule cong :premises (@p71) :args (@t21)) % 0.82/1.07 (step @p73 :rule nary_cong :premises (@p72 @p60) :args (@t22)) % 0.82/1.07 (step @p74 :rule cong :premises (@p73 @p48) :args (@t23)) % 0.82/1.07 (step @p75 :rule cong :premises (@p74) :args (@t25)) % 0.82/1.07 (step @p76 :rule trans :premises (@p75 @p36)) % 0.82/1.07 (step @p77 :rule refl :args (@t64)) % 0.82/1.07 (step @p78 :rule refl :args (@t26)) % 0.82/1.07 (step @p79 :rule cong :premises (@p78 @p77) :args ((= @t26 @t64))) % 0.82/1.07 (step @p80 :rule symm :premises (@p79)) % 0.82/1.07 (step @p81 :rule eq_resolve :premises (@p78 @p80)) % 0.82/1.07 (step @p82 :rule refl :args (@t65)) % 0.82/1.07 (step @p83 :rule refl :args (@t27)) % 0.82/1.07 (step @p84 :rule cong :premises (@p83 @p82) :args ((= @t27 @t65))) % 0.82/1.07 (step @p85 :rule symm :premises (@p84)) % 0.82/1.07 (step @p86 :rule eq_resolve :premises (@p83 @p85)) % 0.82/1.07 (step @p87 :rule nary_cong :premises (@p86 @p81) :args (@t28)) % 0.82/1.07 (step @p88 :rule cong :premises (@p87) :args (@t30)) % 0.82/1.07 (step @p89 :rule aci_norm :args ((= @t97 @t75))) % 0.82/1.07 (step @p90 :rule cong :premises (@p89) :args (@t98)) % 0.82/1.07 (step @p91 :rule quant-merge-prenex :args ((= (forall @t43 @t100) @t98))) % 0.82/1.07 (step @p92 :rule alpha_equiv :args (@t101 (@list @t68) (@list @t31))) % 0.82/1.07 (step @p93 :rule refl :args (@t74)) % 0.82/1.07 (step @p94 :rule nary_cong :premises (@p93 @p92) :args (@t102)) % 0.82/1.07 (step @p95 :rule quant-miniscope-or :args ((= @t100 @t102))) % 0.82/1.07 (step @p96 :rule trans :premises (@p95 @p94)) % 0.82/1.07 (step @p97 :rule symm :premises (@p96)) % 0.82/1.07 (step @p98 :rule cong :premises (@p97) :args ((forall @t43 (or @t74 @t105)))) % 0.82/1.07 (step @p99 :rule trans :premises (@p98 @p91)) % 0.82/1.07 (step @p100 :rule trans :premises (@p99 @p90)) % 0.82/1.07 (step @p101 :rule bool-impl-elim :args (@t73 @t105)) % 0.82/1.07 (step @p102 :rule cong :premises (@p101) :args ((forall @t43 (=> @t73 @t105)))) % 0.82/1.07 (step @p103 :rule trans :premises (@p102 @p100)) % 0.82/1.07 (step @p104 :rule refl :args (@t103)) % 0.82/1.07 (step @p105 :rule refl :args (@t33)) % 0.82/1.07 (step @p106 :rule cong :premises (@p105 @p104) :args ((= @t33 @t103))) % 0.82/1.07 (step @p107 :rule symm :premises (@p106)) % 0.82/1.07 (step @p108 :rule eq_resolve :premises (@p105 @p107)) % 0.82/1.07 (step @p109 :rule refl :args (@t104)) % 0.82/1.07 (step @p110 :rule refl :args (@t35)) % 0.82/1.07 (step @p111 :rule cong :premises (@p110 @p109) :args ((= @t35 @t104))) % 0.82/1.07 (step @p112 :rule symm :premises (@p111)) % 0.82/1.07 (step @p113 :rule eq_resolve :premises (@p110 @p112)) % 0.82/1.07 (step @p114 :rule cong :premises (@p113) :args (@t106)) % 0.82/1.07 (step @p115 :rule nary_cong :premises (@p114 @p108) :args (@t107)) % 0.82/1.07 (step @p116 :rule cong :premises (@p115) :args ((forall @t36 @t107))) % 0.82/1.07 (step @p117 :rule bool-impl-elim :args (@t35 @t33)) % 0.82/1.07 (step @p118 :rule cong :premises (@p117) :args (@t37)) % 0.82/1.07 (step @p119 :rule trans :premises (@p118 @p116)) % 0.82/1.07 (step @p120 :rule refl :args (@t71)) % 0.82/1.07 (step @p121 :rule refl :args (@t38)) % 0.82/1.07 (step @p122 :rule cong :premises (@p121 @p120) :args ((= @t38 @t71))) % 0.82/1.07 (step @p123 :rule symm :premises (@p122)) % 0.82/1.07 (step @p124 :rule eq_resolve :premises (@p121 @p123)) % 0.82/1.07 (step @p125 :rule refl :args (@t72)) % 0.82/1.07 (step @p126 :rule refl :args (@t39)) % 0.82/1.07 (step @p127 :rule cong :premises (@p126 @p125) :args ((= @t39 @t72))) % 0.82/1.07 (step @p128 :rule symm :premises (@p127)) % 0.82/1.07 (step @p129 :rule eq_resolve :premises (@p126 @p128)) % 0.82/1.07 (step @p130 :rule nary_cong :premises (@p129 @p124) :args (@t40)) % 0.82/1.07 (step @p131 :rule cong :premises (@p130) :args (@t41)) % 0.82/1.07 (step @p132 :rule cong :premises (@p131 @p119) :args (@t42)) % 0.82/1.07 (step @p133 :rule cong :premises (@p132) :args (@t44)) % 0.82/1.07 (step @p134 :rule trans :premises (@p133 @p103)) % 0.82/1.07 (step @p135 :rule nary_cong :premises (@p134 @p88 @p76) :args (@t45)) % 0.82/1.07 (step @p136 :rule cong :premises (@p135) :args (@t47)) % 0.82/1.07 (step @p137 :rule trans :premises (@p136 @p14)) % 0.82/1.07 (step @p138 :rule cong :premises (@p137) :args (@t48)) % 0.82/1.07 (step @p139 :rule trans :premises (@p138 @p3)) % 0.82/1.07 (step @p140 :rule eq_resolve :premises (@p1 @p139)) % 0.82/1.07 (step @p141 :rule bool-impl-false1 :args (@t80)) % 0.82/1.07 (step @p142 :rule evaluate :args ((or false false false))) % 0.82/1.07 (step @p143 :rule evaluate :args ((not true))) % 0.82/1.07 (step @p144 :rule quant-unused-vars :args ((= (forall @t108 true) true))) % 0.82/1.07 (step @p145 :rule bool-or-taut2 :args (false @t109 false false)) % 0.82/1.07 (step @p146 :rule cong :premises (@p145) :args ((forall @t108 @t111))) % 0.82/1.07 (step @p147 :rule trans :premises (@p146 @p144)) % 0.82/1.07 (step @p148 :rule aci_norm :args ((= (or false @t110 @t109) @t111))) % 0.82/1.07 (step @p149 :rule refl :args (@t109)) % 0.82/1.07 (step @p150 :rule refl :args (@t110)) % 0.82/1.07 (step @p151 :rule eq-refl :args (@t13)) % 0.82/1.07 (step @p152 :rule cong :premises (@p151) :args (@t112)) % 0.82/1.07 (step @p153 :rule trans :premises (@p152 @p143)) % 0.82/1.07 (step @p154 :rule nary_cong :premises (@p153 @p150 @p149) :args (@t113)) % 0.82/1.07 (step @p155 :rule trans :premises (@p154 @p148)) % 0.82/1.07 (step @p156 :rule cong :premises (@p155) :args ((forall @t108 @t113))) % 0.82/1.07 (step @p157 :rule trans :premises (@p156 @p147)) % 0.82/1.07 (step @p158 :rule quant-var-elim-eq :args ((= (forall @t118 @t117) @t113))) % 0.82/1.07 (step @p159 :rule aci_norm :args ((= @t119 @t117))) % 0.82/1.07 (step @p160 :rule cong :premises (@p159) :args (@t120)) % 0.82/1.07 (step @p161 :rule trans :premises (@p160 @p158)) % 0.82/1.07 (step @p162 :rule cong :premises (@p161) :args (@t121)) % 0.82/1.07 (step @p163 :rule quant-merge-prenex :args ((= @t121 @t122))) % 0.82/1.07 (step @p164 :rule symm :premises (@p163)) % 0.82/1.07 (step @p165 :rule quant_var_reordering :args ((= @t123 @t122))) % 0.82/1.07 (step @p166 :rule trans :premises (@p165 @p164 @p162)) % 0.82/1.07 (step @p167 :rule trans :premises (@p166 @p157)) % 0.82/1.07 (step @p168 :rule quant-unused-vars :args ((= (forall @t61 @t119) @t123))) % 0.82/1.07 (step @p169 :rule trans :premises (@p168 @p167)) % 0.82/1.07 (step @p170 :rule aci_norm :args ((= (or @t116 @t110 false @t114) @t119))) % 0.82/1.07 (step @p171 :rule beta-reduce :args ((= @t127 @t114))) % 0.82/1.07 (step @p172 :rule beta-reduce :args ((= @t129 false))) % 0.82/1.07 (step @p173 :rule quant-unused-vars :args ((= (forall @t11 @t109) @t109))) % 0.82/1.07 (step @p174 :rule aci_norm :args ((= (or false @t109) @t109))) % 0.82/1.07 (step @p175 :rule beta-reduce :args ((= @t130 @t109))) % 0.82/1.07 (step @p176 :rule beta-reduce :args ((= @t131 false))) % 0.82/1.07 (step @p177 :rule nary_cong :premises (@p176 @p175) :args (@t132)) % 0.82/1.07 (step @p178 :rule trans :premises (@p177 @p174)) % 0.82/1.07 (step @p179 :rule cong :premises (@p178) :args (@t133)) % 0.82/1.07 (step @p180 :rule trans :premises (@p179 @p173)) % 0.82/1.07 (step @p181 :rule cong :premises (@p180) :args (@t134)) % 0.82/1.07 (step @p182 :rule quant-unused-vars :args ((= (forall @t11 @t115) @t115))) % 0.82/1.07 (step @p183 :rule aci_norm :args ((= (or false @t115) @t115))) % 0.82/1.07 (step @p184 :rule beta-reduce :args ((= @t135 @t115))) % 0.82/1.07 (step @p185 :rule beta-reduce :args ((= @t136 false))) % 0.82/1.07 (step @p186 :rule nary_cong :premises (@p185 @p184) :args (@t137)) % 0.82/1.07 (step @p187 :rule trans :premises (@p186 @p183)) % 0.82/1.07 (step @p188 :rule cong :premises (@p187) :args (@t138)) % 0.82/1.07 (step @p189 :rule trans :premises (@p188 @p182)) % 0.82/1.07 (step @p190 :rule cong :premises (@p189) :args (@t139)) % 0.82/1.07 (step @p191 :rule nary_cong :premises (@p190 @p181 @p172 @p171) :args (@t140)) % 0.82/1.07 (step @p192 :rule trans :premises (@p191 @p170)) % 0.82/1.07 (step @p193 :rule cong :premises (@p192) :args (@t141)) % 0.82/1.07 (step @p194 :rule trans :premises (@p193 @p169)) % 0.82/1.07 (step @p195 :rule cong :premises (@p194) :args (@t142)) % 0.82/1.07 (step @p196 :rule trans :premises (@p195 @p143)) % 0.82/1.07 (step @p197 :rule quant-unused-vars :args ((= (forall @t29 true) true))) % 0.82/1.07 (step @p198 :rule evaluate :args ((or false true))) % 0.82/1.07 (step @p199 :rule eq-refl :args (@t3)) % 0.82/1.07 (step @p200 :rule beta-reduce :args ((= @t143 (= @t3 @t3)))) % 0.82/1.07 (step @p201 :rule trans :premises (@p200 @p199)) % 0.82/1.07 (step @p202 :rule beta-reduce :args ((= @t144 false))) % 0.82/1.07 (step @p203 :rule nary_cong :premises (@p202 @p201) :args (@t145)) % 0.82/1.07 (step @p204 :rule trans :premises (@p203 @p198)) % 0.82/1.07 (step @p205 :rule cong :premises (@p204) :args (@t146)) % 0.82/1.07 (step @p206 :rule trans :premises (@p205 @p197)) % 0.82/1.07 (step @p207 :rule cong :premises (@p206) :args (@t147)) % 0.82/1.07 (step @p208 :rule trans :premises (@p207 @p143)) % 0.82/1.07 (step @p209 :rule quant-unused-vars :args ((= (forall @t148 true) true))) % 0.82/1.07 (step @p210 :rule bool-or-taut2 :args (false @t69 false false)) % 0.82/1.07 (step @p211 :rule cong :premises (@p210) :args ((forall @t148 @t150))) % 0.82/1.07 (step @p212 :rule trans :premises (@p211 @p209)) % 0.82/1.07 (step @p213 :rule aci_norm :args ((= (or false @t149 @t69) @t150))) % 0.82/1.07 (step @p214 :rule refl :args (@t69)) % 0.82/1.07 (step @p215 :rule refl :args (@t149)) % 0.82/1.07 (step @p216 :rule eq-refl :args (@t32)) % 0.82/1.07 (step @p217 :rule cong :premises (@p216) :args (@t151)) % 0.82/1.07 (step @p218 :rule trans :premises (@p217 @p143)) % 0.82/1.07 (step @p219 :rule nary_cong :premises (@p218 @p215 @p214) :args (@t152)) % 0.82/1.07 (step @p220 :rule trans :premises (@p219 @p213)) % 0.82/1.07 (step @p221 :rule cong :premises (@p220) :args ((forall @t148 @t152))) % 0.82/1.07 (step @p222 :rule trans :premises (@p221 @p212)) % 0.82/1.07 (step @p223 :rule quant-var-elim-eq :args ((= (forall @t156 @t155) @t152))) % 0.82/1.07 (step @p224 :rule aci_norm :args ((= @t157 @t155))) % 0.82/1.07 (step @p225 :rule cong :premises (@p224) :args (@t158)) % 0.82/1.07 (step @p226 :rule trans :premises (@p225 @p223)) % 0.82/1.07 (step @p227 :rule cong :premises (@p226) :args (@t159)) % 0.82/1.07 (step @p228 :rule quant-merge-prenex :args ((= @t159 @t160))) % 0.82/1.07 (step @p229 :rule symm :premises (@p228)) % 0.82/1.07 (step @p230 :rule quant_var_reordering :args ((= (forall @t76 @t157) @t160))) % 0.82/1.07 (step @p231 :rule trans :premises (@p230 @p229 @p227)) % 0.82/1.07 (step @p232 :rule trans :premises (@p231 @p222)) % 0.82/1.07 (step @p233 :rule refl :args (@t70)) % 0.82/1.07 (step @p234 :rule quant-unused-vars :args ((= (forall @t11 @t153) @t153))) % 0.82/1.07 (step @p235 :rule aci_norm :args ((= (or false @t153) @t153))) % 0.82/1.07 (step @p236 :rule beta-reduce :args ((= @t161 @t153))) % 0.82/1.07 (step @p237 :rule beta-reduce :args ((= @t162 false))) % 0.82/1.07 (step @p238 :rule nary_cong :premises (@p237 @p236) :args (@t163)) % 0.82/1.07 (step @p239 :rule trans :premises (@p238 @p235)) % 0.82/1.07 (step @p240 :rule cong :premises (@p239) :args (@t164)) % 0.82/1.07 (step @p241 :rule trans :premises (@p240 @p234)) % 0.82/1.07 (step @p242 :rule cong :premises (@p241) :args (@t165)) % 0.82/1.07 (step @p243 :rule nary_cong :premises (@p242 @p233 @p214) :args (@t166)) % 0.82/1.07 (step @p244 :rule cong :premises (@p243) :args (@t167)) % 0.82/1.07 (step @p245 :rule trans :premises (@p244 @p232)) % 0.82/1.07 (step @p246 :rule cong :premises (@p245) :args (@t168)) % 0.82/1.07 (step @p247 :rule trans :premises (@p246 @p143)) % 0.82/1.07 (step @p248 :rule nary_cong :premises (@p247 @p208 @p196) :args (@t169)) % 0.82/1.07 (step @p249 :rule trans :premises (@p248 @p142)) % 0.82/1.07 (step @p250 :rule refl :args (@t80)) % 0.82/1.07 (step @p251 :rule cong :premises (@p250 @p249) :args ((=> @t80 @t169))) % 0.82/1.07 (step @p252 :rule trans :premises (@p251 @p141)) % 0.82/1.07 (assume-push @p259 @t80) % 0.82/1.07 (step @p254 :rule instantiate :premises (@p140) :args ((@list @t126 @t128))) % 0.82/1.07 (step-pop @p260 :rule scope :premises (@p254)) % 0.82/1.07 (step @p255 :rule process_scope :premises (@p260) :args (@t169)) % 0.82/1.07 (step @p257 :rule eq_resolve :premises (@p255 @p252)) % 0.82/1.07 (step @p258 false :rule chain_m_resolution :premises (@p257 @p140) :args (false (@list false) (@list @t80))) % 0.82/1.07 ) % 0.82/1.07 % SZS output end Proof % 0.82/1.07 % cvc5 exiting %------------------------------------------------------------------------------