%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV126^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n004.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 08:55:29 AM UTC 2026 % Result : Theorem 1.01s 1.26s % Output : Proof 1.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV126^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n004.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 18:14:37 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 1.01/1.26 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 1.01/1.26 % SZS status Theorem % 1.01/1.26 % SZS output start Proof % 1.01/1.26 ( % 1.01/1.26 (declare-sort tptp.a 0) % 1.01/1.26 (define @t1 () (@var "Xy" tptp.a)) % 1.01/1.26 (define @t2 () (@var "Xx" tptp.a)) % 1.01/1.26 (define @t3 () (@var "Xp" (-> tptp.a tptp.a Bool))) % 1.01/1.26 (define @t4 () (_ (_ @t3 @t2) @t1)) % 1.01/1.26 (define @t5 () (@var "P" (-> (-> tptp.a tptp.a Bool) Bool))) % 1.01/1.26 (define @t6 () (_ @t5 @t3)) % 1.01/1.26 (define @t7 () (@var "Xy0" tptp.a)) % 1.01/1.26 (define @t8 () (@var "Xx0" tptp.a)) % 1.01/1.26 (define @t9 () (_ (_ @t3 @t8) @t7)) % 1.01/1.26 (define @t10 () (@var "Xp0" (-> tptp.a tptp.a Bool))) % 1.01/1.26 (define @t11 () (_ (_ @t10 @t8) @t7)) % 1.01/1.26 (define @t12 () (_ @t5 @t10)) % 1.01/1.26 (define @t13 () (@var "Xy1" tptp.a)) % 1.01/1.26 (define @t14 () (@var "Xx1" tptp.a)) % 1.01/1.26 (define @t15 () (_ (_ @t10 @t14) @t13)) % 1.01/1.26 (define @t16 () (@var "S" (-> tptp.a tptp.a Bool))) % 1.01/1.26 (define @t17 () (_ (_ @t16 @t14) @t13)) % 1.01/1.26 (define @t18 () (@list @t14 @t13)) % 1.01/1.26 (define @t19 () (forall @t18 (=> @t17 @t15))) % 1.01/1.26 (define @t20 () (and @t19 @t12)) % 1.01/1.26 (define @t21 () (=> @t20 @t11)) % 1.01/1.26 (define @t22 () (@list @t10)) % 1.01/1.26 (define @t23 () (forall @t22 @t21)) % 1.01/1.26 (define @t24 () (@var "R" (-> tptp.a tptp.a Bool))) % 1.01/1.26 (define @t25 () (_ (_ @t24 @t14) @t13)) % 1.01/1.26 (define @t26 () (forall @t18 (=> @t25 @t15))) % 1.01/1.26 (define @t27 () (and @t26 @t12)) % 1.01/1.26 (define @t28 () (=> @t27 @t11)) % 1.01/1.26 (define @t29 () (forall @t22 @t28)) % 1.01/1.26 (define @t30 () (or @t29 @t23)) % 1.01/1.26 (define @t31 () (=> @t30 @t9)) % 1.01/1.26 (define @t32 () (@list @t8 @t7)) % 1.01/1.26 (define @t33 () (forall @t32 @t31)) % 1.01/1.26 (define @t34 () (and @t33 @t6)) % 1.01/1.26 (define @t35 () (=> @t34 @t4)) % 1.01/1.26 (define @t36 () (@list @t3)) % 1.01/1.26 (define @t37 () (forall @t36 @t35)) % 1.01/1.26 (define @t38 () (_ (_ @t16 @t8) @t7)) % 1.01/1.26 (define @t39 () (_ (_ @t24 @t8) @t7)) % 1.01/1.26 (define @t40 () (or @t39 @t38)) % 1.01/1.26 (define @t41 () (forall @t32 (=> @t40 @t9))) % 1.01/1.26 (define @t42 () (and @t41 @t6)) % 1.01/1.26 (define @t43 () (=> @t42 @t4)) % 1.01/1.26 (define @t44 () (forall @t36 @t43)) % 1.01/1.26 (define @t45 () (=> @t44 @t37)) % 1.01/1.26 (define @t46 () (@list @t5 @t24 @t16 @t2 @t1)) % 1.01/1.26 (define @t47 () (forall @t46 @t45)) % 1.01/1.26 (define @t48 () (not @t47)) % 1.01/1.26 (define @t49 () (@var "BOUND_VARIABLE_7562" (-> tptp.a tptp.a Bool))) % 1.01/1.26 (define @t50 () (_ @t49 @t2 @t1)) % 1.01/1.26 (define @t51 () (not (_ @t5 @t49))) % 1.01/1.26 (define @t52 () (_ @t10 @t8 @t7)) % 1.01/1.26 (define @t53 () (_ @t5 @t10)) % 1.01/1.26 (define @t54 () (not @t53)) % 1.01/1.26 (define @t55 () (_ @t10 @t14 @t13)) % 1.01/1.26 (define @t56 () (_ @t16 @t14 @t13)) % 1.01/1.26 (define @t57 () (forall @t18 (or (not @t56) @t55))) % 1.01/1.26 (define @t58 () (not @t57)) % 1.01/1.26 (define @t59 () (forall @t22 (or @t58 @t54 @t52))) % 1.01/1.26 (define @t60 () (_ @t24 @t14 @t13)) % 1.01/1.26 (define @t61 () (forall @t18 (or (not @t60) @t55))) % 1.01/1.26 (define @t62 () (not @t61)) % 1.01/1.26 (define @t63 () (forall @t22 (or @t62 @t54 @t52))) % 1.01/1.26 (define @t64 () (and (not @t63) (not @t59))) % 1.01/1.26 (define @t65 () (not (forall @t32 (or @t64 (_ @t49 @t8 @t7))))) % 1.01/1.26 (define @t66 () (_ @t3 @t2 @t1)) % 1.01/1.26 (define @t67 () (_ @t5 @t3)) % 1.01/1.26 (define @t68 () (not @t67)) % 1.01/1.26 (define @t69 () (_ @t3 @t8 @t7)) % 1.01/1.26 (define @t70 () (_ @t16 @t8 @t7)) % 1.01/1.26 (define @t71 () (_ @t24 @t8 @t7)) % 1.01/1.26 (define @t72 () (forall @t32 (or (and (not @t71) (not @t70)) @t69))) % 1.01/1.26 (define @t73 () (not @t72)) % 1.01/1.26 (define @t74 () (forall @t36 (or @t73 @t68 @t66))) % 1.01/1.26 (define @t75 () (not @t74)) % 1.01/1.26 (define @t76 () (or @t75 @t65 @t51 @t50)) % 1.01/1.26 (define @t77 () (or @t65 @t51 @t50)) % 1.01/1.26 (define @t78 () (or @t75 @t77)) % 1.01/1.26 (define @t79 () (@list @t5 @t24 @t16 @t2 @t1 @t49)) % 1.01/1.26 (define @t80 () (forall @t79 @t78)) % 1.01/1.26 (define @t81 () (@list @t49)) % 1.01/1.26 (define @t82 () (forall @t81 @t78)) % 1.01/1.26 (define @t83 () (forall @t81 @t77)) % 1.01/1.26 (define @t84 () (or @t75 @t83)) % 1.01/1.26 (define @t85 () (forall @t32 (or @t64 @t69))) % 1.01/1.26 (define @t86 () (not @t85)) % 1.01/1.26 (define @t87 () (forall @t36 (or @t86 @t68 @t66))) % 1.01/1.26 (define @t88 () (not @t6)) % 1.01/1.26 (define @t89 () (or @t86 @t88 @t4)) % 1.01/1.26 (define @t90 () (and @t85 @t6)) % 1.01/1.26 (define @t91 () (or @t64 @t9)) % 1.01/1.26 (define @t92 () (or @t63 @t59)) % 1.01/1.26 (define @t93 () (not @t12)) % 1.01/1.26 (define @t94 () (or @t58 @t93 @t11)) % 1.01/1.26 (define @t95 () (and @t57 @t12)) % 1.01/1.26 (define @t96 () (not @t17)) % 1.01/1.26 (define @t97 () (or @t96 @t15)) % 1.01/1.26 (define @t98 () (or @t62 @t93 @t11)) % 1.01/1.26 (define @t99 () (and @t61 @t12)) % 1.01/1.26 (define @t100 () (not @t25)) % 1.01/1.26 (define @t101 () (or @t100 @t15)) % 1.01/1.26 (define @t102 () (or @t73 @t88 @t4)) % 1.01/1.26 (define @t103 () (and @t72 @t6)) % 1.01/1.26 (define @t104 () (not @t38)) % 1.01/1.26 (define @t105 () (not @t39)) % 1.01/1.26 (define @t106 () (and @t105 @t104)) % 1.01/1.26 (define @t107 () (or @t106 @t9)) % 1.01/1.26 (define @t108 () (forall @t79 @t76)) % 1.01/1.26 (define @t109 () (@quantifiers_skolemize @t108 5)) % 1.01/1.26 (define @t110 () (_ @t109 @t8 @t7)) % 1.01/1.26 (define @t111 () (@quantifiers_skolemize @t108 0)) % 1.01/1.26 (define @t112 () (not (_ @t111 @t10))) % 1.01/1.26 (define @t113 () (@quantifiers_skolemize @t108 2)) % 1.01/1.26 (define @t114 () (not (_ @t113 @t14 @t13))) % 1.01/1.26 (define @t115 () (not (forall @t18 (or @t114 @t55)))) % 1.01/1.26 (define @t116 () (@quantifiers_skolemize @t108 1)) % 1.01/1.26 (define @t117 () (not (_ @t116 @t14 @t13))) % 1.01/1.26 (define @t118 () (not (forall @t18 (or @t117 @t55)))) % 1.01/1.26 (define @t119 () (forall @t32 (or (and (not (forall @t22 (or @t118 @t112 @t52))) (not (forall @t22 (or @t115 @t112 @t52)))) @t110))) % 1.01/1.26 (define @t120 () (@quantifiers_skolemize @t108 4)) % 1.01/1.26 (define @t121 () (@quantifiers_skolemize @t108 3)) % 1.01/1.26 (define @t122 () (_ @t109 @t121 @t120)) % 1.01/1.26 (define @t123 () (_ @t111 @t109)) % 1.01/1.26 (define @t124 () (not @t123)) % 1.01/1.26 (define @t125 () (not @t119)) % 1.01/1.26 (define @t126 () (and (not (_ @t116 @t8 @t7)) (not (_ @t113 @t8 @t7)))) % 1.01/1.26 (define @t127 () (forall @t36 (or (not (forall @t32 (or @t126 @t69))) (not (_ @t111 @t3)) (_ @t3 @t121 @t120)))) % 1.01/1.26 (define @t128 () (not @t127)) % 1.01/1.26 (define @t129 () (or @t128 @t125 @t124 @t122)) % 1.01/1.26 (define @t130 () (@list true)) % 1.01/1.26 (define @t131 () (@list @t129)) % 1.01/1.26 (define @t132 () (forall @t32 (or @t126 @t110))) % 1.01/1.26 (define @t133 () (@quantifiers_skolemize @t132 1)) % 1.01/1.26 (define @t134 () (@quantifiers_skolemize @t132 0)) % 1.01/1.26 (define @t135 () (@list @t134 @t133)) % 1.01/1.26 (define @t136 () (not @t132)) % 1.01/1.26 (define @t137 () (or @t136 @t124 @t122)) % 1.01/1.26 (define @t138 () (_ @t109 @t134 @t133)) % 1.01/1.26 (define @t139 () (_ @t113 @t134 @t133)) % 1.01/1.26 (define @t140 () (not @t139)) % 1.01/1.26 (define @t141 () (_ @t116 @t134 @t133)) % 1.01/1.26 (define @t142 () (not @t141)) % 1.01/1.26 (define @t143 () (and @t142 @t140)) % 1.01/1.26 (define @t144 () (or @t143 @t138)) % 1.01/1.26 (define @t145 () (@list @t144)) % 1.01/1.26 (define @t146 () (_ @t10 @t134 @t133)) % 1.01/1.26 (define @t147 () (forall @t22 (or @t115 @t112 @t146))) % 1.01/1.26 (define @t148 () (not @t147)) % 1.01/1.26 (define @t149 () (forall @t22 (or @t118 @t112 @t146))) % 1.01/1.26 (define @t150 () (not @t149)) % 1.01/1.26 (define @t151 () (and @t150 @t148)) % 1.01/1.26 (define @t152 () (or @t151 @t138)) % 1.01/1.26 (define @t153 () (@list true false)) % 1.01/1.26 (define @t154 () (not @t151)) % 1.01/1.26 (define @t155 () (@list false)) % 1.01/1.26 (define @t156 () (@list @t151)) % 1.01/1.26 (define @t157 () (@quantifiers_skolemize @t147 0)) % 1.01/1.26 (define @t158 () (forall @t18 (or @t114 (_ @t157 @t14 @t13)))) % 1.01/1.26 (define @t159 () (_ @t157 @t134 @t133)) % 1.01/1.26 (define @t160 () (not @t158)) % 1.01/1.26 (define @t161 () (or @t160 (not (_ @t111 @t157)) @t159)) % 1.01/1.26 (define @t162 () (@list @t161)) % 1.01/1.26 (define @t163 () (@quantifiers_skolemize @t149 0)) % 1.01/1.26 (define @t164 () (forall @t18 (or @t117 (_ @t163 @t14 @t13)))) % 1.01/1.26 (define @t165 () (_ @t163 @t134 @t133)) % 1.01/1.26 (define @t166 () (not @t164)) % 1.01/1.26 (define @t167 () (or @t166 (not (_ @t111 @t163)) @t165)) % 1.01/1.26 (define @t168 () (@list @t167)) % 1.01/1.26 (define @t169 () (or @t142 @t165)) % 1.01/1.26 (define @t170 () (or @t140 @t159)) % 1.01/1.26 (define @t171 () (not @t170)) % 1.01/1.26 (assume @p1 @t48) % 1.01/1.26 (assume @p2 true) % 1.01/1.26 (step @p3 :rule aci_norm :args ((= @t78 @t76))) % 1.01/1.26 (step @p4 :rule cong :premises (@p3) :args (@t80)) % 1.01/1.26 (step @p5 :rule quant-merge-prenex :args ((= (forall @t46 @t82) @t80))) % 1.01/1.26 (step @p6 :rule alpha_equiv :args (@t83 (@list @t49) (@list @t3))) % 1.01/1.26 (step @p7 :rule refl :args (@t75)) % 1.01/1.26 (step @p8 :rule nary_cong :premises (@p7 @p6) :args (@t84)) % 1.01/1.26 (step @p9 :rule quant-miniscope-or :args ((= @t82 @t84))) % 1.01/1.26 (step @p10 :rule trans :premises (@p9 @p8)) % 1.01/1.26 (step @p11 :rule symm :premises (@p10)) % 1.01/1.26 (step @p12 :rule cong :premises (@p11) :args ((forall @t46 (or @t75 @t87)))) % 1.01/1.26 (step @p13 :rule trans :premises (@p12 @p5)) % 1.01/1.26 (step @p14 :rule trans :premises (@p13 @p4)) % 1.01/1.26 (step @p15 :rule bool-impl-elim :args (@t74 @t87)) % 1.01/1.26 (step @p16 :rule cong :premises (@p15) :args ((forall @t46 (=> @t74 @t87)))) % 1.01/1.26 (step @p17 :rule trans :premises (@p16 @p14)) % 1.01/1.26 (step @p18 :rule refl :args (@t66)) % 1.01/1.26 (step @p19 :rule refl :args (@t4)) % 1.01/1.26 (step @p20 :rule cong :premises (@p19 @p18) :args ((= @t4 @t66))) % 1.01/1.26 (step @p21 :rule symm :premises (@p20)) % 1.01/1.26 (step @p22 :rule eq_resolve :premises (@p19 @p21)) % 1.01/1.26 (step @p23 :rule refl :args (@t67)) % 1.01/1.26 (step @p24 :rule refl :args (@t6)) % 1.01/1.26 (step @p25 :rule cong :premises (@p24 @p23) :args ((= @t6 @t67))) % 1.01/1.26 (step @p26 :rule symm :premises (@p25)) % 1.01/1.26 (step @p27 :rule eq_resolve :premises (@p24 @p26)) % 1.01/1.26 (step @p28 :rule cong :premises (@p27) :args (@t88)) % 1.01/1.26 (step @p29 :rule refl :args (@t86)) % 1.01/1.26 (step @p30 :rule nary_cong :premises (@p29 @p28 @p22) :args (@t89)) % 1.01/1.26 (step @p31 :rule cong :premises (@p30) :args ((forall @t36 @t89))) % 1.01/1.26 (step @p32 :rule aci_norm :args ((= (or (or @t86 @t88) @t4) @t89))) % 1.01/1.26 (step @p33 :rule bool-and-de-morgan :args (@t85 @t6 true)) % 1.01/1.26 (step @p34 :rule nary_cong :premises (@p33 @p19) :args ((or (not @t90) @t4))) % 1.01/1.26 (step @p35 :rule trans :premises (@p34 @p32)) % 1.01/1.26 (step @p36 :rule bool-impl-elim :args (@t90 @t4)) % 1.01/1.26 (step @p37 :rule trans :premises (@p36 @p35)) % 1.01/1.26 (step @p38 :rule cong :premises (@p37) :args ((forall @t36 (=> @t90 @t4)))) % 1.01/1.26 (step @p39 :rule trans :premises (@p38 @p31)) % 1.01/1.26 (step @p40 :rule refl :args (@t4)) % 1.01/1.26 (step @p41 :rule refl :args (@t6)) % 1.01/1.26 (step @p42 :rule refl :args (@t69)) % 1.01/1.26 (step @p43 :rule refl :args (@t9)) % 1.01/1.26 (step @p44 :rule cong :premises (@p43 @p42) :args ((= @t9 @t69))) % 1.01/1.26 (step @p45 :rule symm :premises (@p44)) % 1.01/1.26 (step @p46 :rule eq_resolve :premises (@p43 @p45)) % 1.01/1.26 (step @p47 :rule refl :args (@t64)) % 1.01/1.26 (step @p48 :rule nary_cong :premises (@p47 @p46) :args (@t91)) % 1.01/1.26 (step @p49 :rule cong :premises (@p48) :args ((forall @t32 @t91))) % 1.01/1.26 (step @p50 :rule bool-or-de-morgan :args (@t63 @t59 false)) % 1.01/1.26 (step @p51 :rule nary_cong :premises (@p50 @p43) :args ((or (not @t92) @t9))) % 1.01/1.26 (step @p52 :rule bool-impl-elim :args (@t92 @t9)) % 1.01/1.26 (step @p53 :rule trans :premises (@p52 @p51)) % 1.01/1.26 (step @p54 :rule cong :premises (@p53) :args ((forall @t32 (=> @t92 @t9)))) % 1.01/1.26 (step @p55 :rule trans :premises (@p54 @p49)) % 1.01/1.26 (step @p56 :rule refl :args (@t9)) % 1.01/1.26 (step @p57 :rule refl :args (@t52)) % 1.01/1.26 (step @p58 :rule refl :args (@t11)) % 1.01/1.26 (step @p59 :rule cong :premises (@p58 @p57) :args ((= @t11 @t52))) % 1.01/1.26 (step @p60 :rule symm :premises (@p59)) % 1.01/1.26 (step @p61 :rule eq_resolve :premises (@p58 @p60)) % 1.01/1.26 (step @p62 :rule refl :args (@t53)) % 1.01/1.26 (step @p63 :rule refl :args (@t12)) % 1.01/1.26 (step @p64 :rule cong :premises (@p63 @p62) :args ((= @t12 @t53))) % 1.01/1.26 (step @p65 :rule symm :premises (@p64)) % 1.01/1.26 (step @p66 :rule eq_resolve :premises (@p63 @p65)) % 1.01/1.26 (step @p67 :rule cong :premises (@p66) :args (@t93)) % 1.01/1.26 (step @p68 :rule refl :args (@t58)) % 1.01/1.26 (step @p69 :rule nary_cong :premises (@p68 @p67 @p61) :args (@t94)) % 1.01/1.26 (step @p70 :rule cong :premises (@p69) :args ((forall @t22 @t94))) % 1.01/1.26 (step @p71 :rule aci_norm :args ((= (or (or @t58 @t93) @t11) @t94))) % 1.01/1.26 (step @p72 :rule bool-and-de-morgan :args (@t57 @t12 true)) % 1.01/1.26 (step @p73 :rule nary_cong :premises (@p72 @p58) :args ((or (not @t95) @t11))) % 1.01/1.26 (step @p74 :rule trans :premises (@p73 @p71)) % 1.01/1.26 (step @p75 :rule bool-impl-elim :args (@t95 @t11)) % 1.01/1.26 (step @p76 :rule trans :premises (@p75 @p74)) % 1.01/1.26 (step @p77 :rule cong :premises (@p76) :args ((forall @t22 (=> @t95 @t11)))) % 1.01/1.26 (step @p78 :rule trans :premises (@p77 @p70)) % 1.01/1.26 (step @p79 :rule refl :args (@t11)) % 1.01/1.26 (step @p80 :rule refl :args (@t12)) % 1.01/1.26 (step @p81 :rule refl :args (@t55)) % 1.01/1.26 (step @p82 :rule refl :args (@t15)) % 1.01/1.26 (step @p83 :rule cong :premises (@p82 @p81) :args ((= @t15 @t55))) % 1.01/1.26 (step @p84 :rule symm :premises (@p83)) % 1.01/1.26 (step @p85 :rule eq_resolve :premises (@p82 @p84)) % 1.01/1.26 (step @p86 :rule refl :args (@t56)) % 1.01/1.26 (step @p87 :rule refl :args (@t17)) % 1.01/1.26 (step @p88 :rule cong :premises (@p87 @p86) :args ((= @t17 @t56))) % 1.01/1.26 (step @p89 :rule symm :premises (@p88)) % 1.01/1.26 (step @p90 :rule eq_resolve :premises (@p87 @p89)) % 1.01/1.26 (step @p91 :rule cong :premises (@p90) :args (@t96)) % 1.01/1.26 (step @p92 :rule nary_cong :premises (@p91 @p85) :args (@t97)) % 1.01/1.26 (step @p93 :rule cong :premises (@p92) :args ((forall @t18 @t97))) % 1.01/1.26 (step @p94 :rule bool-impl-elim :args (@t17 @t15)) % 1.01/1.26 (step @p95 :rule cong :premises (@p94) :args (@t19)) % 1.01/1.26 (step @p96 :rule trans :premises (@p95 @p93)) % 1.01/1.26 (step @p97 :rule nary_cong :premises (@p96 @p80) :args (@t20)) % 1.01/1.26 (step @p98 :rule cong :premises (@p97 @p79) :args (@t21)) % 1.01/1.26 (step @p99 :rule cong :premises (@p98) :args (@t23)) % 1.01/1.26 (step @p100 :rule trans :premises (@p99 @p78)) % 1.01/1.26 (step @p101 :rule refl :args (@t62)) % 1.01/1.26 (step @p102 :rule nary_cong :premises (@p101 @p67 @p61) :args (@t98)) % 1.01/1.26 (step @p103 :rule cong :premises (@p102) :args ((forall @t22 @t98))) % 1.01/1.26 (step @p104 :rule aci_norm :args ((= (or (or @t62 @t93) @t11) @t98))) % 1.01/1.26 (step @p105 :rule bool-and-de-morgan :args (@t61 @t12 true)) % 1.01/1.26 (step @p106 :rule nary_cong :premises (@p105 @p58) :args ((or (not @t99) @t11))) % 1.01/1.26 (step @p107 :rule trans :premises (@p106 @p104)) % 1.01/1.26 (step @p108 :rule bool-impl-elim :args (@t99 @t11)) % 1.01/1.26 (step @p109 :rule trans :premises (@p108 @p107)) % 1.01/1.26 (step @p110 :rule cong :premises (@p109) :args ((forall @t22 (=> @t99 @t11)))) % 1.01/1.26 (step @p111 :rule trans :premises (@p110 @p103)) % 1.01/1.26 (step @p112 :rule refl :args (@t60)) % 1.01/1.26 (step @p113 :rule refl :args (@t25)) % 1.01/1.26 (step @p114 :rule cong :premises (@p113 @p112) :args ((= @t25 @t60))) % 1.01/1.26 (step @p115 :rule symm :premises (@p114)) % 1.01/1.26 (step @p116 :rule eq_resolve :premises (@p113 @p115)) % 1.01/1.26 (step @p117 :rule cong :premises (@p116) :args (@t100)) % 1.01/1.26 (step @p118 :rule nary_cong :premises (@p117 @p85) :args (@t101)) % 1.01/1.26 (step @p119 :rule cong :premises (@p118) :args ((forall @t18 @t101))) % 1.01/1.26 (step @p120 :rule bool-impl-elim :args (@t25 @t15)) % 1.01/1.26 (step @p121 :rule cong :premises (@p120) :args (@t26)) % 1.01/1.26 (step @p122 :rule trans :premises (@p121 @p119)) % 1.01/1.26 (step @p123 :rule nary_cong :premises (@p122 @p80) :args (@t27)) % 1.01/1.26 (step @p124 :rule cong :premises (@p123 @p79) :args (@t28)) % 1.01/1.26 (step @p125 :rule cong :premises (@p124) :args (@t29)) % 1.01/1.26 (step @p126 :rule trans :premises (@p125 @p111)) % 1.01/1.26 (step @p127 :rule nary_cong :premises (@p126 @p100) :args (@t30)) % 1.01/1.26 (step @p128 :rule cong :premises (@p127 @p56) :args (@t31)) % 1.01/1.26 (step @p129 :rule cong :premises (@p128) :args (@t33)) % 1.01/1.26 (step @p130 :rule trans :premises (@p129 @p55)) % 1.01/1.26 (step @p131 :rule nary_cong :premises (@p130 @p41) :args (@t34)) % 1.01/1.26 (step @p132 :rule cong :premises (@p131 @p40) :args (@t35)) % 1.01/1.26 (step @p133 :rule cong :premises (@p132) :args (@t37)) % 1.01/1.26 (step @p134 :rule trans :premises (@p133 @p39)) % 1.01/1.26 (step @p135 :rule refl :args (@t73)) % 1.01/1.26 (step @p136 :rule nary_cong :premises (@p135 @p28 @p22) :args (@t102)) % 1.01/1.26 (step @p137 :rule cong :premises (@p136) :args ((forall @t36 @t102))) % 1.01/1.26 (step @p138 :rule aci_norm :args ((= (or (or @t73 @t88) @t4) @t102))) % 1.01/1.26 (step @p139 :rule bool-and-de-morgan :args (@t72 @t6 true)) % 1.01/1.26 (step @p140 :rule nary_cong :premises (@p139 @p19) :args ((or (not @t103) @t4))) % 1.01/1.26 (step @p141 :rule trans :premises (@p140 @p138)) % 1.01/1.26 (step @p142 :rule bool-impl-elim :args (@t103 @t4)) % 1.01/1.26 (step @p143 :rule trans :premises (@p142 @p141)) % 1.01/1.26 (step @p144 :rule cong :premises (@p143) :args ((forall @t36 (=> @t103 @t4)))) % 1.01/1.26 (step @p145 :rule trans :premises (@p144 @p137)) % 1.01/1.26 (step @p146 :rule refl :args (@t70)) % 1.01/1.26 (step @p147 :rule refl :args (@t38)) % 1.01/1.26 (step @p148 :rule cong :premises (@p147 @p146) :args ((= @t38 @t70))) % 1.01/1.26 (step @p149 :rule symm :premises (@p148)) % 1.01/1.26 (step @p150 :rule eq_resolve :premises (@p147 @p149)) % 1.01/1.26 (step @p151 :rule cong :premises (@p150) :args (@t104)) % 1.01/1.26 (step @p152 :rule refl :args (@t71)) % 1.01/1.26 (step @p153 :rule refl :args (@t39)) % 1.01/1.26 (step @p154 :rule cong :premises (@p153 @p152) :args ((= @t39 @t71))) % 1.01/1.26 (step @p155 :rule symm :premises (@p154)) % 1.01/1.26 (step @p156 :rule eq_resolve :premises (@p153 @p155)) % 1.01/1.26 (step @p157 :rule cong :premises (@p156) :args (@t105)) % 1.01/1.26 (step @p158 :rule nary_cong :premises (@p157 @p151) :args (@t106)) % 1.01/1.26 (step @p159 :rule nary_cong :premises (@p158 @p46) :args (@t107)) % 1.01/1.26 (step @p160 :rule cong :premises (@p159) :args ((forall @t32 @t107))) % 1.01/1.26 (step @p161 :rule bool-or-de-morgan :args (@t39 @t38 false)) % 1.01/1.26 (step @p162 :rule nary_cong :premises (@p161 @p43) :args ((or (not @t40) @t9))) % 1.01/1.26 (step @p163 :rule bool-impl-elim :args (@t40 @t9)) % 1.01/1.26 (step @p164 :rule trans :premises (@p163 @p162)) % 1.01/1.26 (step @p165 :rule cong :premises (@p164) :args (@t41)) % 1.01/1.26 (step @p166 :rule trans :premises (@p165 @p160)) % 1.01/1.26 (step @p167 :rule nary_cong :premises (@p166 @p41) :args (@t42)) % 1.01/1.26 (step @p168 :rule cong :premises (@p167 @p40) :args (@t43)) % 1.01/1.26 (step @p169 :rule cong :premises (@p168) :args (@t44)) % 1.01/1.26 (step @p170 :rule trans :premises (@p169 @p145)) % 1.01/1.26 (step @p171 :rule cong :premises (@p170 @p134) :args (@t45)) % 1.01/1.26 (step @p172 :rule cong :premises (@p171) :args (@t47)) % 1.01/1.26 (step @p173 :rule trans :premises (@p172 @p17)) % 1.01/1.26 (step @p174 :rule cong :premises (@p173) :args (@t48)) % 1.01/1.26 (step @p175 :rule eq_resolve :premises (@p1 @p174)) % 1.01/1.26 (step @p176 :rule skolemize :premises (@p175)) % 1.01/1.26 (step @p177 :rule bool-double-not-elim :args (@t119)) % 1.01/1.26 (step @p178 :rule refl :args (@t129)) % 1.01/1.26 (step @p179 :rule nary_cong :premises (@p178 @p177) :args ((or @t129 (not @t125)))) % 1.01/1.26 (step @p180 :rule cnf_or_neg :args (@t129 1)) % 1.01/1.26 (step @p181 :rule eq_resolve :premises (@p180 @p179)) % 1.01/1.26 (step @p182 :rule reordering :premises (@p181) :args ((or @t119 @t129))) % 1.01/1.26 (step @p183 :rule chain_m_resolution :premises (@p182 @p176) :args (@t119 @t130 @t131)) % 1.01/1.26 (step @p184 :rule instantiate :premises (@p183) :args (@t135)) % 1.01/1.26 (step @p185 :rule bool-double-not-elim :args (@t127)) % 1.01/1.26 (step @p186 :rule nary_cong :premises (@p178 @p185) :args ((or @t129 (not @t128)))) % 1.01/1.26 (step @p187 :rule cnf_or_neg :args (@t129 0)) % 1.01/1.26 (step @p188 :rule eq_resolve :premises (@p187 @p186)) % 1.01/1.26 (step @p189 :rule reordering :premises (@p188) :args ((or @t127 @t129))) % 1.01/1.26 (step @p190 :rule chain_m_resolution :premises (@p189 @p176) :args (@t127 @t130 @t131)) % 1.01/1.26 (step @p191 :rule instantiate :premises (@p190) :args ((@list @t109))) % 1.01/1.26 (step @p192 :rule cnf_or_neg :args (@t129 3)) % 1.01/1.26 (step @p193 :rule chain_m_resolution :premises (@p192 @p176) :args ((not @t122) @t130 @t131)) % 1.01/1.26 (step @p194 :rule bool-double-not-elim :args (@t123)) % 1.01/1.26 (step @p195 :rule nary_cong :premises (@p178 @p194) :args ((or @t129 (not @t124)))) % 1.01/1.26 (step @p196 :rule cnf_or_neg :args (@t129 2)) % 1.01/1.26 (step @p197 :rule eq_resolve :premises (@p196 @p195)) % 1.01/1.26 (step @p198 :rule reordering :premises (@p197) :args ((or @t123 @t129))) % 1.01/1.26 (step @p199 :rule chain_m_resolution :premises (@p198 @p176) :args (@t123 @t130 @t131)) % 1.01/1.26 (step @p200 :rule cnf_or_pos :args (@t137)) % 1.01/1.26 (step @p201 :rule reordering :premises (@p200) :args ((or @t124 @t122 @t136 (not @t137)))) % 1.01/1.26 (step @p202 :rule chain_m_resolution :premises (@p201 @p199 @p193 @p191) :args (@t136 (@list false true false) (@list @t123 @t122 @t137))) % 1.01/1.26 (step @p203 :rule skolemize :premises (@p202)) % 1.01/1.26 (step @p204 :rule cnf_or_neg :args (@t144 1)) % 1.01/1.26 (step @p205 :rule chain_m_resolution :premises (@p204 @p203) :args ((not @t138) @t130 @t145)) % 1.01/1.26 (step @p206 :rule cnf_or_pos :args (@t152)) % 1.01/1.26 (step @p207 :rule reordering :premises (@p206) :args ((or @t138 @t151 (not @t152)))) % 1.01/1.26 (step @p208 :rule chain_m_resolution :premises (@p207 @p205 @p184) :args (@t151 @t153 (@list @t138 @t152))) % 1.01/1.26 (step @p209 :rule cnf_and_pos :args (@t151 1)) % 1.01/1.26 (step @p210 :rule reordering :premises (@p209) :args ((or @t148 @t154))) % 1.01/1.26 (step @p211 :rule chain_m_resolution :premises (@p210 @p208) :args (@t148 @t155 @t156)) % 1.01/1.26 (step @p212 :rule skolemize :premises (@p211)) % 1.01/1.26 (step @p213 :rule bool-double-not-elim :args (@t158)) % 1.01/1.26 (step @p214 :rule refl :args (@t161)) % 1.01/1.26 (step @p215 :rule nary_cong :premises (@p214 @p213) :args ((or @t161 (not @t160)))) % 1.01/1.26 (step @p216 :rule cnf_or_neg :args (@t161 0)) % 1.01/1.26 (step @p217 :rule eq_resolve :premises (@p216 @p215)) % 1.01/1.26 (step @p218 :rule reordering :premises (@p217) :args ((or @t158 @t161))) % 1.01/1.26 (step @p219 :rule chain_m_resolution :premises (@p218 @p212) :args (@t158 @t130 @t162)) % 1.01/1.26 (step @p220 :rule cnf_or_neg :args (@t161 2)) % 1.01/1.26 (step @p221 :rule chain_m_resolution :premises (@p220 @p212) :args ((not @t159) @t130 @t162)) % 1.01/1.26 (step @p222 :rule cnf_or_neg :args (@t144 0)) % 1.01/1.26 (step @p223 :rule chain_m_resolution :premises (@p222 @p203) :args ((not @t143) @t130 @t145)) % 1.01/1.26 (step @p224 :rule cnf_and_pos :args (@t151 0)) % 1.01/1.26 (step @p225 :rule reordering :premises (@p224) :args ((or @t150 @t154))) % 1.01/1.26 (step @p226 :rule chain_m_resolution :premises (@p225 @p208) :args (@t150 @t155 @t156)) % 1.01/1.26 (step @p227 :rule skolemize :premises (@p226)) % 1.01/1.26 (step @p228 :rule bool-double-not-elim :args (@t164)) % 1.01/1.26 (step @p229 :rule refl :args (@t167)) % 1.01/1.26 (step @p230 :rule nary_cong :premises (@p229 @p228) :args ((or @t167 (not @t166)))) % 1.01/1.26 (step @p231 :rule cnf_or_neg :args (@t167 0)) % 1.01/1.26 (step @p232 :rule eq_resolve :premises (@p231 @p230)) % 1.01/1.26 (step @p233 :rule reordering :premises (@p232) :args ((or @t164 @t167))) % 1.01/1.26 (step @p234 :rule chain_m_resolution :premises (@p233 @p227) :args (@t164 @t130 @t168)) % 1.01/1.26 (step @p235 :rule instantiate :premises (@p234) :args (@t135)) % 1.01/1.26 (step @p236 :rule cnf_or_neg :args (@t167 2)) % 1.01/1.26 (step @p237 :rule chain_m_resolution :premises (@p236 @p227) :args ((not @t165) @t130 @t168)) % 1.01/1.26 (step @p238 :rule cnf_or_pos :args (@t169)) % 1.01/1.26 (step @p239 :rule reordering :premises (@p238) :args ((or @t142 @t165 (not @t169)))) % 1.01/1.26 (step @p240 :rule chain_m_resolution :premises (@p239 @p237 @p235) :args (@t142 @t153 (@list @t165 @t169))) % 1.01/1.26 (step @p241 :rule bool-double-not-elim :args (@t139)) % 1.01/1.26 (step @p242 :rule bool-double-not-elim :args (@t141)) % 1.01/1.26 (step @p243 :rule refl :args (@t143)) % 1.01/1.26 (step @p244 :rule nary_cong :premises (@p243 @p242 @p241) :args ((or @t143 (not @t142) (not @t140)))) % 1.01/1.26 (step @p245 :rule cnf_and_neg :args (@t143)) % 1.01/1.26 (step @p246 :rule eq_resolve :premises (@p245 @p244)) % 1.01/1.26 (step @p247 :rule reordering :premises (@p246) :args ((or @t141 @t139 @t143))) % 1.01/1.26 (step @p248 :rule chain_m_resolution :premises (@p247 @p240 @p223) :args (@t139 (@list true true) (@list @t141 @t143))) % 1.01/1.26 (step @p249 :rule cnf_or_pos :args (@t170)) % 1.01/1.26 (step @p250 :rule reordering :premises (@p249) :args ((or @t140 @t159 @t171))) % 1.01/1.26 (step @p251 :rule chain_m_resolution :premises (@p250 @p248 @p221) :args (@t171 (@list false true) (@list @t139 @t159))) % 1.01/1.26 (assume-push @p258 @t158) % 1.01/1.26 (step @p253 :rule instantiate :premises (@p219) :args (@t135)) % 1.01/1.26 (step-pop @p259 :rule scope :premises (@p253)) % 1.01/1.26 (step @p254 :rule process_scope :premises (@p259) :args (@t170)) % 1.01/1.26 (step @p256 :rule implies_elim :premises (@p254)) % 1.01/1.26 (step @p257 false :rule chain_m_resolution :premises (@p256 @p251 @p219) :args (false @t153 (@list @t170 @t158))) % 1.01/1.26 ) % 1.01/1.26 % SZS output end Proof % 1.01/1.26 % cvc5 exiting %------------------------------------------------------------------------------