%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYN319+1 : TPTP v9.2.1. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n013.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 09:08:32 AM UTC 2026 % Result : Theorem 0.32s 0.58s % Output : Proof 0.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SYN319+1 : TPTP v9.2.1. Released v2.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n013.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 23:23:15 EDT 2026 % 0.16/0.35 % CPUTime : % 0.32/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.32/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.32/0.58 % SZS status Theorem % 0.32/0.58 % SZS output start Proof % 0.32/0.58 ( % 0.32/0.58 (declare-sort $$unsorted 0) % 0.32/0.58 (declare-const tptp.big_f (-> $$unsorted Bool)) % 0.32/0.58 (declare-const tptp.big_g (-> $$unsorted Bool)) % 0.32/0.58 (declare-const tptp.big_h (-> $$unsorted Bool)) % 0.32/0.58 (define @t1 () (@var "Z2" $$unsorted)) % 0.32/0.58 (define @t2 () (tptp.big_h @t1)) % 0.32/0.58 (define @t3 () (tptp.big_g @t1)) % 0.32/0.58 (define @t4 () (tptp.big_f @t1)) % 0.32/0.58 (define @t5 () (or @t4 @t3)) % 0.32/0.58 (define @t6 () (=> @t5 @t2)) % 0.32/0.58 (define @t7 () (@var "Y" $$unsorted)) % 0.32/0.58 (define @t8 () (tptp.big_h @t7)) % 0.32/0.58 (define @t9 () (and @t2 (=> @t8 @t6))) % 0.32/0.58 (define @t10 () (@var "X" $$unsorted)) % 0.32/0.58 (define @t11 () (tptp.big_h @t10)) % 0.32/0.58 (define @t12 () (tptp.big_g @t10)) % 0.32/0.58 (define @t13 () (tptp.big_f @t10)) % 0.32/0.58 (define @t14 () (or @t13 @t12)) % 0.32/0.58 (define @t15 () (=> @t14 @t11)) % 0.32/0.58 (define @t16 () (=> @t15 @t9)) % 0.32/0.58 (define @t17 () (@var "Z1" $$unsorted)) % 0.32/0.58 (define @t18 () (tptp.big_f @t17)) % 0.32/0.58 (define @t19 () (not @t18)) % 0.32/0.58 (define @t20 () (and @t12 @t19)) % 0.32/0.58 (define @t21 () (tptp.big_g @t17)) % 0.32/0.58 (define @t22 () (tptp.big_f @t7)) % 0.32/0.58 (define @t23 () (=> @t22 @t21)) % 0.32/0.58 (define @t24 () (=> @t23 @t20)) % 0.32/0.58 (define @t25 () (@list @t17 @t1)) % 0.32/0.58 (define @t26 () (forall @t25 (=> @t24 @t16))) % 0.32/0.58 (define @t27 () (@list @t10 @t7)) % 0.32/0.58 (define @t28 () (exists @t27 @t26)) % 0.32/0.58 (define @t29 () (not @t28)) % 0.32/0.58 (define @t30 () (@var "BOUND_VARIABLE_7491" $$unsorted)) % 0.32/0.58 (define @t31 () (tptp.big_h @t30)) % 0.32/0.58 (define @t32 () (and (not (tptp.big_f @t30)) (not (tptp.big_g @t30)))) % 0.32/0.58 (define @t33 () (or @t32 @t31)) % 0.32/0.58 (define @t34 () (@list @t30)) % 0.32/0.58 (define @t35 () (forall @t34 @t33)) % 0.32/0.58 (define @t36 () (not @t35)) % 0.32/0.58 (define @t37 () (@var "BOUND_VARIABLE_7594" $$unsorted)) % 0.32/0.58 (define @t38 () (and (forall (@list @t37) (tptp.big_h @t37)) @t36)) % 0.32/0.58 (define @t39 () (@var "BOUND_VARIABLE_7486" $$unsorted)) % 0.32/0.58 (define @t40 () (forall (@list @t39) (tptp.big_h @t39))) % 0.32/0.58 (define @t41 () (not @t40)) % 0.32/0.58 (define @t42 () (@var "BOUND_VARIABLE_7474" $$unsorted)) % 0.32/0.58 (define @t43 () (tptp.big_f @t42)) % 0.32/0.58 (define @t44 () (@list @t42)) % 0.32/0.58 (define @t45 () (forall @t44 @t43)) % 0.32/0.58 (define @t46 () (not @t45)) % 0.32/0.58 (define @t47 () (@var "BOUND_VARIABLE_7582" $$unsorted)) % 0.32/0.58 (define @t48 () (forall (@list @t47) (tptp.big_g @t47))) % 0.32/0.58 (define @t49 () (and @t48 @t46)) % 0.32/0.58 (define @t50 () (@var "BOUND_VARIABLE_7468" $$unsorted)) % 0.32/0.58 (define @t51 () (tptp.big_g @t50)) % 0.32/0.58 (define @t52 () (@list @t50)) % 0.32/0.58 (define @t53 () (forall @t52 @t51)) % 0.32/0.58 (define @t54 () (not @t53)) % 0.32/0.58 (define @t55 () (@var "BOUND_VARIABLE_7574" $$unsorted)) % 0.32/0.58 (define @t56 () (forall (@list @t55) (tptp.big_f @t55))) % 0.32/0.58 (define @t57 () (and @t56 @t54)) % 0.32/0.58 (define @t58 () (@var "BOUND_VARIABLE_7533" $$unsorted)) % 0.32/0.58 (define @t59 () (or (and (not (tptp.big_f @t58)) (not (tptp.big_g @t58))) (tptp.big_h @t58))) % 0.32/0.58 (define @t60 () (forall (@list @t58) @t59)) % 0.32/0.58 (define @t61 () (@var "BOUND_VARIABLE_7559" $$unsorted)) % 0.32/0.58 (define @t62 () (@list @t61)) % 0.32/0.58 (define @t63 () (forall @t62 @t36)) % 0.32/0.58 (define @t64 () (tptp.big_h @t61)) % 0.32/0.58 (define @t65 () (forall @t62 @t64)) % 0.32/0.58 (define @t66 () (and @t65 @t63)) % 0.32/0.58 (define @t67 () (and @t64 @t36)) % 0.32/0.58 (define @t68 () (forall @t62 @t67)) % 0.32/0.58 (define @t69 () (or @t41 @t68)) % 0.32/0.58 (define @t70 () (or @t41 @t67)) % 0.32/0.58 (define @t71 () (forall @t62 @t70)) % 0.32/0.58 (define @t72 () (@var "BOUND_VARIABLE_7557" $$unsorted)) % 0.32/0.58 (define @t73 () (forall (@list @t72 @t61) @t70)) % 0.32/0.58 (define @t74 () (@var "BOUND_VARIABLE_7546" $$unsorted)) % 0.32/0.58 (define @t75 () (@list @t74)) % 0.32/0.58 (define @t76 () (forall @t75 @t46)) % 0.32/0.58 (define @t77 () (tptp.big_g @t74)) % 0.32/0.58 (define @t78 () (forall @t75 @t77)) % 0.32/0.58 (define @t79 () (@list @t47)) % 0.32/0.58 (define @t80 () (and @t78 @t76)) % 0.32/0.58 (define @t81 () (and @t77 @t46)) % 0.32/0.58 (define @t82 () (forall @t75 @t81)) % 0.32/0.58 (define @t83 () (@var "BOUND_VARIABLE_7548" $$unsorted)) % 0.32/0.58 (define @t84 () (@list @t83)) % 0.32/0.58 (define @t85 () (forall @t84 @t54)) % 0.32/0.58 (define @t86 () (tptp.big_f @t83)) % 0.32/0.58 (define @t87 () (forall @t84 @t86)) % 0.32/0.58 (define @t88 () (and @t87 @t85)) % 0.32/0.58 (define @t89 () (and @t86 @t54)) % 0.32/0.58 (define @t90 () (forall @t84 @t89)) % 0.32/0.58 (define @t91 () (or @t90 @t82)) % 0.32/0.58 (define @t92 () (or @t89 @t81)) % 0.32/0.58 (define @t93 () (forall (@list @t83 @t74) @t92)) % 0.32/0.58 (define @t94 () (forall (@list @t74 @t83) @t92)) % 0.32/0.58 (define @t95 () (@var "BOUND_VARIABLE_7535" $$unsorted)) % 0.32/0.58 (define @t96 () (forall (@list @t58 @t95) @t59)) % 0.32/0.58 (define @t97 () (or @t41 (and @t8 @t36))) % 0.32/0.58 (define @t98 () (forall @t27 @t97)) % 0.32/0.58 (define @t99 () (@list @t10 @t7)) % 0.32/0.58 (define @t100 () (or (and @t22 @t54) (and @t12 @t46))) % 0.32/0.58 (define @t101 () (forall @t27 @t100)) % 0.32/0.58 (define @t102 () (not @t12)) % 0.32/0.58 (define @t103 () (or (and (not @t13) @t102) @t11)) % 0.32/0.58 (define @t104 () (forall @t27 @t103)) % 0.32/0.58 (define @t105 () (and @t104 @t101 @t98)) % 0.32/0.58 (define @t106 () (not @t8)) % 0.32/0.58 (define @t107 () (or @t106 @t35)) % 0.32/0.58 (define @t108 () (not @t22)) % 0.32/0.58 (define @t109 () (or @t102 @t45)) % 0.32/0.58 (define @t110 () (or @t108 @t53)) % 0.32/0.58 (define @t111 () (not @t14)) % 0.32/0.58 (define @t112 () (not @t11)) % 0.32/0.58 (define @t113 () (and @t40 @t107)) % 0.32/0.58 (define @t114 () (not @t113)) % 0.32/0.58 (define @t115 () (and @t110 @t109)) % 0.32/0.58 (define @t116 () (not @t115)) % 0.32/0.58 (define @t117 () (and @t14 @t112)) % 0.32/0.58 (define @t118 () (not @t117)) % 0.32/0.58 (define @t119 () (and @t118 @t116 @t114)) % 0.32/0.58 (define @t120 () (or @t117 @t115 @t113)) % 0.32/0.58 (define @t121 () (forall @t27 (not @t120))) % 0.32/0.58 (define @t122 () (not @t121)) % 0.32/0.58 (define @t123 () (or @t106 @t33)) % 0.32/0.58 (define @t124 () (or @t106 @t32 @t31)) % 0.32/0.58 (define @t125 () (forall @t34 @t124)) % 0.32/0.58 (define @t126 () (and (not @t4) (not @t3))) % 0.32/0.58 (define @t127 () (or @t106 @t126 @t2)) % 0.32/0.58 (define @t128 () (@list @t1)) % 0.32/0.58 (define @t129 () (forall @t128 @t127)) % 0.32/0.58 (define @t130 () (@list @t1)) % 0.32/0.58 (define @t131 () (@list @t30)) % 0.32/0.58 (define @t132 () (forall @t128 @t2)) % 0.32/0.58 (define @t133 () (and @t132 @t129)) % 0.32/0.58 (define @t134 () (and @t2 @t127)) % 0.32/0.58 (define @t135 () (forall @t128 @t134)) % 0.32/0.58 (define @t136 () (forall @t44 (or @t102 @t43))) % 0.32/0.58 (define @t137 () (forall @t52 (or @t108 @t51))) % 0.32/0.58 (define @t138 () (or @t102 @t18)) % 0.32/0.58 (define @t139 () (@list @t17)) % 0.32/0.58 (define @t140 () (forall @t139 @t138)) % 0.32/0.58 (define @t141 () (@list @t17)) % 0.32/0.58 (define @t142 () (or @t108 @t21)) % 0.32/0.58 (define @t143 () (forall @t139 @t142)) % 0.32/0.58 (define @t144 () (@list @t50)) % 0.32/0.58 (define @t145 () (and @t143 @t140)) % 0.32/0.58 (define @t146 () (and @t142 @t138)) % 0.32/0.58 (define @t147 () (forall @t139 @t146)) % 0.32/0.58 (define @t148 () (or @t117 @t147 @t135)) % 0.32/0.58 (define @t149 () (or @t117 @t146 @t134)) % 0.32/0.58 (define @t150 () (or @t146 @t117 @t134)) % 0.32/0.58 (define @t151 () (@quantifiers_skolemize @t40 0)) % 0.32/0.58 (define @t152 () (@list @t151)) % 0.32/0.58 (define @t153 () (@list false)) % 0.32/0.58 (define @t154 () (not @t38)) % 0.32/0.58 (define @t155 () (@list true)) % 0.32/0.58 (define @t156 () (tptp.big_h @t151)) % 0.32/0.58 (define @t157 () (tptp.big_g @t151)) % 0.32/0.58 (define @t158 () (not @t157)) % 0.32/0.58 (define @t159 () (tptp.big_f @t151)) % 0.32/0.58 (define @t160 () (not @t159)) % 0.32/0.58 (define @t161 () (and @t160 @t158)) % 0.32/0.58 (define @t162 () (or @t161 @t156)) % 0.32/0.58 (define @t163 () (not @t161)) % 0.32/0.58 (define @t164 () (@list @t161)) % 0.32/0.58 (define @t165 () (not @t49)) % 0.32/0.58 (assume @p1 @t29) % 0.32/0.58 (assume @p2 true) % 0.32/0.58 (step @p3 :rule bool-double-not-elim :args ((and @t60 (or @t57 @t49) (or @t41 @t38)))) % 0.32/0.58 (step @p4 :rule quant-unused-vars :args ((= @t63 @t36))) % 0.32/0.58 (step @p5 :rule alpha_equiv :args (@t65 (@list @t61) (@list @t37))) % 0.32/0.58 (step @p6 :rule nary_cong :premises (@p5 @p4) :args (@t66)) % 0.32/0.58 (step @p7 :rule quant-miniscope-and :args ((= @t68 @t66))) % 0.32/0.58 (step @p8 :rule trans :premises (@p7 @p6)) % 0.32/0.58 (step @p9 :rule refl :args (@t41)) % 0.32/0.58 (step @p10 :rule nary_cong :premises (@p9 @p8) :args (@t69)) % 0.32/0.58 (step @p11 :rule quant-miniscope-or :args ((= @t71 @t69))) % 0.32/0.58 (step @p12 :rule aci_norm :args ((= @t70 @t70))) % 0.32/0.58 (step @p13 :rule cong :premises (@p12) :args (@t71)) % 0.32/0.58 (step @p14 :rule quant-unused-vars :args ((= @t73 @t71))) % 0.32/0.58 (step @p15 :rule trans :premises (@p14 @p13 @p11)) % 0.32/0.58 (step @p16 :rule trans :premises (@p15 @p10)) % 0.32/0.58 (step @p17 :rule quant-unused-vars :args ((= @t76 @t46))) % 0.32/0.58 (step @p18 :rule alpha_equiv :args (@t78 (@list @t74) @t79)) % 0.32/0.58 (step @p19 :rule nary_cong :premises (@p18 @p17) :args (@t80)) % 0.32/0.58 (step @p20 :rule quant-miniscope-and :args ((= @t82 @t80))) % 0.32/0.58 (step @p21 :rule trans :premises (@p20 @p19)) % 0.32/0.58 (step @p22 :rule quant-unused-vars :args ((= @t85 @t54))) % 0.32/0.58 (step @p23 :rule alpha_equiv :args (@t87 (@list @t83) (@list @t55))) % 0.32/0.58 (step @p24 :rule nary_cong :premises (@p23 @p22) :args (@t88)) % 0.32/0.58 (step @p25 :rule quant-miniscope-and :args ((= @t90 @t88))) % 0.32/0.58 (step @p26 :rule trans :premises (@p25 @p24)) % 0.32/0.58 (step @p27 :rule nary_cong :premises (@p26 @p21) :args (@t91)) % 0.32/0.58 (step @p28 :rule quant-miniscope-or :args ((= @t93 @t91))) % 0.32/0.58 (step @p29 :rule aci_norm :args ((= @t92 @t92))) % 0.32/0.58 (step @p30 :rule cong :premises (@p29) :args (@t93)) % 0.32/0.58 (step @p31 :rule quant_var_reordering :args ((= @t94 @t93))) % 0.32/0.58 (step @p32 :rule trans :premises (@p31 @p30 @p28)) % 0.32/0.58 (step @p33 :rule trans :premises (@p32 @p27)) % 0.32/0.58 (step @p34 :rule quant-unused-vars :args ((= @t96 @t60))) % 0.32/0.58 (step @p35 :rule nary_cong :premises (@p34 @p33 @p16) :args ((and @t96 @t94 @t73))) % 0.32/0.58 (step @p36 :rule alpha_equiv :args (@t98 @t99 (@list @t72 @t61))) % 0.32/0.58 (step @p37 :rule alpha_equiv :args (@t101 @t99 (@list @t74 @t83))) % 0.32/0.58 (step @p38 :rule alpha_equiv :args (@t104 @t99 (@list @t58 @t95))) % 0.32/0.58 (step @p39 :rule nary_cong :premises (@p38 @p37 @p36) :args (@t105)) % 0.32/0.58 (step @p40 :rule quant-miniscope-and :args ((= (forall @t27 (and @t103 @t100 @t97)) @t105))) % 0.32/0.58 (step @p41 :rule trans :premises (@p40 @p39)) % 0.32/0.58 (step @p42 :rule trans :premises (@p41 @p35)) % 0.32/0.58 (step @p43 :rule refl :args (@t36)) % 0.32/0.58 (step @p44 :rule bool-double-not-elim :args (@t8)) % 0.32/0.58 (step @p45 :rule nary_cong :premises (@p44 @p43) :args ((and (not @t106) @t36))) % 0.32/0.58 (step @p46 :rule bool-or-de-morgan :args (@t106 @t35 false)) % 0.32/0.58 (step @p47 :rule trans :premises (@p46 @p45)) % 0.32/0.58 (step @p48 :rule refl :args (@t41)) % 0.32/0.58 (step @p49 :rule nary_cong :premises (@p48 @p47) :args ((or @t41 (not @t107)))) % 0.32/0.58 (step @p50 :rule bool-and-de-morgan :args (@t40 @t107 true)) % 0.32/0.58 (step @p51 :rule trans :premises (@p50 @p49)) % 0.32/0.58 (step @p52 :rule refl :args (@t46)) % 0.32/0.58 (step @p53 :rule bool-double-not-elim :args (@t12)) % 0.32/0.58 (step @p54 :rule nary_cong :premises (@p53 @p52) :args ((and (not @t102) @t46))) % 0.32/0.58 (step @p55 :rule bool-or-de-morgan :args (@t102 @t45 false)) % 0.32/0.58 (step @p56 :rule trans :premises (@p55 @p54)) % 0.32/0.58 (step @p57 :rule refl :args (@t54)) % 0.32/0.58 (step @p58 :rule bool-double-not-elim :args (@t22)) % 0.32/0.58 (step @p59 :rule nary_cong :premises (@p58 @p57) :args ((and (not @t108) @t54))) % 0.32/0.58 (step @p60 :rule bool-or-de-morgan :args (@t108 @t53 false)) % 0.32/0.58 (step @p61 :rule trans :premises (@p60 @p59)) % 0.32/0.58 (step @p62 :rule nary_cong :premises (@p61 @p56) :args ((or (not @t110) (not @t109)))) % 0.32/0.58 (step @p63 :rule bool-and-de-morgan :args (@t110 @t109 true)) % 0.32/0.58 (step @p64 :rule trans :premises (@p63 @p62)) % 0.32/0.58 (step @p65 :rule refl :args (@t11)) % 0.32/0.58 (step @p66 :rule bool-or-de-morgan :args (@t13 @t12 false)) % 0.32/0.58 (step @p67 :rule nary_cong :premises (@p66 @p65) :args ((or @t111 @t11))) % 0.32/0.58 (step @p68 :rule bool-double-not-elim :args (@t11)) % 0.32/0.58 (step @p69 :rule refl :args (@t111)) % 0.32/0.58 (step @p70 :rule nary_cong :premises (@p69 @p68) :args ((or @t111 (not @t112)))) % 0.32/0.58 (step @p71 :rule bool-and-de-morgan :args (@t14 @t112 true)) % 0.32/0.58 (step @p72 :rule trans :premises (@p71 @p70)) % 0.32/0.58 (step @p73 :rule trans :premises (@p72 @p67)) % 0.32/0.58 (step @p74 :rule nary_cong :premises (@p73 @p64 @p51) :args (@t119)) % 0.32/0.58 (step @p75 :rule aci_norm :args ((= (and @t118 (and @t116 @t114)) @t119))) % 0.32/0.58 (step @p76 :rule bool-or-de-morgan :args (@t115 @t113 false)) % 0.32/0.58 (step @p77 :rule refl :args (@t118)) % 0.32/0.58 (step @p78 :rule nary_cong :premises (@p77 @p76) :args ((and @t118 (not (or @t115 @t113))))) % 0.32/0.58 (step @p79 :rule bool-or-de-morgan :args (@t117 @t115 (or @t113))) % 0.32/0.58 (step @p80 :rule trans :premises (@p79 @p78)) % 0.32/0.58 (step @p81 :rule trans :premises (@p80 @p75)) % 0.32/0.58 (step @p82 :rule trans :premises (@p81 @p74)) % 0.32/0.58 (step @p83 :rule cong :premises (@p82) :args (@t121)) % 0.32/0.58 (step @p84 :rule trans :premises (@p83 @p42)) % 0.32/0.58 (step @p85 :rule cong :premises (@p84) :args (@t122)) % 0.32/0.58 (step @p86 :rule exists-elim :args ((= (exists @t27 @t120) @t122))) % 0.32/0.58 (step @p87 :rule trans :premises (@p86 @p85)) % 0.32/0.58 (step @p88 :rule quant-miniscope-or :args ((= (forall @t34 @t123) @t107))) % 0.32/0.58 (step @p89 :rule aci_norm :args ((= @t124 @t123))) % 0.32/0.58 (step @p90 :rule cong :premises (@p89) :args (@t125)) % 0.32/0.58 (step @p91 :rule trans :premises (@p90 @p88)) % 0.32/0.58 (step @p92 :rule refl :args (@t40)) % 0.32/0.58 (step @p93 :rule nary_cong :premises (@p92 @p91) :args ((and @t40 @t125))) % 0.32/0.58 (step @p94 :rule alpha_equiv :args (@t129 @t130 @t131)) % 0.32/0.58 (step @p95 :rule alpha_equiv :args (@t132 @t130 (@list @t39))) % 0.32/0.58 (step @p96 :rule nary_cong :premises (@p95 @p94) :args (@t133)) % 0.32/0.58 (step @p97 :rule quant-miniscope-and :args ((= @t135 @t133))) % 0.32/0.58 (step @p98 :rule trans :premises (@p97 @p96)) % 0.32/0.58 (step @p99 :rule trans :premises (@p98 @p93)) % 0.32/0.58 (step @p100 :rule quant-miniscope-or :args ((= @t136 @t109))) % 0.32/0.58 (step @p101 :rule quant-miniscope-or :args ((= @t137 @t110))) % 0.32/0.58 (step @p102 :rule nary_cong :premises (@p101 @p100) :args ((and @t137 @t136))) % 0.32/0.58 (step @p103 :rule alpha_equiv :args (@t140 @t141 (@list @t42))) % 0.32/0.58 (step @p104 :rule alpha_equiv :args (@t143 @t141 @t144)) % 0.32/0.58 (step @p105 :rule nary_cong :premises (@p104 @p103) :args (@t145)) % 0.32/0.58 (step @p106 :rule quant-miniscope-and :args ((= @t147 @t145))) % 0.32/0.58 (step @p107 :rule trans :premises (@p106 @p105)) % 0.32/0.58 (step @p108 :rule trans :premises (@p107 @p102)) % 0.32/0.58 (step @p109 :rule refl :args (@t117)) % 0.32/0.58 (step @p110 :rule nary_cong :premises (@p109 @p108 @p99) :args (@t148)) % 0.32/0.58 (step @p111 :rule quant-miniscope-or :args ((= (forall @t25 @t149) @t148))) % 0.32/0.58 (step @p112 :rule aci_norm :args ((= @t150 @t149))) % 0.32/0.58 (step @p113 :rule cong :premises (@p112) :args ((forall @t25 @t150))) % 0.32/0.58 (step @p114 :rule trans :premises (@p113 @p111)) % 0.32/0.58 (step @p115 :rule trans :premises (@p114 @p110)) % 0.32/0.58 (step @p116 :rule aci_norm :args ((= (or @t146 (or @t117 @t134)) @t150))) % 0.32/0.58 (step @p117 :rule aci_norm :args ((= (or @t106 (or @t126 @t2)) @t127))) % 0.32/0.58 (step @p118 :rule refl :args (@t2)) % 0.32/0.58 (step @p119 :rule bool-or-de-morgan :args (@t4 @t3 false)) % 0.32/0.58 (step @p120 :rule nary_cong :premises (@p119 @p118) :args ((or (not @t5) @t2))) % 0.32/0.58 (step @p121 :rule bool-impl-elim :args (@t5 @t2)) % 0.32/0.58 (step @p122 :rule trans :premises (@p121 @p120)) % 0.32/0.58 (step @p123 :rule refl :args (@t106)) % 0.32/0.58 (step @p124 :rule nary_cong :premises (@p123 @p122) :args ((or @t106 @t6))) % 0.32/0.58 (step @p125 :rule trans :premises (@p124 @p117)) % 0.32/0.58 (step @p126 :rule bool-impl-elim :args (@t8 @t6)) % 0.32/0.58 (step @p127 :rule trans :premises (@p126 @p125)) % 0.32/0.58 (step @p128 :rule nary_cong :premises (@p118 @p127) :args (@t9)) % 0.32/0.58 (step @p129 :rule bool-implies-de-morgan :args (@t14 @t11)) % 0.32/0.58 (step @p130 :rule nary_cong :premises (@p129 @p128) :args ((or (not @t15) @t9))) % 0.32/0.58 (step @p131 :rule bool-impl-elim :args (@t15 @t9)) % 0.32/0.58 (step @p132 :rule trans :premises (@p131 @p130)) % 0.32/0.58 (step @p133 :rule bool-double-not-elim :args (@t18)) % 0.32/0.58 (step @p134 :rule refl :args (@t102)) % 0.32/0.58 (step @p135 :rule nary_cong :premises (@p134 @p133) :args ((or @t102 (not @t19)))) % 0.32/0.58 (step @p136 :rule bool-and-de-morgan :args (@t12 @t19 true)) % 0.32/0.58 (step @p137 :rule trans :premises (@p136 @p135)) % 0.32/0.58 (step @p138 :rule bool-impl-elim :args (@t22 @t21)) % 0.32/0.58 (step @p139 :rule nary_cong :premises (@p138 @p137) :args ((and @t23 (not @t20)))) % 0.32/0.58 (step @p140 :rule bool-implies-de-morgan :args (@t23 @t20)) % 0.32/0.58 (step @p141 :rule trans :premises (@p140 @p139)) % 0.32/0.58 (step @p142 :rule nary_cong :premises (@p141 @p132) :args ((or (not @t24) @t16))) % 0.32/0.58 (step @p143 :rule trans :premises (@p142 @p116)) % 0.32/0.58 (step @p144 :rule bool-impl-elim :args (@t24 @t16)) % 0.32/0.58 (step @p145 :rule trans :premises (@p144 @p143)) % 0.32/0.58 (step @p146 :rule cong :premises (@p145) :args (@t26)) % 0.32/0.58 (step @p147 :rule trans :premises (@p146 @p115)) % 0.32/0.58 (step @p148 :rule cong :premises (@p147) :args (@t28)) % 0.32/0.58 (step @p149 :rule trans :premises (@p148 @p87)) % 0.32/0.58 (step @p150 :rule cong :premises (@p149) :args (@t29)) % 0.32/0.58 (step @p151 :rule trans :premises (@p150 @p3)) % 0.32/0.58 (step @p152 :rule eq_resolve :premises (@p1 @p151)) % 0.32/0.58 (step @p153 :rule and_elim :premises (@p152) :args (0)) % 0.32/0.58 (step @p154 :rule instantiate :premises (@p153) :args (@t152)) % 0.32/0.58 (step @p155 :rule alpha_equiv :args (@t60 (@list @t58) @t131)) % 0.32/0.58 (step @p156 :rule symm :premises (@p155)) % 0.32/0.58 (step @p157 :rule equiv_elim2 :premises (@p156)) % 0.32/0.58 (step @p158 :rule chain_m_resolution :premises (@p157 @p153) :args (@t35 @t153 (@list @t60))) % 0.32/0.58 (step @p159 :rule cnf_and_pos :args (@t38 1)) % 0.32/0.58 (step @p160 :rule reordering :premises (@p159) :args ((or @t36 @t154))) % 0.32/0.58 (step @p161 :rule chain_m_resolution :premises (@p160 @p158) :args (@t154 @t153 (@list @t35))) % 0.32/0.58 (step @p162 :rule and_elim :premises (@p152) :args (2)) % 0.32/0.58 (step @p163 :rule chain_m_resolution :premises (@p162 @p161) :args (@t41 @t155 (@list @t38))) % 0.32/0.58 (step @p164 :rule skolemize :premises (@p163)) % 0.32/0.58 (step @p165 :rule cnf_or_pos :args (@t162)) % 0.32/0.58 (step @p166 :rule reordering :premises (@p165) :args ((or @t156 @t161 (not @t162)))) % 0.32/0.58 (step @p167 :rule chain_m_resolution :premises (@p166 @p164 @p154) :args (@t161 (@list true false) (@list @t156 @t162))) % 0.32/0.58 (step @p168 :rule cnf_and_pos :args (@t161 0)) % 0.32/0.58 (step @p169 :rule reordering :premises (@p168) :args ((or @t160 @t163))) % 0.32/0.58 (step @p170 :rule chain_m_resolution :premises (@p169 @p167) :args (@t160 @t153 @t164)) % 0.32/0.58 (step @p171 :rule cnf_and_pos :args (@t161 1)) % 0.32/0.58 (step @p172 :rule reordering :premises (@p171) :args ((or @t158 @t163))) % 0.32/0.58 (step @p173 :rule chain_m_resolution :premises (@p172 @p167) :args (@t158 @t153 @t164)) % 0.32/0.58 (assume-push @p197 @t53) % 0.32/0.58 (step @p175 :rule instantiate :premises (@p197) :args (@t152)) % 0.32/0.58 (step-pop @p198 :rule scope :premises (@p175)) % 0.32/0.58 (step @p176 :rule process_scope :premises (@p198) :args (@t157)) % 0.32/0.58 (step @p178 :rule implies_elim :premises (@p176)) % 0.32/0.58 (step @p179 :rule chain_m_resolution :premises (@p178 @p173) :args (@t54 @t155 (@list @t157))) % 0.32/0.58 (step @p180 :rule alpha_equiv :args (@t53 @t144 @t79)) % 0.32/0.58 (step @p181 :rule equiv_elim2 :premises (@p180)) % 0.32/0.58 (step @p182 :rule chain_m_resolution :premises (@p181 @p179) :args ((not @t48) @t155 (@list @t53))) % 0.32/0.58 (step @p183 :rule cnf_and_pos :args (@t49 0)) % 0.32/0.58 (step @p184 :rule reordering :premises (@p183) :args ((or @t48 @t165))) % 0.32/0.58 (step @p185 :rule chain_m_resolution :premises (@p184 @p182) :args (@t165 @t155 (@list @t48))) % 0.32/0.58 (step @p186 :rule and_elim :premises (@p152) :args (1)) % 0.32/0.58 (step @p187 :rule chain_m_resolution :premises (@p186 @p185) :args (@t57 @t155 (@list @t49))) % 0.32/0.58 (step @p188 :rule cnf_and_pos :args (@t57 0)) % 0.32/0.58 (step @p189 :rule reordering :premises (@p188) :args ((or @t56 (not @t57)))) % 0.32/0.58 (step @p190 :rule chain_m_resolution :premises (@p189 @p187) :args (@t56 @t153 (@list @t57))) % 0.32/0.58 (assume-push @p199 @t56) % 0.32/0.58 (step @p192 :rule instantiate :premises (@p199) :args (@t152)) % 0.32/0.58 (step-pop @p200 :rule scope :premises (@p192)) % 0.32/0.58 (step @p193 :rule process_scope :premises (@p200) :args (@t159)) % 0.32/0.58 (step @p195 :rule implies_elim :premises (@p193)) % 0.32/0.58 (step @p196 false :rule chain_m_resolution :premises (@p195 @p190 @p170) :args (false (@list false true) (@list @t56 @t159))) % 0.32/0.58 ) % 0.32/0.58 % SZS output end Proof % 0.32/0.58 % cvc5 exiting %------------------------------------------------------------------------------