%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU277+1 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/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 08:51:13 AM UTC 2026 % Result : Theorem 0.36s 0.59s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU277+1 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/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 16:50:08 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.59 % SZS status Theorem % 0.36/0.59 % SZS output start Proof % 0.36/0.59 ( % 0.36/0.59 (declare-sort $$unsorted 0) % 0.36/0.59 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.ordinal (-> $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.function (-> $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.epsilon_transitive (-> $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.epsilon_connected (-> $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.59 (define @t1 () (@var "B" $$unsorted)) % 0.36/0.59 (define @t2 () (@var "G" $$unsorted)) % 0.36/0.59 (define @t3 () (@var "C" $$unsorted)) % 0.36/0.59 (define @t4 () (tptp.apply @t3 @t2)) % 0.36/0.59 (define @t5 () (@var "F" $$unsorted)) % 0.36/0.59 (define @t6 () (tptp.in (tptp.ordered_pair (tptp.apply @t3 @t5) @t4) @t1)) % 0.36/0.59 (define @t7 () (@var "E" $$unsorted)) % 0.36/0.59 (define @t8 () (= @t7 (tptp.ordered_pair @t5 @t2))) % 0.36/0.59 (define @t9 () (and @t8 @t6)) % 0.36/0.59 (define @t10 () (@list @t5 @t2)) % 0.36/0.59 (define @t11 () (exists @t10 @t9)) % 0.36/0.59 (define @t12 () (@var "A" $$unsorted)) % 0.36/0.59 (define @t13 () (tptp.cartesian_product2 @t12 @t12)) % 0.36/0.59 (define @t14 () (tptp.in @t7 @t13)) % 0.36/0.59 (define @t15 () (and @t14 @t11)) % 0.36/0.59 (define @t16 () (@var "D" $$unsorted)) % 0.36/0.59 (define @t17 () (tptp.in @t7 @t16)) % 0.36/0.59 (define @t18 () (= @t17 @t15)) % 0.36/0.59 (define @t19 () (@list @t7)) % 0.36/0.59 (define @t20 () (forall @t19 @t18)) % 0.36/0.59 (define @t21 () (@list @t16)) % 0.36/0.59 (define @t22 () (exists @t21 @t20)) % 0.36/0.59 (define @t23 () (tptp.function @t3)) % 0.36/0.59 (define @t24 () (tptp.relation @t3)) % 0.36/0.59 (define @t25 () (tptp.relation @t1)) % 0.36/0.59 (define @t26 () (and @t25 @t24 @t23)) % 0.36/0.59 (define @t27 () (=> @t26 @t22)) % 0.36/0.59 (define @t28 () (@list @t12 @t1 @t3)) % 0.36/0.59 (define @t29 () (forall @t28 @t27)) % 0.36/0.59 (define @t30 () (not @t29)) % 0.36/0.59 (define @t31 () (tptp.one_to_one @t12)) % 0.36/0.59 (define @t32 () (tptp.function @t12)) % 0.36/0.59 (define @t33 () (tptp.relation @t12)) % 0.36/0.59 (define @t34 () (and @t33 @t32 @t31)) % 0.36/0.59 (define @t35 () (@list @t12)) % 0.36/0.59 (define @t36 () (tptp.epsilon_connected @t12)) % 0.36/0.59 (define @t37 () (tptp.epsilon_transitive @t12)) % 0.36/0.59 (define @t38 () (and @t37 @t36)) % 0.36/0.59 (define @t39 () (tptp.ordinal @t12)) % 0.36/0.59 (define @t40 () (and @t37 @t36 @t39)) % 0.36/0.59 (define @t41 () (tptp.empty @t12)) % 0.36/0.59 (define @t42 () (not @t41)) % 0.36/0.59 (define @t43 () (and @t33 @t41 @t32)) % 0.36/0.59 (define @t44 () (@list @t12 @t1)) % 0.36/0.59 (define @t45 () (@var "L" $$unsorted)) % 0.36/0.59 (define @t46 () (@var "K" $$unsorted)) % 0.36/0.59 (define @t47 () (tptp.in (tptp.ordered_pair (tptp.apply @t3 @t46) (tptp.apply @t3 @t45)) @t1)) % 0.36/0.59 (define @t48 () (= @t7 (tptp.ordered_pair @t46 @t45))) % 0.36/0.59 (define @t49 () (and @t48 @t47)) % 0.36/0.59 (define @t50 () (@list @t46 @t45)) % 0.36/0.59 (define @t51 () (exists @t50 @t49)) % 0.36/0.59 (define @t52 () (= @t5 @t7)) % 0.36/0.59 (define @t53 () (tptp.in @t5 @t13)) % 0.36/0.59 (define @t54 () (and @t53 @t52 @t51)) % 0.36/0.59 (define @t55 () (@list @t5)) % 0.36/0.59 (define @t56 () (exists @t55 @t54)) % 0.36/0.59 (define @t57 () (= @t17 @t56)) % 0.36/0.59 (define @t58 () (forall @t19 @t57)) % 0.36/0.59 (define @t59 () (exists @t21 @t58)) % 0.36/0.59 (define @t60 () (= @t7 @t5)) % 0.36/0.59 (define @t61 () (@var "J" $$unsorted)) % 0.36/0.59 (define @t62 () (@var "I" $$unsorted)) % 0.36/0.59 (define @t63 () (tptp.in (tptp.ordered_pair (tptp.apply @t3 @t62) (tptp.apply @t3 @t61)) @t1)) % 0.36/0.59 (define @t64 () (= @t5 (tptp.ordered_pair @t62 @t61))) % 0.36/0.59 (define @t65 () (and @t64 @t63)) % 0.36/0.59 (define @t66 () (@list @t62 @t61)) % 0.36/0.59 (define @t67 () (exists @t66 @t65)) % 0.36/0.59 (define @t68 () (= @t16 @t5)) % 0.36/0.59 (define @t69 () (@var "H" $$unsorted)) % 0.36/0.59 (define @t70 () (tptp.in (tptp.ordered_pair @t4 (tptp.apply @t3 @t69)) @t1)) % 0.36/0.59 (define @t71 () (= @t7 (tptp.ordered_pair @t2 @t69))) % 0.36/0.59 (define @t72 () (and @t71 @t70)) % 0.36/0.59 (define @t73 () (@list @t2 @t69)) % 0.36/0.59 (define @t74 () (exists @t73 @t72)) % 0.36/0.59 (define @t75 () (= @t16 @t7)) % 0.36/0.59 (define @t76 () (and @t75 @t74 @t68 @t67)) % 0.36/0.59 (define @t77 () (=> @t76 @t60)) % 0.36/0.59 (define @t78 () (@list @t16 @t7 @t5)) % 0.36/0.59 (define @t79 () (forall @t78 @t77)) % 0.36/0.59 (define @t80 () (=> @t79 @t59)) % 0.36/0.59 (define @t81 () (=> @t26 @t80)) % 0.36/0.59 (define @t82 () (forall @t28 @t81)) % 0.36/0.59 (define @t83 () (forall @t19 (= @t17 (and @t14 (not (forall @t10 (or (not @t8) (not @t6)))))))) % 0.36/0.59 (define @t84 () (not (forall @t21 (not @t83)))) % 0.36/0.59 (define @t85 () (not @t23)) % 0.36/0.59 (define @t86 () (not @t24)) % 0.36/0.59 (define @t87 () (not @t25)) % 0.36/0.59 (define @t88 () (or @t87 @t86 @t85 @t84)) % 0.36/0.59 (define @t89 () (or @t87 @t86 @t85)) % 0.36/0.59 (define @t90 () (not @t26)) % 0.36/0.59 (define @t91 () (forall @t10 (not @t9))) % 0.36/0.59 (define @t92 () (not @t91)) % 0.36/0.59 (define @t93 () (forall @t50 (or (not @t48) (not @t47)))) % 0.36/0.59 (define @t94 () (not @t93)) % 0.36/0.59 (define @t95 () (and @t14 @t94)) % 0.36/0.59 (define @t96 () (and @t94 @t14)) % 0.36/0.59 (define @t97 () (= @t17 @t96)) % 0.36/0.59 (define @t98 () (forall @t19 @t97)) % 0.36/0.59 (define @t99 () (not @t98)) % 0.36/0.59 (define @t100 () (forall @t21 @t99)) % 0.36/0.59 (define @t101 () (not @t100)) % 0.36/0.59 (define @t102 () (or @t87 @t86 @t85 @t101)) % 0.36/0.59 (define @t103 () (forall @t28 @t102)) % 0.36/0.59 (define @t104 () (forall @t28 (or @t87 @t86 @t85 (not (forall @t21 (not (forall @t19 (= @t17 @t95)))))))) % 0.36/0.59 (define @t105 () (@var "BOUND_VARIABLE_7872" $$unsorted)) % 0.36/0.59 (define @t106 () (@var "BOUND_VARIABLE_7877" $$unsorted)) % 0.36/0.59 (define @t107 () (@var "BOUND_VARIABLE_7871" $$unsorted)) % 0.36/0.59 (define @t108 () (@var "BOUND_VARIABLE_7876" $$unsorted)) % 0.36/0.59 (define @t109 () (@var "BOUND_VARIABLE_7874" $$unsorted)) % 0.36/0.59 (define @t110 () (@var "BOUND_VARIABLE_7875" $$unsorted)) % 0.36/0.59 (define @t111 () (@var "BOUND_VARIABLE_7873" $$unsorted)) % 0.36/0.59 (define @t112 () (@list @t107 @t105 @t111 @t109 @t110 @t108 @t106)) % 0.36/0.59 (define @t113 () (forall @t28 @t88)) % 0.36/0.59 (define @t114 () (@list true)) % 0.36/0.59 (define @t115 () (not @t14)) % 0.36/0.59 (define @t116 () (= @t17 (not (or @t93 @t115)))) % 0.36/0.59 (define @t117 () (not (= @t7 @t7))) % 0.36/0.59 (define @t118 () (or @t115 @t117)) % 0.36/0.59 (define @t119 () (not @t60)) % 0.36/0.59 (define @t120 () (not @t53)) % 0.36/0.59 (define @t121 () (or @t119 @t120 @t119)) % 0.36/0.59 (define @t122 () (or @t120 @t119)) % 0.36/0.59 (define @t123 () (forall @t55 @t122)) % 0.36/0.59 (define @t124 () (or @t93 @t123)) % 0.36/0.59 (define @t125 () (or @t93 @t122)) % 0.36/0.59 (define @t126 () (or @t120 @t119 @t93)) % 0.36/0.59 (define @t127 () (not @t94)) % 0.36/0.59 (define @t128 () (or @t120 @t119 @t127)) % 0.36/0.59 (define @t129 () (and @t53 @t60 @t94)) % 0.36/0.59 (define @t130 () (forall @t55 (not @t129))) % 0.36/0.59 (define @t131 () (not @t130)) % 0.36/0.59 (define @t132 () (forall @t50 (not @t49))) % 0.36/0.59 (define @t133 () (not @t132)) % 0.36/0.59 (define @t134 () (@var "BOUND_VARIABLE_7691" $$unsorted)) % 0.36/0.59 (define @t135 () (@var "BOUND_VARIABLE_7689" $$unsorted)) % 0.36/0.59 (define @t136 () (@var "BOUND_VARIABLE_7678" $$unsorted)) % 0.36/0.59 (define @t137 () (@var "BOUND_VARIABLE_7676" $$unsorted)) % 0.36/0.59 (define @t138 () (@list @t7 @t5 @t137 @t136 @t135 @t134)) % 0.36/0.59 (define @t139 () (not (tptp.in (tptp.ordered_pair (tptp.apply @t3 @t135) (tptp.apply @t3 @t134)) @t1))) % 0.36/0.59 (define @t140 () (not (= @t5 (tptp.ordered_pair @t135 @t134)))) % 0.36/0.59 (define @t141 () (not (tptp.in (tptp.ordered_pair (tptp.apply @t3 @t137) (tptp.apply @t3 @t136)) @t1))) % 0.36/0.59 (define @t142 () (not (= @t7 (tptp.ordered_pair @t137 @t136)))) % 0.36/0.59 (define @t143 () (or @t119 @t60 @t142 @t141 @t140 @t139)) % 0.36/0.59 (define @t144 () (or @t117 @t119 @t60 @t142 @t141 @t140 @t139)) % 0.36/0.59 (define @t145 () (not @t68)) % 0.36/0.59 (define @t146 () (not @t75)) % 0.36/0.59 (define @t147 () (or @t146 @t146 @t145 @t60 @t142 @t141 @t140 @t139)) % 0.36/0.59 (define @t148 () (or @t146 @t145 @t60 @t142 @t141 @t140 @t139)) % 0.36/0.59 (define @t149 () (forall @t21 @t148)) % 0.36/0.59 (define @t150 () (forall @t138 @t149)) % 0.36/0.59 (define @t151 () (forall (@list @t7 @t5 @t137 @t136 @t135 @t134 @t16) @t148)) % 0.36/0.59 (define @t152 () (@list @t16 @t7 @t5 @t137 @t136 @t135 @t134)) % 0.36/0.59 (define @t153 () (or @t140 @t139)) % 0.36/0.59 (define @t154 () (or @t142 @t141)) % 0.36/0.59 (define @t155 () (or @t146 @t154 @t145 @t153 @t60)) % 0.36/0.59 (define @t156 () (forall @t152 @t155)) % 0.36/0.59 (define @t157 () (forall (@list @t137 @t136 @t135 @t134) @t155)) % 0.36/0.59 (define @t158 () (forall (@list @t135 @t134) @t153)) % 0.36/0.59 (define @t159 () (forall (@list @t137 @t136) @t154)) % 0.36/0.59 (define @t160 () (or @t146 @t159 @t145 @t158 @t60)) % 0.36/0.59 (define @t161 () (forall @t66 (or (not @t64) (not @t63)))) % 0.36/0.59 (define @t162 () (forall @t73 (or (not @t71) (not @t70)))) % 0.36/0.59 (define @t163 () (or @t146 @t162 @t145 @t161 @t60)) % 0.36/0.59 (define @t164 () (not @t161)) % 0.36/0.59 (define @t165 () (not @t164)) % 0.36/0.59 (define @t166 () (not @t162)) % 0.36/0.59 (define @t167 () (not @t166)) % 0.36/0.59 (define @t168 () (or @t146 @t167 @t145 @t165)) % 0.36/0.59 (define @t169 () (and @t75 @t166 @t68 @t164)) % 0.36/0.59 (define @t170 () (forall @t66 (not @t65))) % 0.36/0.59 (define @t171 () (not @t170)) % 0.36/0.59 (define @t172 () (forall @t73 (not @t72))) % 0.36/0.59 (define @t173 () (not @t172)) % 0.36/0.59 (assume @p1 @t30) % 0.36/0.59 (assume @p2 (exists @t35 @t34)) % 0.36/0.59 (assume @p3 (forall @t35 (=> @t39 @t38))) % 0.36/0.59 (assume @p4 (forall @t35 (=> @t38 @t39))) % 0.36/0.59 (assume @p5 (exists @t35 @t40)) % 0.36/0.59 (assume @p6 (exists @t35 (and @t33 @t32 @t31 @t41 @t37 @t36 @t39))) % 0.36/0.59 (assume @p7 (exists @t35 (and @t42 @t37 @t36 @t39))) % 0.36/0.59 (assume @p8 (forall @t35 (=> @t41 @t32))) % 0.36/0.59 (assume @p9 (exists @t35 @t43)) % 0.36/0.59 (assume @p10 (forall @t35 (=> @t43 @t34))) % 0.36/0.59 (assume @p11 (forall @t35 (=> @t41 @t40))) % 0.36/0.59 (assume @p12 (exists @t35 @t41)) % 0.36/0.59 (assume @p13 (exists @t35 @t42)) % 0.36/0.59 (assume @p14 (forall @t44 (=> (tptp.in @t12 @t1) (not (tptp.in @t1 @t12))))) % 0.36/0.59 (assume @p15 true) % 0.36/0.59 (assume @p16 (exists @t35 (and @t33 @t32))) % 0.36/0.59 (assume @p17 (forall @t44 (not (tptp.empty (tptp.ordered_pair @t12 @t1))))) % 0.36/0.59 (assume @p18 @t82) % 0.36/0.59 (step @p19 :rule aci_norm :args ((= (or @t89 @t84) @t88))) % 0.36/0.59 (step @p20 :rule refl :args (@t84)) % 0.36/0.59 (step @p21 :rule aci_norm :args ((= (or @t87 (or @t86 @t85)) @t89))) % 0.36/0.59 (step @p22 :rule bool-and-de-morgan :args (@t24 @t23 true)) % 0.36/0.59 (step @p23 :rule refl :args (@t87)) % 0.36/0.59 (step @p24 :rule nary_cong :premises (@p23 @p22) :args ((or @t87 (not (and @t24 @t23))))) % 0.36/0.59 (step @p25 :rule bool-and-de-morgan :args (@t25 @t24 (and @t23))) % 0.36/0.59 (step @p26 :rule trans :premises (@p25 @p24)) % 0.36/0.59 (step @p27 :rule trans :premises (@p26 @p21)) % 0.36/0.59 (step @p28 :rule nary_cong :premises (@p27 @p20) :args ((or @t90 @t84))) % 0.36/0.59 (step @p29 :rule trans :premises (@p28 @p19)) % 0.36/0.59 (step @p30 :rule bool-impl-elim :args (@t26 @t84)) % 0.36/0.59 (step @p31 :rule trans :premises (@p30 @p29)) % 0.36/0.59 (step @p32 :rule cong :premises (@p31) :args ((forall @t28 (=> @t26 @t84)))) % 0.36/0.59 (step @p33 :rule exists-elim :args ((= (exists @t21 @t83) @t84))) % 0.36/0.59 (step @p34 :rule bool-and-de-morgan :args (@t8 @t6 true)) % 0.36/0.59 (step @p35 :rule cong :premises (@p34) :args (@t91)) % 0.36/0.59 (step @p36 :rule cong :premises (@p35) :args (@t92)) % 0.36/0.59 (step @p37 :rule exists-elim :args ((= @t11 @t92))) % 0.36/0.59 (step @p38 :rule trans :premises (@p37 @p36)) % 0.36/0.59 (step @p39 :rule refl :args (@t14)) % 0.36/0.59 (step @p40 :rule nary_cong :premises (@p39 @p38) :args (@t15)) % 0.36/0.59 (step @p41 :rule refl :args (@t17)) % 0.36/0.59 (step @p42 :rule cong :premises (@p41 @p40) :args (@t18)) % 0.36/0.59 (step @p43 :rule cong :premises (@p42) :args (@t20)) % 0.36/0.59 (step @p44 :rule cong :premises (@p43) :args (@t22)) % 0.36/0.59 (step @p45 :rule trans :premises (@p44 @p33)) % 0.36/0.59 (step @p46 :rule refl :args (@t26)) % 0.36/0.59 (step @p47 :rule cong :premises (@p46 @p45) :args (@t27)) % 0.36/0.59 (step @p48 :rule cong :premises (@p47) :args (@t29)) % 0.36/0.59 (step @p49 :rule trans :premises (@p48 @p32)) % 0.36/0.59 (step @p50 :rule cong :premises (@p49) :args (@t30)) % 0.36/0.59 (step @p51 :rule eq_resolve :premises (@p1 @p50)) % 0.36/0.59 (step @p52 :rule aci_norm :args ((= @t96 @t95))) % 0.36/0.59 (step @p53 :rule refl :args (@t17)) % 0.36/0.59 (step @p54 :rule cong :premises (@p53 @p52) :args (@t97)) % 0.36/0.59 (step @p55 :rule cong :premises (@p54) :args (@t98)) % 0.36/0.59 (step @p56 :rule cong :premises (@p55) :args (@t99)) % 0.36/0.59 (step @p57 :rule cong :premises (@p56) :args (@t100)) % 0.36/0.59 (step @p58 :rule cong :premises (@p57) :args (@t101)) % 0.36/0.59 (step @p59 :rule refl :args (@t85)) % 0.36/0.59 (step @p60 :rule refl :args (@t86)) % 0.36/0.59 (step @p61 :rule nary_cong :premises (@p23 @p60 @p59 @p58) :args (@t102)) % 0.36/0.59 (step @p62 :rule cong :premises (@p61) :args (@t103)) % 0.36/0.59 (step @p63 :rule symm :premises (@p62)) % 0.36/0.59 (step @p64 :rule true_intro :premises (@p63)) % 0.36/0.59 (step @p65 :rule eq-symm :args (@t103 @t104)) % 0.36/0.59 (step @p66 :rule trans :premises (@p65 @p64)) % 0.36/0.59 (step @p67 :rule cong :premises (@p63 @p62) :args ((= @t104 @t103))) % 0.36/0.59 (step @p68 :rule trans :premises (@p67 @p66)) % 0.36/0.59 (step @p69 :rule true_elim :premises (@p68)) % 0.36/0.59 (step @p70 :rule alpha_equiv :args ((forall (@list @t110 @t105 @t107) (or (not (tptp.relation @t105)) (not (tptp.relation @t107)) (not (tptp.function @t107)) (not (forall (@list @t111) (not (forall (@list @t109) (= (tptp.in @t109 @t111) (and (tptp.in @t109 (tptp.cartesian_product2 @t110 @t110)) (not (forall (@list @t108 @t106) (or (not (= @t109 (tptp.ordered_pair @t108 @t106))) (not (tptp.in (tptp.ordered_pair (tptp.apply @t107 @t108) (tptp.apply @t107 @t106)) @t105))))))))))))) @t112 (@list @t3 @t1 @t16 @t7 @t12 @t46 @t45))) % 0.36/0.59 (step @p71 :rule alpha_equiv :args (@t113 (@list @t3 @t1 @t16 @t7 @t12 @t5 @t2) @t112)) % 0.36/0.59 (step @p72 :rule trans :premises (@p71 @p70 @p69)) % 0.36/0.59 (step @p73 :rule equiv_elim2 :premises (@p72)) % 0.36/0.59 (step @p74 :rule chain_m_resolution :premises (@p73 @p51) :args ((not @t103) @t114 (@list @t113))) % 0.36/0.59 (step @p75 :rule aci_norm :args ((= (or @t89 @t101) @t102))) % 0.36/0.59 (step @p76 :rule refl :args (@t101)) % 0.36/0.59 (step @p77 :rule nary_cong :premises (@p27 @p76) :args ((or @t90 @t101))) % 0.36/0.59 (step @p78 :rule trans :premises (@p77 @p75)) % 0.36/0.59 (step @p79 :rule bool-impl-elim :args (@t26 @t101)) % 0.36/0.59 (step @p80 :rule trans :premises (@p79 @p78)) % 0.36/0.59 (step @p81 :rule cong :premises (@p80) :args ((forall @t28 (=> @t26 @t101)))) % 0.36/0.59 (step @p82 :rule bool-impl-true2 :args (@t101)) % 0.36/0.59 (step @p83 :rule exists-elim :args ((= (exists @t21 @t98) @t101))) % 0.36/0.59 (step @p84 :rule bool-double-not-elim :args (@t14)) % 0.36/0.59 (step @p85 :rule refl :args (@t94)) % 0.36/0.59 (step @p86 :rule nary_cong :premises (@p85 @p84) :args ((and @t94 (not @t115)))) % 0.36/0.59 (step @p87 :rule bool-or-de-morgan :args (@t93 @t115 false)) % 0.36/0.59 (step @p88 :rule trans :premises (@p87 @p86)) % 0.36/0.59 (step @p89 :rule cong :premises (@p53 @p88) :args (@t116)) % 0.36/0.59 (step @p90 :rule cong :premises (@p89) :args ((forall @t19 @t116))) % 0.36/0.59 (step @p91 :rule aci_norm :args ((= (or @t115 false) @t115))) % 0.36/0.59 (step @p92 :rule evaluate :args ((not true))) % 0.36/0.59 (step @p93 :rule eq-refl :args (@t7)) % 0.36/0.59 (step @p94 :rule cong :premises (@p93) :args (@t117)) % 0.36/0.59 (step @p95 :rule trans :premises (@p94 @p92)) % 0.36/0.59 (step @p96 :rule refl :args (@t115)) % 0.36/0.59 (step @p97 :rule nary_cong :premises (@p96 @p95) :args (@t118)) % 0.36/0.59 (step @p98 :rule trans :premises (@p97 @p91)) % 0.36/0.59 (step @p99 :rule quant-var-elim-eq :args ((= (forall @t55 (or (not @t52) @t120 @t119)) @t118))) % 0.36/0.59 (step @p100 :rule refl :args (@t119)) % 0.36/0.59 (step @p101 :rule refl :args (@t120)) % 0.36/0.59 (step @p102 :rule eq-symm :args (@t7 @t5)) % 0.36/0.59 (step @p103 :rule cong :premises (@p102) :args (@t119)) % 0.36/0.59 (step @p104 :rule nary_cong :premises (@p103 @p101 @p100) :args (@t121)) % 0.36/0.59 (step @p105 :rule aci_norm :args ((= @t122 @t121))) % 0.36/0.59 (step @p106 :rule trans :premises (@p105 @p104)) % 0.36/0.59 (step @p107 :rule cong :premises (@p106) :args (@t123)) % 0.36/0.59 (step @p108 :rule trans :premises (@p107 @p99)) % 0.36/0.59 (step @p109 :rule trans :premises (@p108 @p98)) % 0.36/0.59 (step @p110 :rule refl :args (@t93)) % 0.36/0.59 (step @p111 :rule nary_cong :premises (@p110 @p109) :args (@t124)) % 0.36/0.59 (step @p112 :rule quant-miniscope-or :args ((= (forall @t55 @t125) @t124))) % 0.36/0.59 (step @p113 :rule aci_norm :args ((= @t126 @t125))) % 0.36/0.59 (step @p114 :rule cong :premises (@p113) :args ((forall @t55 @t126))) % 0.36/0.59 (step @p115 :rule trans :premises (@p114 @p112)) % 0.36/0.59 (step @p116 :rule trans :premises (@p115 @p111)) % 0.36/0.59 (step @p117 :rule bool-double-not-elim :args (@t93)) % 0.36/0.59 (step @p118 :rule nary_cong :premises (@p101 @p100 @p117) :args (@t128)) % 0.36/0.59 (step @p119 :rule aci_norm :args ((= (or @t120 (or @t119 @t127)) @t128))) % 0.36/0.59 (step @p120 :rule trans :premises (@p119 @p118)) % 0.36/0.59 (step @p121 :rule bool-and-de-morgan :args (@t60 @t94 true)) % 0.36/0.59 (step @p122 :rule nary_cong :premises (@p101 @p121) :args ((or @t120 (not (and @t60 @t94))))) % 0.36/0.59 (step @p123 :rule bool-and-de-morgan :args (@t53 @t60 (and @t94))) % 0.36/0.59 (step @p124 :rule trans :premises (@p123 @p122)) % 0.36/0.59 (step @p125 :rule trans :premises (@p124 @p120)) % 0.36/0.59 (step @p126 :rule cong :premises (@p125) :args (@t130)) % 0.36/0.59 (step @p127 :rule trans :premises (@p126 @p116)) % 0.36/0.59 (step @p128 :rule cong :premises (@p127) :args (@t131)) % 0.36/0.59 (step @p129 :rule exists-elim :args ((= (exists @t55 @t129) @t131))) % 0.36/0.59 (step @p130 :rule trans :premises (@p129 @p128)) % 0.36/0.59 (step @p131 :rule bool-and-de-morgan :args (@t48 @t47 true)) % 0.36/0.59 (step @p132 :rule cong :premises (@p131) :args (@t132)) % 0.36/0.59 (step @p133 :rule cong :premises (@p132) :args (@t133)) % 0.36/0.59 (step @p134 :rule exists-elim :args ((= @t51 @t133))) % 0.36/0.59 (step @p135 :rule trans :premises (@p134 @p133)) % 0.36/0.59 (step @p136 :rule eq-symm :args (@t5 @t7)) % 0.36/0.59 (step @p137 :rule refl :args (@t53)) % 0.36/0.59 (step @p138 :rule nary_cong :premises (@p137 @p136 @p135) :args (@t54)) % 0.36/0.59 (step @p139 :rule cong :premises (@p138) :args (@t56)) % 0.36/0.59 (step @p140 :rule trans :premises (@p139 @p130)) % 0.36/0.59 (step @p141 :rule cong :premises (@p41 @p140) :args (@t57)) % 0.36/0.59 (step @p142 :rule cong :premises (@p141) :args (@t58)) % 0.36/0.59 (step @p143 :rule trans :premises (@p142 @p90)) % 0.36/0.59 (step @p144 :rule cong :premises (@p143) :args (@t59)) % 0.36/0.59 (step @p145 :rule trans :premises (@p144 @p83)) % 0.36/0.59 (step @p146 :rule quant-unused-vars :args ((= (forall @t138 true) true))) % 0.36/0.59 (step @p147 :rule bool-or-taut2 :args (false @t60 false (or @t142 @t141 @t140 @t139))) % 0.36/0.59 (step @p148 :rule cong :premises (@p147) :args ((forall @t138 @t143))) % 0.36/0.59 (step @p149 :rule trans :premises (@p148 @p146)) % 0.36/0.59 (step @p150 :rule aci_norm :args ((= (or false @t119 @t60 @t142 @t141 @t140 @t139) @t143))) % 0.36/0.59 (step @p151 :rule refl :args (@t139)) % 0.36/0.59 (step @p152 :rule refl :args (@t140)) % 0.36/0.59 (step @p153 :rule refl :args (@t141)) % 0.36/0.59 (step @p154 :rule refl :args (@t142)) % 0.36/0.59 (step @p155 :rule refl :args (@t60)) % 0.36/0.59 (step @p156 :rule refl :args (@t119)) % 0.36/0.59 (step @p157 :rule nary_cong :premises (@p95 @p156 @p155 @p154 @p153 @p152 @p151) :args (@t144)) % 0.36/0.59 (step @p158 :rule trans :premises (@p157 @p150)) % 0.36/0.59 (step @p159 :rule cong :premises (@p158) :args ((forall @t138 @t144))) % 0.36/0.59 (step @p160 :rule trans :premises (@p159 @p149)) % 0.36/0.59 (step @p161 :rule quant-var-elim-eq :args ((= (forall @t21 @t147) @t144))) % 0.36/0.59 (step @p162 :rule aci_norm :args ((= @t148 @t147))) % 0.36/0.59 (step @p163 :rule cong :premises (@p162) :args (@t149)) % 0.36/0.59 (step @p164 :rule trans :premises (@p163 @p161)) % 0.36/0.59 (step @p165 :rule cong :premises (@p164) :args (@t150)) % 0.36/0.59 (step @p166 :rule quant-merge-prenex :args ((= @t150 @t151))) % 0.36/0.59 (step @p167 :rule symm :premises (@p166)) % 0.36/0.59 (step @p168 :rule quant_var_reordering :args ((= (forall @t152 @t148) @t151))) % 0.36/0.59 (step @p169 :rule trans :premises (@p168 @p167 @p165)) % 0.36/0.59 (step @p170 :rule trans :premises (@p169 @p160)) % 0.36/0.59 (step @p171 :rule aci_norm :args ((= @t155 @t148))) % 0.36/0.59 (step @p172 :rule cong :premises (@p171) :args (@t156)) % 0.36/0.59 (step @p173 :rule trans :premises (@p172 @p170)) % 0.36/0.59 (step @p174 :rule quant-merge-prenex :args ((= (forall @t78 @t157) @t156))) % 0.36/0.59 (step @p175 :rule refl :args (@t60)) % 0.36/0.59 (step @p176 :rule alpha_equiv :args (@t158 (@list @t135 @t134) (@list @t62 @t61))) % 0.36/0.59 (step @p177 :rule refl :args (@t145)) % 0.36/0.59 (step @p178 :rule alpha_equiv :args (@t159 (@list @t137 @t136) (@list @t2 @t69))) % 0.36/0.59 (step @p179 :rule refl :args (@t146)) % 0.36/0.59 (step @p180 :rule nary_cong :premises (@p179 @p178 @p177 @p176 @p175) :args (@t160)) % 0.36/0.59 (step @p181 :rule quant-miniscope-or :args ((= @t157 @t160))) % 0.36/0.59 (step @p182 :rule trans :premises (@p181 @p180)) % 0.36/0.59 (step @p183 :rule symm :premises (@p182)) % 0.36/0.59 (step @p184 :rule cong :premises (@p183) :args ((forall @t78 @t163))) % 0.36/0.59 (step @p185 :rule trans :premises (@p184 @p174)) % 0.36/0.59 (step @p186 :rule trans :premises (@p185 @p173)) % 0.36/0.59 (step @p187 :rule aci_norm :args ((= (or (or @t146 @t162 @t145 @t161) @t60) @t163))) % 0.36/0.59 (step @p188 :rule bool-double-not-elim :args (@t161)) % 0.36/0.59 (step @p189 :rule bool-double-not-elim :args (@t162)) % 0.36/0.59 (step @p190 :rule nary_cong :premises (@p179 @p189 @p177 @p188) :args (@t168)) % 0.36/0.59 (step @p191 :rule aci_norm :args ((= (or @t146 (or @t167 (or @t145 @t165))) @t168))) % 0.36/0.59 (step @p192 :rule trans :premises (@p191 @p190)) % 0.36/0.59 (step @p193 :rule bool-and-de-morgan :args (@t68 @t164 true)) % 0.36/0.59 (step @p194 :rule refl :args (@t167)) % 0.36/0.59 (step @p195 :rule nary_cong :premises (@p194 @p193) :args ((or @t167 (not (and @t68 @t164))))) % 0.36/0.59 (step @p196 :rule bool-and-de-morgan :args (@t166 @t68 (and @t164))) % 0.36/0.59 (step @p197 :rule trans :premises (@p196 @p195)) % 0.36/0.59 (step @p198 :rule nary_cong :premises (@p179 @p197) :args ((or @t146 (not (and @t166 @t68 @t164))))) % 0.36/0.59 (step @p199 :rule bool-and-de-morgan :args (@t75 @t166 (and @t68 @t164))) % 0.36/0.59 (step @p200 :rule trans :premises (@p199 @p198)) % 0.36/0.59 (step @p201 :rule trans :premises (@p200 @p192)) % 0.36/0.59 (step @p202 :rule nary_cong :premises (@p201 @p175) :args ((or (not @t169) @t60))) % 0.36/0.59 (step @p203 :rule trans :premises (@p202 @p187)) % 0.36/0.59 (step @p204 :rule bool-impl-elim :args (@t169 @t60)) % 0.36/0.59 (step @p205 :rule trans :premises (@p204 @p203)) % 0.36/0.59 (step @p206 :rule cong :premises (@p205) :args ((forall @t78 (=> @t169 @t60)))) % 0.36/0.59 (step @p207 :rule trans :premises (@p206 @p186)) % 0.36/0.59 (step @p208 :rule bool-and-de-morgan :args (@t64 @t63 true)) % 0.36/0.59 (step @p209 :rule cong :premises (@p208) :args (@t170)) % 0.36/0.59 (step @p210 :rule cong :premises (@p209) :args (@t171)) % 0.36/0.59 (step @p211 :rule exists-elim :args ((= @t67 @t171))) % 0.36/0.59 (step @p212 :rule trans :premises (@p211 @p210)) % 0.36/0.59 (step @p213 :rule refl :args (@t68)) % 0.36/0.59 (step @p214 :rule bool-and-de-morgan :args (@t71 @t70 true)) % 0.36/0.59 (step @p215 :rule cong :premises (@p214) :args (@t172)) % 0.36/0.59 (step @p216 :rule cong :premises (@p215) :args (@t173)) % 0.36/0.59 (step @p217 :rule exists-elim :args ((= @t74 @t173))) % 0.36/0.59 (step @p218 :rule trans :premises (@p217 @p216)) % 0.36/0.59 (step @p219 :rule refl :args (@t75)) % 0.36/0.59 (step @p220 :rule nary_cong :premises (@p219 @p218 @p213 @p212) :args (@t76)) % 0.36/0.59 (step @p221 :rule cong :premises (@p220 @p155) :args (@t77)) % 0.36/0.59 (step @p222 :rule cong :premises (@p221) :args (@t79)) % 0.36/0.59 (step @p223 :rule trans :premises (@p222 @p207)) % 0.36/0.59 (step @p224 :rule cong :premises (@p223 @p145) :args (@t80)) % 0.36/0.59 (step @p225 :rule trans :premises (@p224 @p82)) % 0.36/0.59 (step @p226 :rule cong :premises (@p46 @p225) :args (@t81)) % 0.36/0.59 (step @p227 :rule cong :premises (@p226) :args (@t82)) % 0.36/0.59 (step @p228 :rule trans :premises (@p227 @p81)) % 0.36/0.59 (step @p229 :rule eq_resolve :premises (@p18 @p228)) % 0.36/0.59 (step @p230 false :rule chain_m_resolution :premises (@p229 @p74) :args (false @t114 (@list @t103))) % 0.36/0.59 ) % 0.36/0.59 % SZS output end Proof % 0.36/0.59 % cvc5 exiting %------------------------------------------------------------------------------