%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU669^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n015.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 08:52:39 AM UTC 2026 % Result : Theorem 0.37s 0.58s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU669^2 : TPTP v9.2.1. Released v3.7.0. % 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n015.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 17:46:19 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.48 %----Proving TH0 % 0.37/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.58 % SZS status Theorem % 0.37/0.58 % SZS output start Proof % 0.37/0.58 ( % 0.37/0.58 (declare-sort $$unsorted 0) % 0.37/0.58 (declare-const tptp.kpair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.cartprod (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.37/0.58 (declare-const tptp.cartprodpairmemEL Bool) % 0.37/0.58 (declare-const tptp.dsetconstrEL Bool) % 0.37/0.58 (define tptp.dpsetconstr () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (@var "Xu" $$unsorted))) (let ((_let_4 (@var "Xphi" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (@var "B" $$unsorted))) (let ((_let_6 (@var "A" $$unsorted))) (lambda (@list _let_6 _let_5 _let_4) (_ (_ tptp.dsetconstr (_ (_ tptp.cartprod _let_6) _let_5)) (lambda (@list _let_3) (exists (@list _let_2) (and (_ (_ tptp.in _let_2) _let_6) (exists (@list _let_1) (and (_ (_ tptp.in _let_1) _let_5) (_ (_ _let_4 _let_2) _let_1) (= _let_3 (_ (_ tptp.kpair _let_2) _let_1)))))))))))))))) % 0.37/0.58 (define @t1 () (@var "A" $$unsorted)) % 0.37/0.58 (define @t2 () (@var "Xx" $$unsorted)) % 0.37/0.58 (define @t3 () (_ tptp.in @t2)) % 0.37/0.58 (define @t4 () (_ @t3 @t1)) % 0.37/0.58 (define @t5 () (@var "Xy" $$unsorted)) % 0.37/0.58 (define @t6 () (@var "Xphi" (-> $$unsorted Bool))) % 0.37/0.58 (define @t7 () (_ @t6 @t5)) % 0.37/0.58 (define @t8 () (@list @t5)) % 0.37/0.58 (define @t9 () (lambda @t8 @t7)) % 0.37/0.58 (define @t10 () (_ tptp.dsetconstr @t1)) % 0.37/0.58 (define @t11 () (_ @t10 @t9)) % 0.37/0.58 (define @t12 () (_ @t3 @t11)) % 0.37/0.58 (define @t13 () (@list @t1 @t6 @t2)) % 0.37/0.58 (define @t14 () (forall @t13 (=> @t12 @t4))) % 0.37/0.58 (define @t15 () (= tptp.dsetconstrEL @t14)) % 0.37/0.58 (define @t16 () (@var "B" $$unsorted)) % 0.37/0.58 (define @t17 () (_ (_ tptp.cartprod @t1) @t16)) % 0.37/0.58 (define @t18 () (_ (_ tptp.kpair @t2) @t5)) % 0.37/0.58 (define @t19 () (_ tptp.in @t18)) % 0.37/0.58 (define @t20 () (_ @t19 @t17)) % 0.37/0.58 (define @t21 () (@list @t1 @t16 @t2 @t5)) % 0.37/0.58 (define @t22 () (forall @t21 (=> @t20 @t4))) % 0.37/0.58 (define @t23 () (= tptp.cartprodpairmemEL @t22)) % 0.37/0.58 (define @t24 () (@var "Xu" $$unsorted)) % 0.37/0.58 (define @t25 () (@var "Xz" $$unsorted)) % 0.37/0.58 (define @t26 () (@var "Xphi" (-> $$unsorted $$unsorted Bool))) % 0.37/0.58 (define @t27 () (lambda (@list @t25 @t24) (_ (_ @t26 @t25) @t24))) % 0.37/0.58 (define @t28 () (=> (_ @t19 (_ (_ (_ tptp.dpsetconstr @t1) @t16) @t27)) @t4)) % 0.37/0.58 (define @t29 () (@list @t1 @t16 @t26 @t2 @t5)) % 0.37/0.58 (define @t30 () (forall @t29 @t28)) % 0.37/0.58 (define @t31 () (=> tptp.cartprodpairmemEL @t30)) % 0.37/0.58 (define @t32 () (=> tptp.dsetconstrEL @t31)) % 0.37/0.58 (define @t33 () (not @t32)) % 0.37/0.58 (define @t34 () (_ @t26 @t2)) % 0.37/0.58 (define @t35 () (_ @t34 @t5)) % 0.37/0.58 (define @t36 () (_ (_ tptp.in @t5) @t16)) % 0.37/0.58 (define @t37 () (and @t36 @t35 (= @t24 @t18))) % 0.37/0.58 (define @t38 () (exists @t8 @t37)) % 0.37/0.58 (define @t39 () (and @t4 @t38)) % 0.37/0.58 (define @t40 () (@list @t2)) % 0.37/0.58 (define @t41 () (exists @t40 @t39)) % 0.37/0.58 (define @t42 () (@list @t24)) % 0.37/0.58 (define @t43 () (lambda @t42 @t41)) % 0.37/0.58 (define @t44 () (_ tptp.dsetconstr @t17)) % 0.37/0.58 (define @t45 () (@list @t1 @t16 @t26)) % 0.37/0.58 (define @t46 () (lambda @t45 (_ @t44 @t43))) % 0.37/0.58 (define @t47 () (tptp.in @t2 @t1)) % 0.37/0.58 (define @t48 () (@var "BOUND_VARIABLE_7502" $$unsorted)) % 0.37/0.58 (define @t49 () (@var "BOUND_VARIABLE_7609" $$unsorted)) % 0.37/0.58 (define @t50 () (tptp.kpair @t49 @t48)) % 0.37/0.58 (define @t51 () (= @t24 @t50)) % 0.37/0.58 (define @t52 () (not @t51)) % 0.37/0.58 (define @t53 () (_ @t26 @t49 @t48)) % 0.37/0.58 (define @t54 () (not @t53)) % 0.37/0.58 (define @t55 () (tptp.in @t48 @t16)) % 0.37/0.58 (define @t56 () (not @t55)) % 0.37/0.58 (define @t57 () (tptp.in @t49 @t1)) % 0.37/0.58 (define @t58 () (not @t57)) % 0.37/0.58 (define @t59 () (or @t58 @t56 @t54 @t52)) % 0.37/0.58 (define @t60 () (@list @t49 @t48)) % 0.37/0.58 (define @t61 () (forall @t60 @t59)) % 0.37/0.58 (define @t62 () (not @t61)) % 0.37/0.58 (define @t63 () (lambda @t42 @t62)) % 0.37/0.58 (define @t64 () (tptp.cartprod @t1 @t16)) % 0.37/0.58 (define @t65 () (tptp.dsetconstr @t64 @t63)) % 0.37/0.58 (define @t66 () (tptp.kpair @t2 @t5)) % 0.37/0.58 (define @t67 () (tptp.in @t66 @t65)) % 0.37/0.58 (define @t68 () (forall @t29 (or (not @t67) @t47))) % 0.37/0.58 (define @t69 () (tptp.in @t66 @t64)) % 0.37/0.58 (define @t70 () (_ tptp.in @t66)) % 0.37/0.58 (define @t71 () (not @t20)) % 0.37/0.58 (define @t72 () (or @t71 @t4)) % 0.37/0.58 (define @t73 () (=> tptp.cartprodpairmemEL @t68)) % 0.37/0.58 (define @t74 () (_ @t6 @t5)) % 0.37/0.58 (define @t75 () (lambda @t8 @t74)) % 0.37/0.58 (define @t76 () (tptp.dsetconstr @t1 @t75)) % 0.37/0.58 (define @t77 () (tptp.in @t2 @t76)) % 0.37/0.58 (define @t78 () (not @t77)) % 0.37/0.58 (define @t79 () (or @t78 @t47)) % 0.37/0.58 (define @t80 () (not @t12)) % 0.37/0.58 (define @t81 () (or @t80 @t4)) % 0.37/0.58 (define @t82 () (=> tptp.dsetconstrEL @t73)) % 0.37/0.58 (define @t83 () (lambda @t42 (not (forall @t60 (or (not (_ (_ tptp.in @t49) @t1)) (not (_ (_ tptp.in @t48) @t16)) (not (_ (_ @t26 @t49) @t48)) (not (= @t24 (_ (_ tptp.kpair @t49) @t48)))))))) % 0.37/0.58 (define @t84 () (_ @t44 @t83)) % 0.37/0.58 (define @t85 () (_ @t19 (_ @t44 @t63))) % 0.37/0.58 (define @t86 () (not @t85)) % 0.37/0.58 (define @t87 () (or @t86 @t4)) % 0.37/0.58 (define @t88 () (not (= @t24 (tptp.kpair @t2 @t48)))) % 0.37/0.58 (define @t89 () (_ @t26 @t2 @t48)) % 0.37/0.58 (define @t90 () (not @t89)) % 0.37/0.58 (define @t91 () (not @t47)) % 0.37/0.58 (define @t92 () (or @t91 @t56 @t90 @t88)) % 0.37/0.58 (define @t93 () (@list @t2 @t48)) % 0.37/0.58 (define @t94 () (forall @t93 @t92)) % 0.37/0.58 (define @t95 () (not @t94)) % 0.37/0.58 (define @t96 () (lambda @t42 @t95)) % 0.37/0.58 (define @t97 () (_ @t44 @t96)) % 0.37/0.58 (define @t98 () (=> (_ @t19 @t97) @t4)) % 0.37/0.58 (define @t99 () (_ @t34 @t48)) % 0.37/0.58 (define @t100 () (not @t99)) % 0.37/0.58 (define @t101 () (or @t91 @t56 @t100 @t88)) % 0.37/0.58 (define @t102 () (_ @t27 @t2 @t48)) % 0.37/0.58 (define @t103 () (not @t102)) % 0.37/0.58 (define @t104 () (or @t91 @t56 @t103 @t88)) % 0.37/0.58 (define @t105 () (forall @t93 @t104)) % 0.37/0.58 (define @t106 () (not @t105)) % 0.37/0.58 (define @t107 () (lambda @t42 @t106)) % 0.37/0.58 (define @t108 () (lambda (@list @t26) @t97)) % 0.37/0.58 (define @t109 () (lambda (@list @t16 @t26) @t97)) % 0.37/0.58 (define @t110 () (_ (lambda @t45 @t97) @t1)) % 0.37/0.58 (define @t111 () (=> (_ @t19 (_ (_ @t110 @t16) @t27)) @t4)) % 0.37/0.58 (define @t112 () (forall @t29 @t111)) % 0.37/0.58 (define @t113 () (=> tptp.cartprodpairmemEL @t112)) % 0.37/0.58 (define @t114 () (=> tptp.dsetconstrEL @t113)) % 0.37/0.58 (define @t115 () (or @t56 @t90 @t88)) % 0.37/0.58 (define @t116 () (or @t91 @t115)) % 0.37/0.58 (define @t117 () (forall @t93 @t116)) % 0.37/0.58 (define @t118 () (@list @t48)) % 0.37/0.58 (define @t119 () (forall @t118 @t116)) % 0.37/0.58 (define @t120 () (forall @t118 @t115)) % 0.37/0.58 (define @t121 () (or @t91 @t120)) % 0.37/0.58 (define @t122 () (_ @t26 @t2 @t5)) % 0.37/0.58 (define @t123 () (not @t122)) % 0.37/0.58 (define @t124 () (tptp.in @t5 @t16)) % 0.37/0.58 (define @t125 () (not @t124)) % 0.37/0.58 (define @t126 () (forall @t8 (or @t125 @t123 (not (= @t24 @t66))))) % 0.37/0.58 (define @t127 () (not @t4)) % 0.37/0.58 (define @t128 () (or @t127 @t126)) % 0.37/0.58 (define @t129 () (not @t126)) % 0.37/0.58 (define @t130 () (and @t4 @t129)) % 0.37/0.58 (define @t131 () (forall @t40 (not @t130))) % 0.37/0.58 (define @t132 () (not @t131)) % 0.37/0.58 (define @t133 () (not (= @t66 @t24))) % 0.37/0.58 (define @t134 () (or @t125 @t123 @t133)) % 0.37/0.58 (define @t135 () (= @t18 @t24)) % 0.37/0.58 (define @t136 () (not @t135)) % 0.37/0.58 (define @t137 () (not @t35)) % 0.37/0.58 (define @t138 () (not @t36)) % 0.37/0.58 (define @t139 () (or @t138 @t137 @t136)) % 0.37/0.58 (define @t140 () (and @t36 @t35 @t135)) % 0.37/0.58 (define @t141 () (forall @t8 (not @t140))) % 0.37/0.58 (define @t142 () (not @t141)) % 0.37/0.58 (define @t143 () (@quantifiers_skolemize @t68 4)) % 0.37/0.58 (define @t144 () (@quantifiers_skolemize @t68 3)) % 0.37/0.58 (define @t145 () (tptp.kpair @t144 @t143)) % 0.37/0.58 (define @t146 () (@quantifiers_skolemize @t68 1)) % 0.37/0.58 (define @t147 () (@quantifiers_skolemize @t68 0)) % 0.37/0.58 (define @t148 () (lambda @t42 (not (forall @t60 (or (not (tptp.in @t49 @t147)) (not (tptp.in @t48 @t146)) (not (_ (@quantifiers_skolemize @t68 2) @t49 @t48)) @t52))))) % 0.37/0.58 (define @t149 () (@purify @t148)) % 0.37/0.58 (define @t150 () (tptp.cartprod @t147 @t146)) % 0.37/0.58 (define @t151 () (tptp.in @t144 @t147)) % 0.37/0.58 (define @t152 () (tptp.in @t145 (tptp.dsetconstr @t150 @t149))) % 0.37/0.58 (define @t153 () (not @t152)) % 0.37/0.58 (define @t154 () (or @t153 @t151)) % 0.37/0.58 (define @t155 () (not @t154)) % 0.37/0.58 (define @t156 () (not @t68)) % 0.37/0.58 (define @t157 () (tptp.dsetconstr @t150 @t148)) % 0.37/0.58 (define @t158 () (tptp.in @t145 @t157)) % 0.37/0.58 (define @t159 () (not @t158)) % 0.37/0.58 (define @t160 () (or @t159 @t151)) % 0.37/0.58 (define @t161 () (not @t160)) % 0.37/0.58 (define @t162 () (@list true)) % 0.37/0.58 (define @t163 () (@list @t154)) % 0.37/0.58 (define @t164 () (tptp.in @t145 @t150)) % 0.37/0.58 (define @t165 () (or @t153 @t164)) % 0.37/0.58 (define @t166 () (not @t164)) % 0.37/0.58 (define @t167 () (or @t166 @t151)) % 0.37/0.58 (define @t168 () (not @t167)) % 0.37/0.58 (define @t169 () (@list true false)) % 0.37/0.58 (define @t170 () (forall @t21 (or (not @t69) @t47))) % 0.37/0.58 (assume @p1 @t15) % 0.37/0.58 (assume @p2 @t23) % 0.37/0.58 (assume @p3 @t33) % 0.37/0.58 (assume @p4 true) % 0.37/0.58 (step @p5 (= tptp.dpsetconstr @t46) :rule refl :args (@t46)) % 0.37/0.58 (step @p6 :rule refl :args (@t68)) % 0.37/0.58 (step @p7 :rule refl :args (@t47)) % 0.37/0.58 (step @p8 :rule refl :args (@t4)) % 0.37/0.58 (step @p9 :rule cong :premises (@p8 @p7) :args ((= @t4 @t47))) % 0.37/0.58 (step @p10 :rule symm :premises (@p9)) % 0.37/0.58 (step @p11 :rule eq_resolve :premises (@p8 @p10)) % 0.37/0.58 (step @p12 :rule refl :args ((tptp.in @t18 @t17))) % 0.37/0.58 (step @p13 :rule refl :args (@t64)) % 0.37/0.58 (step @p14 :rule refl :args (@t66)) % 0.37/0.58 (step @p15 :rule cong :premises (@p14 @p13) :args (@t69)) % 0.37/0.58 (step @p16 :rule trans :premises (@p15 @p12)) % 0.37/0.58 (step @p17 :rule refl :args (tptp.in)) % 0.37/0.58 (step @p18 :rule ho_cong :premises (@p17 @p14)) % 0.37/0.58 (step @p19 :rule ho_cong :premises (@p18 @p13)) % 0.37/0.58 (step @p20 :rule cong :premises (@p19 @p16) :args ((= (_ @t70 @t64) @t69))) % 0.37/0.58 (step @p21 :rule symm :premises (@p20)) % 0.37/0.58 (step @p22 :rule refl :args (@t20)) % 0.37/0.58 (step @p23 :rule eq_resolve :premises (@p22 @p21)) % 0.37/0.58 (step @p24 :rule refl :args (@t17)) % 0.37/0.58 (step @p25 :rule cong :premises (@p24 @p13) :args ((= @t17 @t64))) % 0.37/0.58 (step @p26 :rule symm :premises (@p25)) % 0.37/0.58 (step @p27 :rule eq_resolve :premises (@p24 @p26)) % 0.37/0.58 (step @p28 :rule refl :args (@t18)) % 0.37/0.58 (step @p29 :rule cong :premises (@p28 @p14) :args ((= @t18 @t66))) % 0.37/0.58 (step @p30 :rule symm :premises (@p29)) % 0.37/0.58 (step @p31 :rule eq_resolve :premises (@p28 @p30)) % 0.37/0.58 (step @p32 :rule ho_cong :premises (@p17 @p31)) % 0.37/0.58 (step @p33 :rule ho_cong :premises (@p32 @p27)) % 0.37/0.58 (step @p34 :rule trans :premises (@p33 @p23)) % 0.37/0.58 (step @p35 :rule cong :premises (@p34) :args (@t71)) % 0.37/0.58 (step @p36 :rule nary_cong :premises (@p35 @p11) :args (@t72)) % 0.37/0.58 (step @p37 :rule cong :premises (@p36) :args ((forall @t21 @t72))) % 0.37/0.58 (step @p38 :rule bool-impl-elim :args (@t20 @t4)) % 0.37/0.58 (step @p39 :rule cong :premises (@p38) :args (@t22)) % 0.37/0.58 (step @p40 :rule trans :premises (@p39 @p37)) % 0.37/0.58 (step @p41 :rule refl :args (tptp.cartprodpairmemEL)) % 0.37/0.58 (step @p42 :rule cong :premises (@p41 @p40) :args (@t23)) % 0.37/0.58 (step @p43 :rule eq_resolve :premises (@p2 @p42)) % 0.37/0.58 (step @p44 :rule cong :premises (@p43 @p6) :args (@t73)) % 0.37/0.58 (step @p45 :rule refl :args (@t47)) % 0.37/0.58 (step @p46 :rule lambda-elim :args ((= @t75 @t6))) % 0.37/0.58 (step @p47 :rule refl :args (@t1)) % 0.37/0.58 (step @p48 :rule cong :premises (@p47 @p46) :args (@t76)) % 0.37/0.58 (step @p49 :rule refl :args (@t2)) % 0.37/0.58 (step @p50 :rule cong :premises (@p49 @p48) :args (@t77)) % 0.37/0.58 (step @p51 :rule cong :premises (@p50) :args (@t78)) % 0.37/0.58 (step @p52 :rule nary_cong :premises (@p51 @p45) :args (@t79)) % 0.37/0.58 (step @p53 :rule cong :premises (@p52) :args ((forall @t13 @t79))) % 0.37/0.58 (step @p54 :rule refl :args ((tptp.in @t2 @t11))) % 0.37/0.58 (step @p55 :rule refl :args ((tptp.dsetconstr @t1 @t9))) % 0.37/0.58 (step @p56 :rule refl :args (@t74)) % 0.37/0.58 (step @p57 :rule cong :premises (@p56) :args (@t75)) % 0.37/0.58 (step @p58 :rule refl :args (@t1)) % 0.37/0.58 (step @p59 :rule cong :premises (@p58 @p57) :args (@t76)) % 0.37/0.58 (step @p60 :rule trans :premises (@p59 @p55)) % 0.37/0.58 (step @p61 :rule refl :args (@t2)) % 0.37/0.58 (step @p62 :rule cong :premises (@p61 @p60) :args (@t77)) % 0.37/0.58 (step @p63 :rule trans :premises (@p62 @p54)) % 0.37/0.58 (step @p64 :rule refl :args (@t3)) % 0.37/0.58 (step @p65 :rule ho_cong :premises (@p64 @p60)) % 0.37/0.58 (step @p66 :rule cong :premises (@p65 @p63) :args ((= (_ @t3 @t76) @t77))) % 0.37/0.58 (step @p67 :rule symm :premises (@p66)) % 0.37/0.58 (step @p68 :rule refl :args (@t12)) % 0.37/0.58 (step @p69 :rule eq_resolve :premises (@p68 @p67)) % 0.37/0.58 (step @p70 :rule refl :args (@t10)) % 0.37/0.58 (step @p71 :rule ho_cong :premises (@p70 @p57)) % 0.37/0.58 (step @p72 :rule cong :premises (@p71 @p60) :args ((= (_ @t10 @t75) @t76))) % 0.37/0.58 (step @p73 :rule symm :premises (@p72)) % 0.37/0.58 (step @p74 :rule refl :args (@t11)) % 0.37/0.58 (step @p75 :rule eq_resolve :premises (@p74 @p73)) % 0.37/0.58 (step @p76 :rule refl :args (@t7)) % 0.37/0.58 (step @p77 :rule cong :premises (@p76 @p56) :args ((= @t7 @t74))) % 0.37/0.58 (step @p78 :rule symm :premises (@p77)) % 0.37/0.58 (step @p79 :rule eq_resolve :premises (@p76 @p78)) % 0.37/0.58 (step @p80 :rule cong :premises (@p79) :args (@t9)) % 0.37/0.58 (step @p81 :rule ho_cong :premises (@p70 @p80)) % 0.37/0.58 (step @p82 :rule trans :premises (@p81 @p75)) % 0.37/0.58 (step @p83 :rule ho_cong :premises (@p64 @p82)) % 0.37/0.58 (step @p84 :rule trans :premises (@p83 @p69)) % 0.37/0.58 (step @p85 :rule cong :premises (@p84) :args (@t80)) % 0.37/0.58 (step @p86 :rule nary_cong :premises (@p85 @p11) :args (@t81)) % 0.37/0.58 (step @p87 :rule cong :premises (@p86) :args ((forall @t13 @t81))) % 0.37/0.58 (step @p88 :rule trans :premises (@p87 @p53)) % 0.37/0.58 (step @p89 :rule bool-impl-elim :args (@t12 @t4)) % 0.37/0.58 (step @p90 :rule cong :premises (@p89) :args (@t14)) % 0.37/0.58 (step @p91 :rule trans :premises (@p90 @p88)) % 0.37/0.58 (step @p92 :rule refl :args (tptp.dsetconstrEL)) % 0.37/0.58 (step @p93 :rule cong :premises (@p92 @p91) :args (@t15)) % 0.37/0.58 (step @p94 :rule eq_resolve :premises (@p1 @p93)) % 0.37/0.58 (step @p95 :rule cong :premises (@p94 @p44) :args (@t82)) % 0.37/0.58 (step @p96 :rule cong :premises (@p95) :args ((not @t82))) % 0.37/0.58 (step @p97 :rule refl :args ((tptp.in @t18 @t84))) % 0.37/0.58 (step @p98 :rule refl :args ((tptp.dsetconstr @t17 @t83))) % 0.37/0.58 (step @p99 :rule refl :args (@t50)) % 0.37/0.58 (step @p100 :rule refl :args (@t24)) % 0.37/0.58 (step @p101 :rule cong :premises (@p100 @p99) :args (@t51)) % 0.37/0.58 (step @p102 :rule cong :premises (@p101) :args (@t52)) % 0.37/0.58 (step @p103 :rule refl :args (@t53)) % 0.37/0.58 (step @p104 :rule cong :premises (@p103) :args (@t54)) % 0.37/0.58 (step @p105 :rule refl :args (@t55)) % 0.37/0.58 (step @p106 :rule cong :premises (@p105) :args (@t56)) % 0.37/0.58 (step @p107 :rule refl :args (@t57)) % 0.37/0.58 (step @p108 :rule cong :premises (@p107) :args (@t58)) % 0.37/0.58 (step @p109 :rule nary_cong :premises (@p108 @p106 @p104 @p102) :args (@t59)) % 0.37/0.58 (step @p110 :rule cong :premises (@p109) :args (@t61)) % 0.37/0.58 (step @p111 :rule cong :premises (@p110) :args (@t62)) % 0.37/0.58 (step @p112 :rule cong :premises (@p111) :args (@t63)) % 0.37/0.58 (step @p113 :rule cong :premises (@p13 @p112) :args (@t65)) % 0.37/0.58 (step @p114 :rule trans :premises (@p113 @p98)) % 0.37/0.58 (step @p115 :rule cong :premises (@p14 @p114) :args (@t67)) % 0.37/0.58 (step @p116 :rule trans :premises (@p115 @p97)) % 0.37/0.58 (step @p117 :rule ho_cong :premises (@p18 @p114)) % 0.37/0.58 (step @p118 :rule cong :premises (@p117 @p116) :args ((= (_ @t70 @t65) @t67))) % 0.37/0.58 (step @p119 :rule symm :premises (@p118)) % 0.37/0.58 (step @p120 :rule refl :args ((_ @t19 @t84))) % 0.37/0.58 (step @p121 :rule eq_resolve :premises (@p120 @p119)) % 0.37/0.58 (step @p122 :rule refl :args (tptp.dsetconstr)) % 0.37/0.58 (step @p123 :rule ho_cong :premises (@p122 @p13)) % 0.37/0.58 (step @p124 :rule ho_cong :premises (@p123 @p112)) % 0.37/0.58 (step @p125 :rule cong :premises (@p124 @p114) :args ((= (_ (_ tptp.dsetconstr @t64) @t63) @t65))) % 0.37/0.58 (step @p126 :rule symm :premises (@p125)) % 0.37/0.58 (step @p127 :rule refl :args (@t84)) % 0.37/0.58 (step @p128 :rule eq_resolve :premises (@p127 @p126)) % 0.37/0.58 (step @p129 :rule refl :args (@t63)) % 0.37/0.58 (step @p130 :rule ho_cong :premises (@p122 @p27)) % 0.37/0.58 (step @p131 :rule ho_cong :premises (@p130 @p129)) % 0.37/0.58 (step @p132 :rule trans :premises (@p131 @p128)) % 0.37/0.58 (step @p133 :rule ho_cong :premises (@p32 @p132)) % 0.37/0.58 (step @p134 :rule trans :premises (@p133 @p121)) % 0.37/0.58 (step @p135 :rule cong :premises (@p134) :args (@t86)) % 0.37/0.58 (step @p136 :rule nary_cong :premises (@p135 @p11) :args (@t87)) % 0.37/0.58 (step @p137 :rule cong :premises (@p136) :args ((forall @t29 @t87))) % 0.37/0.58 (step @p138 :rule bool-impl-elim :args (@t85 @t4)) % 0.37/0.58 (step @p139 :rule cong :premises (@p138) :args ((forall @t29 (=> @t85 @t4)))) % 0.37/0.58 (step @p140 :rule trans :premises (@p139 @p137)) % 0.37/0.58 (step @p141 :rule alpha_equiv :args (@t94 (@list @t2) (@list @t49))) % 0.37/0.58 (step @p142 :rule cong :premises (@p141) :args (@t95)) % 0.37/0.58 (step @p143 :rule cong :premises (@p142) :args (@t96)) % 0.37/0.58 (step @p144 :rule refl :args (@t44)) % 0.37/0.58 (step @p145 :rule ho_cong :premises (@p144 @p143)) % 0.37/0.58 (step @p146 :rule refl :args (@t19)) % 0.37/0.58 (step @p147 :rule ho_cong :premises (@p146 @p145)) % 0.37/0.58 (step @p148 :rule cong :premises (@p147 @p8) :args (@t98)) % 0.37/0.58 (step @p149 :rule cong :premises (@p148) :args ((forall @t29 @t98))) % 0.37/0.58 (step @p150 :rule trans :premises (@p149 @p140)) % 0.37/0.58 (step @p151 :rule refl :args (@t4)) % 0.37/0.58 (step @p152 :rule refl :args (@t88)) % 0.37/0.58 (step @p153 :rule refl :args (@t89)) % 0.37/0.58 (step @p154 :rule refl :args (@t99)) % 0.37/0.58 (step @p155 :rule cong :premises (@p154 @p153) :args ((= @t99 @t89))) % 0.37/0.58 (step @p156 :rule symm :premises (@p155)) % 0.37/0.58 (step @p157 :rule eq_resolve :premises (@p154 @p156)) % 0.37/0.58 (step @p158 :rule cong :premises (@p157) :args (@t100)) % 0.37/0.58 (step @p159 :rule refl :args (@t56)) % 0.37/0.58 (step @p160 :rule refl :args (@t91)) % 0.37/0.58 (step @p161 :rule nary_cong :premises (@p160 @p159 @p158 @p152) :args (@t101)) % 0.37/0.58 (step @p162 :rule cong :premises (@p161) :args ((forall @t93 @t101))) % 0.37/0.58 (step @p163 :rule refl :args (@t88)) % 0.37/0.58 (step @p164 :rule beta-reduce :args ((= @t102 @t99))) % 0.37/0.58 (step @p165 :rule cong :premises (@p164) :args (@t103)) % 0.37/0.58 (step @p166 :rule refl :args (@t56)) % 0.37/0.58 (step @p167 :rule refl :args (@t91)) % 0.37/0.58 (step @p168 :rule nary_cong :premises (@p167 @p166 @p165 @p163) :args (@t104)) % 0.37/0.58 (step @p169 :rule cong :premises (@p168) :args (@t105)) % 0.37/0.58 (step @p170 :rule trans :premises (@p169 @p162)) % 0.37/0.58 (step @p171 :rule cong :premises (@p170) :args (@t106)) % 0.37/0.58 (step @p172 :rule cong :premises (@p171) :args (@t107)) % 0.37/0.58 (step @p173 :rule refl :args (@t44)) % 0.37/0.58 (step @p174 :rule ho_cong :premises (@p173 @p172)) % 0.37/0.58 (step @p175 :rule beta-reduce :args ((= (_ @t108 @t27) (_ @t44 @t107)))) % 0.37/0.58 (step @p176 :rule trans :premises (@p175 @p174)) % 0.37/0.58 (step @p177 :rule refl :args (@t27)) % 0.37/0.58 (step @p178 :rule beta-reduce :args ((= (_ @t109 @t16) @t108))) % 0.37/0.58 (step @p179 :rule refl :args (@t16)) % 0.37/0.58 (step @p180 :rule beta-reduce :args ((= @t110 @t109))) % 0.37/0.58 (step @p181 :rule ho_cong :premises (@p180 @p179)) % 0.37/0.58 (step @p182 :rule trans :premises (@p181 @p178)) % 0.37/0.58 (step @p183 :rule ho_cong :premises (@p182 @p177)) % 0.37/0.58 (step @p184 :rule trans :premises (@p183 @p176)) % 0.37/0.58 (step @p185 :rule refl :args (@t19)) % 0.37/0.58 (step @p186 :rule ho_cong :premises (@p185 @p184)) % 0.37/0.58 (step @p187 :rule cong :premises (@p186 @p151) :args (@t111)) % 0.37/0.58 (step @p188 :rule cong :premises (@p187) :args (@t112)) % 0.37/0.58 (step @p189 :rule trans :premises (@p188 @p150)) % 0.37/0.58 (step @p190 :rule cong :premises (@p41 @p189) :args (@t113)) % 0.37/0.58 (step @p191 :rule cong :premises (@p92 @p190) :args (@t114)) % 0.37/0.58 (step @p192 :rule cong :premises (@p191) :args ((not @t114))) % 0.37/0.58 (step @p193 :rule aci_norm :args ((= @t116 @t92))) % 0.37/0.58 (step @p194 :rule cong :premises (@p193) :args (@t117)) % 0.37/0.58 (step @p195 :rule quant-merge-prenex :args ((= (forall @t40 @t119) @t117))) % 0.37/0.58 (step @p196 :rule alpha_equiv :args (@t120 (@list @t48) (@list @t5))) % 0.37/0.58 (step @p197 :rule nary_cong :premises (@p160 @p196) :args (@t121)) % 0.37/0.58 (step @p198 :rule quant-miniscope-or :args ((= @t119 @t121))) % 0.37/0.58 (step @p199 :rule trans :premises (@p198 @p197)) % 0.37/0.58 (step @p200 :rule symm :premises (@p199)) % 0.37/0.58 (step @p201 :rule cong :premises (@p200) :args ((forall @t40 (or @t91 @t126)))) % 0.37/0.58 (step @p202 :rule trans :premises (@p201 @p195)) % 0.37/0.58 (step @p203 :rule trans :premises (@p202 @p194)) % 0.37/0.58 (step @p204 :rule refl :args (@t126)) % 0.37/0.58 (step @p205 :rule cong :premises (@p11) :args (@t127)) % 0.37/0.58 (step @p206 :rule nary_cong :premises (@p205 @p204) :args (@t128)) % 0.37/0.58 (step @p207 :rule cong :premises (@p206) :args ((forall @t40 @t128))) % 0.37/0.58 (step @p208 :rule trans :premises (@p207 @p203)) % 0.37/0.58 (step @p209 :rule bool-double-not-elim :args (@t126)) % 0.37/0.58 (step @p210 :rule refl :args (@t127)) % 0.37/0.58 (step @p211 :rule nary_cong :premises (@p210 @p209) :args ((or @t127 (not @t129)))) % 0.37/0.58 (step @p212 :rule bool-and-de-morgan :args (@t4 @t129 true)) % 0.37/0.58 (step @p213 :rule trans :premises (@p212 @p211)) % 0.37/0.58 (step @p214 :rule cong :premises (@p213) :args (@t131)) % 0.37/0.58 (step @p215 :rule trans :premises (@p214 @p208)) % 0.37/0.58 (step @p216 :rule cong :premises (@p215) :args (@t132)) % 0.37/0.58 (step @p217 :rule exists-elim :args ((= (exists @t40 @t130) @t132))) % 0.37/0.58 (step @p218 :rule trans :premises (@p217 @p216)) % 0.37/0.58 (step @p219 :rule eq-symm :args (@t66 @t24)) % 0.37/0.58 (step @p220 :rule cong :premises (@p219) :args (@t133)) % 0.37/0.58 (step @p221 :rule refl :args (@t123)) % 0.37/0.58 (step @p222 :rule refl :args (@t125)) % 0.37/0.58 (step @p223 :rule nary_cong :premises (@p222 @p221 @p220) :args (@t134)) % 0.37/0.58 (step @p224 :rule cong :premises (@p223) :args ((forall @t8 @t134))) % 0.37/0.58 (step @p225 :rule cong :premises (@p31 @p100) :args (@t135)) % 0.37/0.58 (step @p226 :rule cong :premises (@p225) :args (@t136)) % 0.37/0.58 (step @p227 :rule refl :args (@t122)) % 0.37/0.58 (step @p228 :rule refl :args (@t35)) % 0.37/0.58 (step @p229 :rule cong :premises (@p228 @p227) :args ((= @t35 @t122))) % 0.37/0.58 (step @p230 :rule symm :premises (@p229)) % 0.37/0.58 (step @p231 :rule eq_resolve :premises (@p228 @p230)) % 0.37/0.58 (step @p232 :rule cong :premises (@p231) :args (@t137)) % 0.37/0.58 (step @p233 :rule refl :args (@t124)) % 0.37/0.58 (step @p234 :rule refl :args (@t36)) % 0.37/0.58 (step @p235 :rule cong :premises (@p234 @p233) :args ((= @t36 @t124))) % 0.37/0.58 (step @p236 :rule symm :premises (@p235)) % 0.37/0.58 (step @p237 :rule eq_resolve :premises (@p234 @p236)) % 0.37/0.58 (step @p238 :rule cong :premises (@p237) :args (@t138)) % 0.37/0.58 (step @p239 :rule nary_cong :premises (@p238 @p232 @p226) :args (@t139)) % 0.37/0.58 (step @p240 :rule cong :premises (@p239) :args ((forall @t8 @t139))) % 0.37/0.58 (step @p241 :rule trans :premises (@p240 @p224)) % 0.37/0.58 (step @p242 :rule aci_norm :args ((= (or @t138 (or @t137 @t136)) @t139))) % 0.37/0.58 (step @p243 :rule bool-and-de-morgan :args (@t35 @t135 true)) % 0.37/0.58 (step @p244 :rule refl :args (@t138)) % 0.37/0.58 (step @p245 :rule nary_cong :premises (@p244 @p243) :args ((or @t138 (not (and @t35 @t135))))) % 0.37/0.58 (step @p246 :rule bool-and-de-morgan :args (@t36 @t35 (and @t135))) % 0.37/0.58 (step @p247 :rule trans :premises (@p246 @p245)) % 0.37/0.58 (step @p248 :rule trans :premises (@p247 @p242)) % 0.37/0.58 (step @p249 :rule cong :premises (@p248) :args (@t141)) % 0.37/0.58 (step @p250 :rule trans :premises (@p249 @p241)) % 0.37/0.58 (step @p251 :rule cong :premises (@p250) :args (@t142)) % 0.37/0.58 (step @p252 :rule exists-elim :args ((= (exists @t8 @t140) @t142))) % 0.37/0.58 (step @p253 :rule trans :premises (@p252 @p251)) % 0.37/0.58 (step @p254 :rule eq-symm :args (@t24 @t18)) % 0.37/0.58 (step @p255 :rule refl :args (@t35)) % 0.37/0.58 (step @p256 :rule refl :args (@t36)) % 0.37/0.58 (step @p257 :rule nary_cong :premises (@p256 @p255 @p254) :args (@t37)) % 0.37/0.58 (step @p258 :rule cong :premises (@p257) :args (@t38)) % 0.37/0.58 (step @p259 :rule trans :premises (@p258 @p253)) % 0.37/0.58 (step @p260 :rule nary_cong :premises (@p151 @p259) :args (@t39)) % 0.37/0.58 (step @p261 :rule cong :premises (@p260) :args (@t41)) % 0.37/0.58 (step @p262 :rule trans :premises (@p261 @p218)) % 0.37/0.58 (step @p263 :rule cong :premises (@p262) :args (@t43)) % 0.37/0.58 (step @p264 :rule ho_cong :premises (@p173 @p263)) % 0.37/0.58 (step @p265 :rule cong :premises (@p264) :args (@t46)) % 0.37/0.58 (step @p266 :rule trans :premises (@p5 @p265)) % 0.37/0.58 (step @p267 :rule ho_cong :premises (@p266 @p47)) % 0.37/0.58 (step @p268 :rule ho_cong :premises (@p267 @p179)) % 0.37/0.58 (step @p269 :rule ho_cong :premises (@p268 @p177)) % 0.37/0.58 (step @p270 :rule ho_cong :premises (@p185 @p269)) % 0.37/0.58 (step @p271 :rule cong :premises (@p270 @p151) :args (@t28)) % 0.37/0.58 (step @p272 :rule cong :premises (@p271) :args (@t30)) % 0.37/0.58 (step @p273 :rule cong :premises (@p41 @p272) :args (@t31)) % 0.37/0.58 (step @p274 :rule cong :premises (@p92 @p273) :args (@t32)) % 0.37/0.58 (step @p275 :rule cong :premises (@p274) :args (@t33)) % 0.37/0.58 (step @p276 :rule trans :premises (@p275 @p192)) % 0.37/0.58 (step @p277 :rule trans :premises (@p276 @p96)) % 0.37/0.58 (step @p278 :rule eq_resolve :premises (@p3 @p277)) % 0.37/0.58 (step @p279 :rule not_implies_elim2 :premises (@p278)) % 0.37/0.58 (step @p280 :rule not_implies_elim1 :premises (@p279)) % 0.37/0.58 (step @p281 :rule not_implies_elim1 :premises (@p278)) % 0.37/0.58 (step @p282 :rule instantiate :premises (@p281) :args ((@list @t150 @t149 @t145))) % 0.37/0.58 (step @p283 :rule not_implies_elim2 :premises (@p279)) % 0.37/0.58 (step @p284 :rule refl :args (@t155)) % 0.37/0.58 (step @p285 :rule bool-double-not-elim :args (@t68)) % 0.37/0.58 (step @p286 :rule nary_cong :premises (@p285 @p284) :args ((or (not @t156) @t155))) % 0.37/0.58 (step @p287 :rule refl :args (@t151)) % 0.37/0.58 (step @p288 :rule eq-refl :args (@t148)) % 0.37/0.58 (step @p289 :rule skolem_intro :args (@t149)) % 0.37/0.58 (step @p290 :rule refl :args (@t148)) % 0.37/0.58 (step @p291 :rule cong :premises (@p290 @p289) :args ((= @t148 @t149))) % 0.37/0.58 (step @p292 :rule trans :premises (@p291 @p288)) % 0.37/0.58 (step @p293 :rule true_elim :premises (@p292)) % 0.37/0.58 (step @p294 :rule refl :args (@t150)) % 0.37/0.58 (step @p295 :rule cong :premises (@p294 @p293) :args (@t157)) % 0.37/0.58 (step @p296 :rule refl :args (@t145)) % 0.37/0.58 (step @p297 :rule cong :premises (@p296 @p295) :args (@t158)) % 0.37/0.58 (step @p298 :rule cong :premises (@p297) :args (@t159)) % 0.37/0.58 (step @p299 :rule nary_cong :premises (@p298 @p287) :args (@t160)) % 0.37/0.58 (step @p300 :rule cong :premises (@p299) :args (@t161)) % 0.37/0.58 (step @p301 :rule refl :args (@t156)) % 0.37/0.58 (step @p302 :rule cong :premises (@p301 @p300) :args ((=> @t156 @t161))) % 0.37/0.58 (assume-push @p332 @t156) % 0.37/0.58 (step @p304 :rule skolemize :premises (@p283)) % 0.37/0.58 (step-pop @p333 :rule scope :premises (@p304)) % 0.37/0.58 (step @p305 :rule process_scope :premises (@p333) :args (@t161)) % 0.37/0.58 (step @p307 :rule eq_resolve :premises (@p305 @p302)) % 0.37/0.58 (step @p308 :rule implies_elim :premises (@p307)) % 0.37/0.58 (step @p309 :rule eq_resolve :premises (@p308 @p286)) % 0.37/0.58 (step @p310 :rule chain_m_resolution :premises (@p309 @p283) :args (@t155 @t162 (@list @t68))) % 0.37/0.58 (step @p311 :rule bool-double-not-elim :args (@t152)) % 0.37/0.58 (step @p312 :rule refl :args (@t154)) % 0.37/0.58 (step @p313 :rule nary_cong :premises (@p312 @p311) :args ((or @t154 (not @t153)))) % 0.37/0.58 (step @p314 :rule cnf_or_neg :args (@t154 0)) % 0.37/0.58 (step @p315 :rule eq_resolve :premises (@p314 @p313)) % 0.37/0.58 (step @p316 :rule reordering :premises (@p315) :args ((or @t152 @t154))) % 0.37/0.58 (step @p317 :rule chain_m_resolution :premises (@p316 @p310) :args (@t152 @t162 @t163)) % 0.37/0.58 (step @p318 :rule cnf_or_pos :args (@t165)) % 0.37/0.58 (step @p319 :rule reordering :premises (@p318) :args ((or @t153 @t164 (not @t165)))) % 0.37/0.58 (step @p320 :rule chain_m_resolution :premises (@p319 @p317 @p282) :args (@t164 (@list false false) (@list @t152 @t165))) % 0.37/0.58 (step @p321 :rule cnf_or_neg :args (@t154 1)) % 0.37/0.58 (step @p322 :rule chain_m_resolution :premises (@p321 @p310) :args ((not @t151) @t162 @t163)) % 0.37/0.58 (step @p323 :rule cnf_or_pos :args (@t167)) % 0.37/0.58 (step @p324 :rule reordering :premises (@p323) :args ((or @t151 @t166 @t168))) % 0.37/0.58 (step @p325 :rule chain_m_resolution :premises (@p324 @p322 @p320) :args (@t168 @t169 (@list @t151 @t164))) % 0.37/0.58 (assume-push @p334 @t170) % 0.37/0.58 (step @p327 :rule instantiate :premises (@p280) :args ((@list @t147 @t146 @t144 @t143))) % 0.37/0.58 (step-pop @p335 :rule scope :premises (@p327)) % 0.37/0.58 (step @p328 :rule process_scope :premises (@p335) :args (@t167)) % 0.37/0.58 (step @p330 :rule implies_elim :premises (@p328)) % 0.37/0.58 (step @p331 false :rule chain_m_resolution :premises (@p330 @p325 @p280) :args (false @t169 (@list @t167 @t170))) % 0.37/0.58 ) % 0.37/0.58 % SZS output end Proof % 0.37/0.58 % cvc5 exiting %------------------------------------------------------------------------------