%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU640^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n003.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 08:52:32 AM UTC 2026 % Result : Theorem 0.37s 0.57s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU640^2 : TPTP v9.2.1. Released v3.7.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n003.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 17:43:44 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.48 %----Proving TH0 % 0.37/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.57 % SZS status Theorem % 0.37/0.57 % SZS output start Proof % 0.37/0.57 ( % 0.37/0.57 (declare-sort $$unsorted 0) % 0.37/0.57 (declare-const tptp.emptyset $$unsorted) % 0.37/0.57 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.37/0.57 (declare-const tptp.singletonprop Bool) % 0.37/0.57 (define tptp.singleton () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (lambda (@list _let_2) (exists (@list _let_1) (and (_ (_ tptp.in _let_1) _let_2) (= _let_2 (_ (_ tptp.setadjoin _let_1) tptp.emptyset)))))))) % 0.37/0.57 (define tptp.ex1 () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "Xphi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" $$unsorted))) (lambda (@list _let_3 _let_2) (_ tptp.singleton (_ (_ tptp.dsetconstr _let_3) (lambda (@list _let_1) (_ _let_2 _let_1))))))))) % 0.37/0.57 (define @t1 () (@var "Xx" $$unsorted)) % 0.37/0.57 (define @t2 () (@var "Xphi" (-> $$unsorted Bool))) % 0.37/0.57 (define @t3 () (_ @t2 @t1)) % 0.37/0.57 (define @t4 () (@list @t1)) % 0.37/0.57 (define @t5 () (lambda @t4 @t3)) % 0.37/0.57 (define @t6 () (@var "A" $$unsorted)) % 0.37/0.57 (define @t7 () (_ tptp.dsetconstr @t6)) % 0.37/0.57 (define @t8 () (_ @t7 @t5)) % 0.37/0.57 (define @t9 () (_ tptp.singleton @t8)) % 0.37/0.57 (define @t10 () (_ (_ tptp.in @t1) @t6)) % 0.37/0.57 (define @t11 () (and @t10 @t3)) % 0.37/0.57 (define @t12 () (exists @t4 @t11)) % 0.37/0.57 (define @t13 () (=> @t12 @t9)) % 0.37/0.57 (define @t14 () (@var "Xy" $$unsorted)) % 0.37/0.57 (define @t15 () (= @t1 @t14)) % 0.37/0.57 (define @t16 () (_ @t2 @t14)) % 0.37/0.57 (define @t17 () (=> @t16 @t15)) % 0.37/0.57 (define @t18 () (=> @t3 @t17)) % 0.37/0.57 (define @t19 () (_ (_ tptp.in @t14) @t6)) % 0.37/0.57 (define @t20 () (@list @t14)) % 0.37/0.57 (define @t21 () (forall @t20 (=> @t19 @t18))) % 0.37/0.57 (define @t22 () (=> @t10 @t21)) % 0.37/0.57 (define @t23 () (forall @t4 @t22)) % 0.37/0.57 (define @t24 () (=> @t23 @t13)) % 0.37/0.57 (define @t25 () (@list @t6 @t2)) % 0.37/0.57 (define @t26 () (forall @t25 @t24)) % 0.37/0.57 (define @t27 () (= tptp.singletonprop @t26)) % 0.37/0.57 (define @t28 () (=> @t12 (_ (_ tptp.ex1 @t6) @t5))) % 0.37/0.57 (define @t29 () (=> @t23 @t28)) % 0.37/0.57 (define @t30 () (forall @t25 @t29)) % 0.37/0.57 (define @t31 () (=> tptp.singletonprop @t30)) % 0.37/0.57 (define @t32 () (not @t31)) % 0.37/0.57 (define @t33 () (_ (_ tptp.setadjoin @t1) tptp.emptyset)) % 0.37/0.57 (define @t34 () (= @t6 @t33)) % 0.37/0.57 (define @t35 () (and @t10 @t34)) % 0.37/0.57 (define @t36 () (exists @t4 @t35)) % 0.37/0.57 (define @t37 () (@list @t6)) % 0.37/0.57 (define @t38 () (lambda @t37 @t36)) % 0.37/0.57 (define @t39 () (lambda @t25 @t9)) % 0.37/0.57 (define @t40 () (@var "BOUND_VARIABLE_7600" $$unsorted)) % 0.37/0.57 (define @t41 () (not (_ @t2 @t40))) % 0.37/0.57 (define @t42 () (not (tptp.in @t40 @t6))) % 0.37/0.57 (define @t43 () (tptp.dsetconstr @t6 @t2)) % 0.37/0.57 (define @t44 () (tptp.setadjoin @t1 tptp.emptyset)) % 0.37/0.57 (define @t45 () (not (forall @t4 (or (not (tptp.in @t1 @t43)) (not (= @t44 @t43)))))) % 0.37/0.57 (define @t46 () (@var "BOUND_VARIABLE_7572" $$unsorted)) % 0.37/0.57 (define @t47 () (= @t1 @t46)) % 0.37/0.57 (define @t48 () (not (_ @t2 @t46))) % 0.37/0.57 (define @t49 () (not (tptp.in @t46 @t6))) % 0.37/0.57 (define @t50 () (_ @t2 @t1)) % 0.37/0.57 (define @t51 () (not @t50)) % 0.37/0.57 (define @t52 () (tptp.in @t1 @t6)) % 0.37/0.57 (define @t53 () (not @t52)) % 0.37/0.57 (define @t54 () (or @t53 @t51 @t49 @t48 @t47)) % 0.37/0.57 (define @t55 () (@list @t1 @t46)) % 0.37/0.57 (define @t56 () (forall @t55 @t54)) % 0.37/0.57 (define @t57 () (not @t56)) % 0.37/0.57 (define @t58 () (or @t57 @t45 @t42 @t41)) % 0.37/0.57 (define @t59 () (or @t42 @t41)) % 0.37/0.57 (define @t60 () (or @t57 @t59 @t45)) % 0.37/0.57 (define @t61 () (@list @t6 @t2 @t40)) % 0.37/0.57 (define @t62 () (forall @t61 @t60)) % 0.37/0.57 (define @t63 () (@list @t40)) % 0.37/0.57 (define @t64 () (forall @t63 @t60)) % 0.37/0.57 (define @t65 () (forall @t63 @t59)) % 0.37/0.57 (define @t66 () (@list @t1)) % 0.37/0.57 (define @t67 () (or @t57 @t65 @t45)) % 0.37/0.57 (define @t68 () (forall @t4 (or @t53 @t51))) % 0.37/0.57 (define @t69 () (or @t57 @t68 @t45)) % 0.37/0.57 (define @t70 () (not @t68)) % 0.37/0.57 (define @t71 () (=> @t70 @t45)) % 0.37/0.57 (define @t72 () (@var "BOUND_VARIABLE_7636" $$unsorted)) % 0.37/0.57 (define @t73 () (_ @t2 @t72)) % 0.37/0.57 (define @t74 () (@list @t72)) % 0.37/0.57 (define @t75 () (lambda @t74 @t73)) % 0.37/0.57 (define @t76 () (tptp.dsetconstr @t6 @t75)) % 0.37/0.57 (define @t77 () (= @t44 @t76)) % 0.37/0.57 (define @t78 () (not @t77)) % 0.37/0.57 (define @t79 () (tptp.in @t1 @t76)) % 0.37/0.57 (define @t80 () (not @t79)) % 0.37/0.57 (define @t81 () (or @t80 @t78)) % 0.37/0.57 (define @t82 () (_ @t2 @t72)) % 0.37/0.57 (define @t83 () (lambda @t74 @t82)) % 0.37/0.57 (define @t84 () (tptp.dsetconstr @t6 @t83)) % 0.37/0.57 (define @t85 () (= @t44 @t84)) % 0.37/0.57 (define @t86 () (not @t85)) % 0.37/0.57 (define @t87 () (tptp.in @t1 @t84)) % 0.37/0.57 (define @t88 () (not @t87)) % 0.37/0.57 (define @t89 () (or @t88 @t86)) % 0.37/0.57 (define @t90 () (tptp.dsetconstr @t6 @t5)) % 0.37/0.57 (define @t91 () (= @t44 @t90)) % 0.37/0.57 (define @t92 () (not @t91)) % 0.37/0.57 (define @t93 () (tptp.in @t1 @t90)) % 0.37/0.57 (define @t94 () (not @t93)) % 0.37/0.57 (define @t95 () (or @t94 @t92)) % 0.37/0.57 (define @t96 () (forall @t4 @t95)) % 0.37/0.57 (define @t97 () (not @t96)) % 0.37/0.57 (define @t98 () (lambda (@list @t2) @t45)) % 0.37/0.57 (define @t99 () (_ (lambda @t25 @t45) @t6)) % 0.37/0.57 (define @t100 () (not @t3)) % 0.37/0.57 (define @t101 () (not @t10)) % 0.37/0.57 (define @t102 () (or @t101 @t100)) % 0.37/0.57 (define @t103 () (forall @t4 (not @t11))) % 0.37/0.57 (define @t104 () (not @t103)) % 0.37/0.57 (define @t105 () (=> @t12 (_ @t99 @t5))) % 0.37/0.57 (define @t106 () (or @t49 @t48 @t47)) % 0.37/0.57 (define @t107 () (or @t53 @t51 @t106)) % 0.37/0.57 (define @t108 () (forall @t55 @t107)) % 0.37/0.57 (define @t109 () (@list @t46)) % 0.37/0.57 (define @t110 () (forall @t109 @t107)) % 0.37/0.57 (define @t111 () (forall @t109 @t106)) % 0.37/0.57 (define @t112 () (or @t53 @t51 @t111)) % 0.37/0.57 (define @t113 () (_ @t2 @t14)) % 0.37/0.57 (define @t114 () (tptp.in @t14 @t6)) % 0.37/0.57 (define @t115 () (forall @t20 (or (not @t114) (not @t113) @t15))) % 0.37/0.57 (define @t116 () (or @t101 @t100 @t115)) % 0.37/0.57 (define @t117 () (or @t100 @t115)) % 0.37/0.57 (define @t118 () (not @t16)) % 0.37/0.57 (define @t119 () (not @t19)) % 0.37/0.57 (define @t120 () (or @t119 @t118 @t15)) % 0.37/0.57 (define @t121 () (forall @t20 @t120)) % 0.37/0.57 (define @t122 () (or @t100 @t121)) % 0.37/0.57 (define @t123 () (or @t100 @t120)) % 0.37/0.57 (define @t124 () (or @t119 @t100 @t118 @t15)) % 0.37/0.57 (define @t125 () (or @t100 @t118 @t15)) % 0.37/0.57 (define @t126 () (=> @t23 @t105)) % 0.37/0.57 (define @t127 () (forall @t25 @t126)) % 0.37/0.57 (define @t128 () (=> tptp.singletonprop @t127)) % 0.37/0.57 (define @t129 () (@var "BOUND_VARIABLE_7494" $$unsorted)) % 0.37/0.57 (define @t130 () (_ @t2 @t129)) % 0.37/0.57 (define @t131 () (@list @t129)) % 0.37/0.57 (define @t132 () (lambda @t131 @t130)) % 0.37/0.57 (define @t133 () (tptp.dsetconstr @t6 @t132)) % 0.37/0.57 (define @t134 () (= @t44 @t133)) % 0.37/0.57 (define @t135 () (not @t134)) % 0.37/0.57 (define @t136 () (tptp.in @t1 @t133)) % 0.37/0.57 (define @t137 () (not @t136)) % 0.37/0.57 (define @t138 () (or @t137 @t135)) % 0.37/0.57 (define @t139 () (_ @t2 @t129)) % 0.37/0.57 (define @t140 () (lambda @t131 @t139)) % 0.37/0.57 (define @t141 () (_ @t7 @t140)) % 0.37/0.57 (define @t142 () (= @t44 @t141)) % 0.37/0.57 (define @t143 () (not @t142)) % 0.37/0.57 (define @t144 () (tptp.in @t1 @t141)) % 0.37/0.57 (define @t145 () (not @t144)) % 0.37/0.57 (define @t146 () (or @t145 @t143)) % 0.37/0.57 (define @t147 () (= @t44 @t8)) % 0.37/0.57 (define @t148 () (not @t147)) % 0.37/0.57 (define @t149 () (tptp.in @t1 @t8)) % 0.37/0.57 (define @t150 () (not @t149)) % 0.37/0.57 (define @t151 () (or @t150 @t148)) % 0.37/0.57 (define @t152 () (not (= @t8 @t44))) % 0.37/0.57 (define @t153 () (or @t150 @t152)) % 0.37/0.57 (define @t154 () (forall @t4 @t153)) % 0.37/0.57 (define @t155 () (not @t154)) % 0.37/0.57 (define @t156 () (_ (lambda @t37 (not (forall @t4 (or @t53 (not (= @t6 @t44)))))) @t8)) % 0.37/0.57 (define @t157 () (not @t34)) % 0.37/0.57 (define @t158 () (or @t101 @t157)) % 0.37/0.57 (define @t159 () (forall @t4 (not @t35))) % 0.37/0.57 (define @t160 () (not @t159)) % 0.37/0.57 (define @t161 () (forall @t61 @t58)) % 0.37/0.57 (define @t162 () (=> @t12 @t156)) % 0.37/0.57 (define @t163 () (=> @t23 @t162)) % 0.37/0.57 (define @t164 () (forall @t25 @t163)) % 0.37/0.57 (assume @p1 @t27) % 0.37/0.57 (assume @p2 @t32) % 0.37/0.57 (assume @p3 true) % 0.37/0.57 (step @p4 (= tptp.singleton @t38) :rule refl :args (@t38)) % 0.37/0.57 (step @p5 (= tptp.ex1 @t39) :rule refl :args (@t39)) % 0.37/0.57 (step @p6 :rule aci_norm :args ((= @t60 @t58))) % 0.37/0.57 (step @p7 :rule cong :premises (@p6) :args (@t62)) % 0.37/0.57 (step @p8 :rule quant-merge-prenex :args ((= (forall @t25 @t64) @t62))) % 0.37/0.57 (step @p9 :rule refl :args (@t45)) % 0.37/0.57 (step @p10 :rule alpha_equiv :args (@t65 (@list @t40) @t66)) % 0.37/0.57 (step @p11 :rule refl :args (@t57)) % 0.37/0.57 (step @p12 :rule nary_cong :premises (@p11 @p10 @p9) :args (@t67)) % 0.37/0.57 (step @p13 :rule quant-miniscope-or :args ((= @t64 @t67))) % 0.37/0.57 (step @p14 :rule trans :premises (@p13 @p12)) % 0.37/0.57 (step @p15 :rule symm :premises (@p14)) % 0.37/0.57 (step @p16 :rule cong :premises (@p15) :args ((forall @t25 @t69))) % 0.37/0.57 (step @p17 :rule trans :premises (@p16 @p8)) % 0.37/0.57 (step @p18 :rule trans :premises (@p17 @p7)) % 0.37/0.57 (step @p19 :rule aci_norm :args ((= (or @t57 (or @t68 @t45)) @t69))) % 0.37/0.57 (step @p20 :rule bool-double-not-elim :args (@t68)) % 0.37/0.57 (step @p21 :rule nary_cong :premises (@p20 @p9) :args ((or (not @t70) @t45))) % 0.37/0.57 (step @p22 :rule bool-impl-elim :args (@t70 @t45)) % 0.37/0.57 (step @p23 :rule trans :premises (@p22 @p21)) % 0.37/0.57 (step @p24 :rule nary_cong :premises (@p11 @p23) :args ((or @t57 @t71))) % 0.37/0.57 (step @p25 :rule trans :premises (@p24 @p19)) % 0.37/0.57 (step @p26 :rule bool-impl-elim :args (@t56 @t71)) % 0.37/0.57 (step @p27 :rule trans :premises (@p26 @p25)) % 0.37/0.57 (step @p28 :rule cong :premises (@p27) :args ((forall @t25 (=> @t56 @t71)))) % 0.37/0.57 (step @p29 :rule trans :premises (@p28 @p18)) % 0.37/0.57 (step @p30 :rule lambda-elim :args ((= @t75 @t2))) % 0.37/0.57 (step @p31 :rule refl :args (@t6)) % 0.37/0.57 (step @p32 :rule cong :premises (@p31 @p30) :args (@t76)) % 0.37/0.57 (step @p33 :rule refl :args (@t44)) % 0.37/0.57 (step @p34 :rule cong :premises (@p33 @p32) :args (@t77)) % 0.37/0.57 (step @p35 :rule cong :premises (@p34) :args (@t78)) % 0.37/0.57 (step @p36 :rule refl :args (@t1)) % 0.37/0.57 (step @p37 :rule cong :premises (@p36 @p32) :args (@t79)) % 0.37/0.57 (step @p38 :rule cong :premises (@p37) :args (@t80)) % 0.37/0.57 (step @p39 :rule nary_cong :premises (@p38 @p35) :args (@t81)) % 0.37/0.57 (step @p40 :rule cong :premises (@p39) :args ((forall @t4 @t81))) % 0.37/0.57 (step @p41 :rule refl :args (@t73)) % 0.37/0.57 (step @p42 :rule refl :args (@t82)) % 0.37/0.57 (step @p43 :rule cong :premises (@p42 @p41) :args ((= @t82 @t73))) % 0.37/0.57 (step @p44 :rule symm :premises (@p43)) % 0.37/0.57 (step @p45 :rule eq_resolve :premises (@p42 @p44)) % 0.37/0.57 (step @p46 :rule cong :premises (@p45) :args (@t83)) % 0.37/0.57 (step @p47 :rule refl :args (@t6)) % 0.37/0.57 (step @p48 :rule cong :premises (@p47 @p46) :args (@t84)) % 0.37/0.57 (step @p49 :rule refl :args (@t44)) % 0.37/0.57 (step @p50 :rule cong :premises (@p49 @p48) :args (@t85)) % 0.37/0.57 (step @p51 :rule cong :premises (@p50) :args (@t86)) % 0.37/0.57 (step @p52 :rule refl :args (@t1)) % 0.37/0.57 (step @p53 :rule cong :premises (@p52 @p48) :args (@t87)) % 0.37/0.57 (step @p54 :rule cong :premises (@p53) :args (@t88)) % 0.37/0.57 (step @p55 :rule nary_cong :premises (@p54 @p51) :args (@t89)) % 0.37/0.57 (step @p56 :rule cong :premises (@p55) :args ((forall @t4 @t89))) % 0.37/0.57 (step @p57 :rule trans :premises (@p56 @p40)) % 0.37/0.57 (step @p58 :rule alpha_equiv :args (@t5 @t66 (@list @t72))) % 0.37/0.57 (step @p59 :rule cong :premises (@p47 @p58) :args (@t90)) % 0.37/0.57 (step @p60 :rule cong :premises (@p49 @p59) :args (@t91)) % 0.37/0.57 (step @p61 :rule cong :premises (@p60) :args (@t92)) % 0.37/0.57 (step @p62 :rule cong :premises (@p52 @p59) :args (@t93)) % 0.37/0.57 (step @p63 :rule cong :premises (@p62) :args (@t94)) % 0.37/0.57 (step @p64 :rule nary_cong :premises (@p63 @p61) :args (@t95)) % 0.37/0.57 (step @p65 :rule cong :premises (@p64) :args (@t96)) % 0.37/0.57 (step @p66 :rule trans :premises (@p65 @p57)) % 0.37/0.57 (step @p67 :rule cong :premises (@p66) :args (@t97)) % 0.37/0.57 (step @p68 :rule beta-reduce :args ((= (_ @t98 @t5) @t97))) % 0.37/0.57 (step @p69 :rule trans :premises (@p68 @p67)) % 0.37/0.57 (step @p70 :rule refl :args (@t5)) % 0.37/0.57 (step @p71 :rule beta-reduce :args ((= @t99 @t98))) % 0.37/0.57 (step @p72 :rule ho_cong :premises (@p71 @p70)) % 0.37/0.57 (step @p73 :rule trans :premises (@p72 @p69)) % 0.37/0.57 (step @p74 :rule refl :args (@t50)) % 0.37/0.57 (step @p75 :rule refl :args (@t3)) % 0.37/0.57 (step @p76 :rule cong :premises (@p75 @p74) :args ((= @t3 @t50))) % 0.37/0.57 (step @p77 :rule symm :premises (@p76)) % 0.37/0.57 (step @p78 :rule eq_resolve :premises (@p75 @p77)) % 0.37/0.57 (step @p79 :rule cong :premises (@p78) :args (@t100)) % 0.37/0.57 (step @p80 :rule refl :args (@t52)) % 0.37/0.57 (step @p81 :rule refl :args (@t10)) % 0.37/0.57 (step @p82 :rule cong :premises (@p81 @p80) :args ((= @t10 @t52))) % 0.37/0.57 (step @p83 :rule symm :premises (@p82)) % 0.37/0.57 (step @p84 :rule eq_resolve :premises (@p81 @p83)) % 0.37/0.57 (step @p85 :rule cong :premises (@p84) :args (@t101)) % 0.37/0.57 (step @p86 :rule nary_cong :premises (@p85 @p79) :args (@t102)) % 0.37/0.57 (step @p87 :rule cong :premises (@p86) :args ((forall @t4 @t102))) % 0.37/0.57 (step @p88 :rule bool-and-de-morgan :args (@t10 @t3 true)) % 0.37/0.57 (step @p89 :rule cong :premises (@p88) :args (@t103)) % 0.37/0.57 (step @p90 :rule trans :premises (@p89 @p87)) % 0.37/0.57 (step @p91 :rule cong :premises (@p90) :args (@t104)) % 0.37/0.57 (step @p92 :rule exists-elim :args ((= @t12 @t104))) % 0.37/0.57 (step @p93 :rule trans :premises (@p92 @p91)) % 0.37/0.57 (step @p94 :rule cong :premises (@p93 @p73) :args (@t105)) % 0.37/0.57 (step @p95 :rule aci_norm :args ((= @t107 @t54))) % 0.37/0.57 (step @p96 :rule cong :premises (@p95) :args (@t108)) % 0.37/0.57 (step @p97 :rule quant-merge-prenex :args ((= (forall @t4 @t110) @t108))) % 0.37/0.57 (step @p98 :rule alpha_equiv :args (@t111 (@list @t46) (@list @t14))) % 0.37/0.57 (step @p99 :rule refl :args (@t51)) % 0.37/0.57 (step @p100 :rule refl :args (@t53)) % 0.37/0.57 (step @p101 :rule nary_cong :premises (@p100 @p99 @p98) :args (@t112)) % 0.37/0.57 (step @p102 :rule quant-miniscope-or :args ((= @t110 @t112))) % 0.37/0.57 (step @p103 :rule trans :premises (@p102 @p101)) % 0.37/0.57 (step @p104 :rule symm :premises (@p103)) % 0.37/0.57 (step @p105 :rule cong :premises (@p104) :args ((forall @t4 (or @t53 @t51 @t115)))) % 0.37/0.57 (step @p106 :rule trans :premises (@p105 @p97)) % 0.37/0.57 (step @p107 :rule trans :premises (@p106 @p96)) % 0.37/0.57 (step @p108 :rule refl :args (@t115)) % 0.37/0.57 (step @p109 :rule nary_cong :premises (@p85 @p79 @p108) :args (@t116)) % 0.37/0.57 (step @p110 :rule cong :premises (@p109) :args ((forall @t4 @t116))) % 0.37/0.57 (step @p111 :rule trans :premises (@p110 @p107)) % 0.37/0.57 (step @p112 :rule aci_norm :args ((= (or @t101 @t117) @t116))) % 0.37/0.57 (step @p113 :rule bool-impl-elim :args (@t10 @t117)) % 0.37/0.57 (step @p114 :rule trans :premises (@p113 @p112)) % 0.37/0.57 (step @p115 :rule cong :premises (@p114) :args ((forall @t4 (=> @t10 @t117)))) % 0.37/0.57 (step @p116 :rule trans :premises (@p115 @p111)) % 0.37/0.57 (step @p117 :rule refl :args (@t15)) % 0.37/0.57 (step @p118 :rule refl :args (@t113)) % 0.37/0.57 (step @p119 :rule refl :args (@t16)) % 0.37/0.57 (step @p120 :rule cong :premises (@p119 @p118) :args ((= @t16 @t113))) % 0.37/0.57 (step @p121 :rule symm :premises (@p120)) % 0.37/0.57 (step @p122 :rule eq_resolve :premises (@p119 @p121)) % 0.37/0.57 (step @p123 :rule cong :premises (@p122) :args (@t118)) % 0.37/0.57 (step @p124 :rule refl :args (@t114)) % 0.37/0.57 (step @p125 :rule refl :args (@t19)) % 0.37/0.57 (step @p126 :rule cong :premises (@p125 @p124) :args ((= @t19 @t114))) % 0.37/0.57 (step @p127 :rule symm :premises (@p126)) % 0.37/0.57 (step @p128 :rule eq_resolve :premises (@p125 @p127)) % 0.37/0.57 (step @p129 :rule cong :premises (@p128) :args (@t119)) % 0.37/0.57 (step @p130 :rule nary_cong :premises (@p129 @p123 @p117) :args (@t120)) % 0.37/0.57 (step @p131 :rule cong :premises (@p130) :args (@t121)) % 0.37/0.57 (step @p132 :rule refl :args (@t100)) % 0.37/0.57 (step @p133 :rule nary_cong :premises (@p132 @p131) :args (@t122)) % 0.37/0.57 (step @p134 :rule quant-miniscope-or :args ((= (forall @t20 @t123) @t122))) % 0.37/0.57 (step @p135 :rule aci_norm :args ((= @t124 @t123))) % 0.37/0.57 (step @p136 :rule cong :premises (@p135) :args ((forall @t20 @t124))) % 0.37/0.57 (step @p137 :rule trans :premises (@p136 @p134)) % 0.37/0.57 (step @p138 :rule trans :premises (@p137 @p133)) % 0.37/0.57 (step @p139 :rule aci_norm :args ((= (or @t119 @t125) @t124))) % 0.37/0.57 (step @p140 :rule aci_norm :args ((= (or @t100 (or @t118 @t15)) @t125))) % 0.37/0.57 (step @p141 :rule bool-impl-elim :args (@t16 @t15)) % 0.37/0.57 (step @p142 :rule refl :args (@t100)) % 0.37/0.57 (step @p143 :rule nary_cong :premises (@p142 @p141) :args ((or @t100 @t17))) % 0.37/0.57 (step @p144 :rule trans :premises (@p143 @p140)) % 0.37/0.57 (step @p145 :rule bool-impl-elim :args (@t3 @t17)) % 0.37/0.57 (step @p146 :rule trans :premises (@p145 @p144)) % 0.37/0.57 (step @p147 :rule refl :args (@t119)) % 0.37/0.57 (step @p148 :rule nary_cong :premises (@p147 @p146) :args ((or @t119 @t18))) % 0.37/0.57 (step @p149 :rule trans :premises (@p148 @p139)) % 0.37/0.57 (step @p150 :rule bool-impl-elim :args (@t19 @t18)) % 0.37/0.57 (step @p151 :rule trans :premises (@p150 @p149)) % 0.37/0.57 (step @p152 :rule cong :premises (@p151) :args (@t21)) % 0.37/0.57 (step @p153 :rule trans :premises (@p152 @p138)) % 0.37/0.57 (step @p154 :rule refl :args (@t10)) % 0.37/0.57 (step @p155 :rule cong :premises (@p154 @p153) :args (@t22)) % 0.37/0.57 (step @p156 :rule cong :premises (@p155) :args (@t23)) % 0.37/0.57 (step @p157 :rule trans :premises (@p156 @p116)) % 0.37/0.57 (step @p158 :rule cong :premises (@p157 @p94) :args (@t126)) % 0.37/0.57 (step @p159 :rule cong :premises (@p158) :args (@t127)) % 0.37/0.57 (step @p160 :rule trans :premises (@p159 @p29)) % 0.37/0.57 (step @p161 :rule refl :args (tptp.singletonprop)) % 0.37/0.57 (step @p162 :rule cong :premises (@p161 @p160) :args (@t128)) % 0.37/0.57 (step @p163 :rule cong :premises (@p162) :args ((not @t128))) % 0.37/0.57 (step @p164 :rule lambda-elim :args ((= @t132 @t2))) % 0.37/0.57 (step @p165 :rule cong :premises (@p31 @p164) :args (@t133)) % 0.37/0.57 (step @p166 :rule cong :premises (@p33 @p165) :args (@t134)) % 0.37/0.57 (step @p167 :rule cong :premises (@p166) :args (@t135)) % 0.37/0.57 (step @p168 :rule cong :premises (@p36 @p165) :args (@t136)) % 0.37/0.57 (step @p169 :rule cong :premises (@p168) :args (@t137)) % 0.37/0.57 (step @p170 :rule nary_cong :premises (@p169 @p167) :args (@t138)) % 0.37/0.57 (step @p171 :rule cong :premises (@p170) :args ((forall @t4 @t138))) % 0.37/0.57 (step @p172 :rule refl :args ((tptp.dsetconstr @t6 @t140))) % 0.37/0.57 (step @p173 :rule refl :args (@t130)) % 0.37/0.57 (step @p174 :rule cong :premises (@p173) :args (@t132)) % 0.37/0.57 (step @p175 :rule cong :premises (@p47 @p174) :args (@t133)) % 0.37/0.57 (step @p176 :rule trans :premises (@p175 @p172)) % 0.37/0.57 (step @p177 :rule refl :args (@t7)) % 0.37/0.57 (step @p178 :rule ho_cong :premises (@p177 @p174)) % 0.37/0.57 (step @p179 :rule cong :premises (@p178 @p176) :args ((= (_ @t7 @t132) @t133))) % 0.37/0.57 (step @p180 :rule symm :premises (@p179)) % 0.37/0.57 (step @p181 :rule refl :args (@t141)) % 0.37/0.57 (step @p182 :rule eq_resolve :premises (@p181 @p180)) % 0.37/0.57 (step @p183 :rule refl :args (@t139)) % 0.37/0.57 (step @p184 :rule cong :premises (@p183 @p173) :args ((= @t139 @t130))) % 0.37/0.57 (step @p185 :rule symm :premises (@p184)) % 0.37/0.57 (step @p186 :rule eq_resolve :premises (@p183 @p185)) % 0.37/0.57 (step @p187 :rule cong :premises (@p186) :args (@t140)) % 0.37/0.57 (step @p188 :rule ho_cong :premises (@p177 @p187)) % 0.37/0.57 (step @p189 :rule trans :premises (@p188 @p182)) % 0.37/0.57 (step @p190 :rule cong :premises (@p49 @p189) :args (@t142)) % 0.37/0.57 (step @p191 :rule cong :premises (@p190) :args (@t143)) % 0.37/0.57 (step @p192 :rule cong :premises (@p52 @p189) :args (@t144)) % 0.37/0.57 (step @p193 :rule cong :premises (@p192) :args (@t145)) % 0.37/0.57 (step @p194 :rule nary_cong :premises (@p193 @p191) :args (@t146)) % 0.37/0.57 (step @p195 :rule cong :premises (@p194) :args ((forall @t4 @t146))) % 0.37/0.57 (step @p196 :rule trans :premises (@p195 @p171)) % 0.37/0.57 (step @p197 :rule alpha_equiv :args (@t5 @t66 (@list @t129))) % 0.37/0.57 (step @p198 :rule ho_cong :premises (@p177 @p197)) % 0.37/0.57 (step @p199 :rule cong :premises (@p49 @p198) :args (@t147)) % 0.37/0.57 (step @p200 :rule cong :premises (@p199) :args (@t148)) % 0.37/0.57 (step @p201 :rule cong :premises (@p52 @p198) :args (@t149)) % 0.37/0.57 (step @p202 :rule cong :premises (@p201) :args (@t150)) % 0.37/0.57 (step @p203 :rule nary_cong :premises (@p202 @p200) :args (@t151)) % 0.37/0.57 (step @p204 :rule cong :premises (@p203) :args ((forall @t4 @t151))) % 0.37/0.57 (step @p205 :rule trans :premises (@p204 @p196)) % 0.37/0.57 (step @p206 :rule eq-symm :args (@t8 @t44)) % 0.37/0.57 (step @p207 :rule cong :premises (@p206) :args (@t152)) % 0.37/0.57 (step @p208 :rule refl :args (@t150)) % 0.37/0.57 (step @p209 :rule nary_cong :premises (@p208 @p207) :args (@t153)) % 0.37/0.57 (step @p210 :rule cong :premises (@p209) :args (@t154)) % 0.37/0.57 (step @p211 :rule trans :premises (@p210 @p205)) % 0.37/0.57 (step @p212 :rule cong :premises (@p211) :args (@t155)) % 0.37/0.57 (step @p213 :rule beta-reduce :args ((= @t156 @t155))) % 0.37/0.57 (step @p214 :rule trans :premises (@p213 @p212)) % 0.37/0.57 (step @p215 :rule refl :args (@t8)) % 0.37/0.57 (step @p216 :rule refl :args (@t44)) % 0.37/0.57 (step @p217 :rule refl :args (@t33)) % 0.37/0.57 (step @p218 :rule cong :premises (@p217 @p216) :args ((= @t33 @t44))) % 0.37/0.57 (step @p219 :rule symm :premises (@p218)) % 0.37/0.57 (step @p220 :rule eq_resolve :premises (@p217 @p219)) % 0.37/0.57 (step @p221 :rule cong :premises (@p47 @p220) :args (@t34)) % 0.37/0.57 (step @p222 :rule cong :premises (@p221) :args (@t157)) % 0.37/0.57 (step @p223 :rule nary_cong :premises (@p85 @p222) :args (@t158)) % 0.37/0.57 (step @p224 :rule cong :premises (@p223) :args ((forall @t4 @t158))) % 0.37/0.57 (step @p225 :rule bool-and-de-morgan :args (@t10 @t34 true)) % 0.37/0.57 (step @p226 :rule cong :premises (@p225) :args (@t159)) % 0.37/0.57 (step @p227 :rule trans :premises (@p226 @p224)) % 0.37/0.57 (step @p228 :rule cong :premises (@p227) :args (@t160)) % 0.37/0.57 (step @p229 :rule exists-elim :args ((= @t36 @t160))) % 0.37/0.57 (step @p230 :rule trans :premises (@p229 @p228)) % 0.37/0.57 (step @p231 :rule cong :premises (@p230) :args (@t38)) % 0.37/0.57 (step @p232 :rule trans :premises (@p4 @p231)) % 0.37/0.57 (step @p233 :rule ho_cong :premises (@p232 @p215)) % 0.37/0.57 (step @p234 :rule trans :premises (@p233 @p214)) % 0.37/0.57 (step @p235 :rule cong :premises (@p234) :args (@t39)) % 0.37/0.57 (step @p236 :rule trans :premises (@p5 @p235)) % 0.37/0.57 (step @p237 :rule ho_cong :premises (@p236 @p31)) % 0.37/0.57 (step @p238 :rule ho_cong :premises (@p237 @p70)) % 0.37/0.57 (step @p239 :rule refl :args (@t12)) % 0.37/0.57 (step @p240 :rule cong :premises (@p239 @p238) :args (@t28)) % 0.37/0.57 (step @p241 :rule refl :args (@t23)) % 0.37/0.57 (step @p242 :rule cong :premises (@p241 @p240) :args (@t29)) % 0.37/0.57 (step @p243 :rule cong :premises (@p242) :args (@t30)) % 0.37/0.57 (step @p244 :rule cong :premises (@p161 @p243) :args (@t31)) % 0.37/0.57 (step @p245 :rule cong :premises (@p244) :args (@t32)) % 0.37/0.57 (step @p246 :rule trans :premises (@p245 @p163)) % 0.37/0.57 (step @p247 :rule eq_resolve :premises (@p2 @p246)) % 0.37/0.57 (step @p248 :rule not_implies_elim2 :premises (@p247)) % 0.37/0.57 (step @p249 :rule not_implies_elim1 :premises (@p247)) % 0.37/0.57 (step @p250 :rule cnf_equiv_pos1 :args ((= tptp.singletonprop @t161))) % 0.37/0.57 (step @p251 :rule chain_resolution :premises (@p250 @p249 @p248) :args ((@list false true) (@list tptp.singletonprop @t161))) % 0.37/0.57 (step @p252 :rule cong :premises (@p93 @p214) :args (@t162)) % 0.37/0.57 (step @p253 :rule cong :premises (@p157 @p252) :args (@t163)) % 0.37/0.57 (step @p254 :rule cong :premises (@p253) :args (@t164)) % 0.37/0.57 (step @p255 :rule trans :premises (@p254 @p29)) % 0.37/0.57 (step @p256 :rule cong :premises (@p161 @p255) :args ((= tptp.singletonprop @t164))) % 0.37/0.57 (step @p257 :rule cong :premises (@p239 @p233) :args (@t13)) % 0.37/0.57 (step @p258 :rule cong :premises (@p241 @p257) :args (@t24)) % 0.37/0.57 (step @p259 :rule cong :premises (@p258) :args (@t26)) % 0.37/0.57 (step @p260 :rule cong :premises (@p161 @p259) :args (@t27)) % 0.37/0.57 (step @p261 :rule trans :premises (@p260 @p256)) % 0.37/0.57 (step @p262 :rule eq_resolve :premises (@p1 @p261)) % 0.37/0.57 (step @p263 false :rule contra :premises (@p262 @p251)) % 0.37/0.57 ) % 0.37/0.57 % SZS output end Proof % 0.37/0.57 % cvc5 exiting %------------------------------------------------------------------------------