%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV101^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n023.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:55:27 AM UTC 2026 % Result : Theorem 1.11s 1.31s % Output : Proof 1.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV101^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n023.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 18:13:43 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 1.11/1.31 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 1.11/1.31 % SZS status Theorem % 1.11/1.31 % SZS output start Proof % 1.11/1.31 ( % 1.11/1.31 (declare-sort $$unsorted 0) % 1.11/1.31 (declare-const tptp.p Bool) % 1.11/1.31 (define @t1 () (@var "Xw_2" $$unsorted)) % 1.11/1.31 (define @t2 () (not tptp.p)) % 1.11/1.31 (define @t3 () (and tptp.p @t2)) % 1.11/1.31 (define @t4 () (@list (@var "Xx" $$unsorted))) % 1.11/1.31 (define @t5 () (lambda @t4 @t3)) % 1.11/1.31 (define @t6 () (or tptp.p @t2)) % 1.11/1.31 (define @t7 () (lambda @t4 @t6)) % 1.11/1.31 (define @t8 () (@var "Xr_28" (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool))) % 1.11/1.31 (define @t9 () (_ (_ (_ @t8 @t7) @t5) @t1)) % 1.11/1.31 (define @t10 () (@var "Xr_27" (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool))) % 1.11/1.31 (define @t11 () (_ (_ (_ @t10 @t7) @t5) @t1)) % 1.11/1.31 (define @t12 () (or @t11 @t9)) % 1.11/1.31 (define @t13 () (@list @t1)) % 1.11/1.31 (define @t14 () (forall @t13 @t12)) % 1.11/1.31 (define @t15 () (not @t14)) % 1.11/1.31 (define @t16 () (@var "Xz" (-> $$unsorted Bool))) % 1.11/1.31 (define @t17 () (@var "Xx" (-> $$unsorted Bool))) % 1.11/1.31 (define @t18 () (_ @t8 @t17)) % 1.11/1.31 (define @t19 () (_ (_ @t18 @t16) @t1)) % 1.11/1.31 (define @t20 () (_ @t10 @t17)) % 1.11/1.31 (define @t21 () (_ (_ @t20 @t16) @t1)) % 1.11/1.31 (define @t22 () (or @t21 @t19)) % 1.11/1.31 (define @t23 () (forall @t13 @t22)) % 1.11/1.31 (define @t24 () (@var "Xy" (-> $$unsorted Bool))) % 1.11/1.31 (define @t25 () (_ (_ (_ @t8 @t24) @t16) @t1)) % 1.11/1.31 (define @t26 () (_ (_ (_ @t10 @t24) @t16) @t1)) % 1.11/1.31 (define @t27 () (or @t26 @t25)) % 1.11/1.31 (define @t28 () (forall @t13 @t27)) % 1.11/1.31 (define @t29 () (_ (_ @t18 @t24) @t1)) % 1.11/1.31 (define @t30 () (_ (_ @t20 @t24) @t1)) % 1.11/1.31 (define @t31 () (or @t30 @t29)) % 1.11/1.31 (define @t32 () (forall @t13 @t31)) % 1.11/1.31 (define @t33 () (and @t32 @t28)) % 1.11/1.31 (define @t34 () (=> @t33 @t23)) % 1.11/1.31 (define @t35 () (@list @t17 @t24 @t16)) % 1.11/1.31 (define @t36 () (forall @t35 @t34)) % 1.11/1.31 (define @t37 () (_ (_ @t18 @t17) @t1)) % 1.11/1.31 (define @t38 () (_ (_ @t20 @t17) @t1)) % 1.11/1.31 (define @t39 () (or @t38 @t37)) % 1.11/1.31 (define @t40 () (@list @t17 @t1)) % 1.11/1.31 (define @t41 () (forall @t40 @t39)) % 1.11/1.31 (define @t42 () (and @t41 @t36 @t15)) % 1.11/1.31 (define @t43 () (@list @t8 @t10)) % 1.11/1.31 (define @t44 () (exists @t43 @t42)) % 1.11/1.31 (define @t45 () (not @t44)) % 1.11/1.31 (define @t46 () (@var "BOUND_VARIABLE_7519" $$unsorted)) % 1.11/1.31 (define @t47 () (_ @t8 @t7 @t5 @t46)) % 1.11/1.31 (define @t48 () (_ @t10 @t7 @t5 @t46)) % 1.11/1.31 (define @t49 () (@var "BOUND_VARIABLE_7495" $$unsorted)) % 1.11/1.31 (define @t50 () (_ @t8 @t17 @t16 @t49)) % 1.11/1.31 (define @t51 () (_ @t10 @t17 @t16 @t49)) % 1.11/1.31 (define @t52 () (_ @t8 @t24 @t16 @t1)) % 1.11/1.31 (define @t53 () (_ @t10 @t24 @t16 @t1)) % 1.11/1.31 (define @t54 () (forall @t13 (or @t53 @t52))) % 1.11/1.31 (define @t55 () (not @t54)) % 1.11/1.31 (define @t56 () (_ @t8 @t17 @t24 @t1)) % 1.11/1.31 (define @t57 () (_ @t10 @t17 @t24 @t1)) % 1.11/1.31 (define @t58 () (forall @t13 (or @t57 @t56))) % 1.11/1.31 (define @t59 () (not @t58)) % 1.11/1.31 (define @t60 () (or @t59 @t55 @t51 @t50)) % 1.11/1.31 (define @t61 () (@list @t17 @t24 @t16 @t49)) % 1.11/1.31 (define @t62 () (forall @t61 @t60)) % 1.11/1.31 (define @t63 () (not @t62)) % 1.11/1.31 (define @t64 () (_ @t8 @t17 @t17 @t1)) % 1.11/1.31 (define @t65 () (_ @t10 @t17 @t17 @t1)) % 1.11/1.31 (define @t66 () (forall @t40 (or @t65 @t64))) % 1.11/1.31 (define @t67 () (not @t66)) % 1.11/1.31 (define @t68 () (or @t67 @t63 @t48 @t47)) % 1.11/1.31 (define @t69 () (@list @t8 @t10 @t46)) % 1.11/1.31 (define @t70 () (forall @t69 @t68)) % 1.11/1.31 (define @t71 () (or @t48 @t47)) % 1.11/1.31 (define @t72 () (or @t67 @t63 @t71)) % 1.11/1.31 (define @t73 () (forall @t69 @t72)) % 1.11/1.31 (define @t74 () (@list @t46)) % 1.11/1.31 (define @t75 () (forall @t74 @t72)) % 1.11/1.31 (define @t76 () (forall @t74 @t71)) % 1.11/1.31 (define @t77 () (@list @t1)) % 1.11/1.31 (define @t78 () (or @t67 @t63 @t76)) % 1.11/1.31 (define @t79 () (_ @t8 @t7 @t5 @t1)) % 1.11/1.31 (define @t80 () (_ @t10 @t7 @t5 @t1)) % 1.11/1.31 (define @t81 () (forall @t13 (or @t80 @t79))) % 1.11/1.31 (define @t82 () (not @t81)) % 1.11/1.31 (define @t83 () (not @t82)) % 1.11/1.31 (define @t84 () (or @t67 @t63 @t83)) % 1.11/1.31 (define @t85 () (and @t66 @t62 @t82)) % 1.11/1.31 (define @t86 () (forall @t43 (not @t85))) % 1.11/1.31 (define @t87 () (not @t86)) % 1.11/1.31 (define @t88 () (or @t51 @t50)) % 1.11/1.31 (define @t89 () (or @t59 @t55 @t88)) % 1.11/1.31 (define @t90 () (forall @t61 @t89)) % 1.11/1.31 (define @t91 () (@list @t49)) % 1.11/1.31 (define @t92 () (forall @t91 @t89)) % 1.11/1.31 (define @t93 () (forall @t91 @t88)) % 1.11/1.31 (define @t94 () (or @t59 @t55 @t93)) % 1.11/1.31 (define @t95 () (_ @t8 @t17 @t16 @t1)) % 1.11/1.31 (define @t96 () (_ @t10 @t17 @t16 @t1)) % 1.11/1.31 (define @t97 () (forall @t13 (or @t96 @t95))) % 1.11/1.31 (define @t98 () (or @t59 @t55 @t97)) % 1.11/1.31 (define @t99 () (and @t58 @t54)) % 1.11/1.31 (define @t100 () (@purify @t7)) % 1.11/1.31 (define @t101 () (@purify @t5)) % 1.11/1.31 (define @t102 () (= @t101 @t100)) % 1.11/1.31 (define @t103 () (= true false)) % 1.11/1.31 (define @t104 () (= @t6 @t3)) % 1.11/1.31 (define @t105 () (forall @t4 (= @t3 @t6))) % 1.11/1.31 (define @t106 () (=> @t102 @t105)) % 1.11/1.31 (define @t107 () (= @t7 @t5)) % 1.11/1.31 (define @t108 () (@purify (as @$$unsorted_0 $$unsorted))) % 1.11/1.31 (define @t109 () (@var "BOUND_VARIABLE_38603" (-> $$unsorted Bool))) % 1.11/1.31 (define @t110 () (@var "BOUND_VARIABLE_38602" (-> $$unsorted Bool))) % 1.11/1.31 (define @t111 () (lambda (@list @t110 @t109 (@var "BOUND_VARIABLE_38604" $$unsorted)) (= @t110 @t109))) % 1.11/1.31 (define @t112 () (_ @t111 @t7 @t5 @t108)) % 1.11/1.31 (define @t113 () (lambda (@list (@var "BOUND_VARIABLE_38826" (-> $$unsorted Bool)) (@var "BOUND_VARIABLE_38827" (-> $$unsorted Bool)) (@var "BOUND_VARIABLE_38828" $$unsorted)) false)) % 1.11/1.31 (define @t114 () (_ @t113 @t7 @t5 @t108)) % 1.11/1.31 (define @t115 () (@list @t24 @t16)) % 1.11/1.31 (define @t116 () (= @t24 @t16)) % 1.11/1.31 (define @t117 () (not @t116)) % 1.11/1.31 (define @t118 () (or @t117 @t116)) % 1.11/1.31 (define @t119 () (not (= @t24 @t24))) % 1.11/1.31 (define @t120 () (or @t119 @t117 @t116)) % 1.11/1.31 (define @t121 () (= @t17 @t16)) % 1.11/1.31 (define @t122 () (= @t17 @t24)) % 1.11/1.31 (define @t123 () (not @t122)) % 1.11/1.31 (define @t124 () (or @t123 @t123 @t117 @t121)) % 1.11/1.31 (define @t125 () (@list @t17)) % 1.11/1.31 (define @t126 () (or @t123 @t117 @t121)) % 1.11/1.31 (define @t127 () (forall @t125 @t126)) % 1.11/1.31 (define @t128 () (forall @t115 @t127)) % 1.11/1.31 (define @t129 () (forall (@list @t24 @t16 @t17) @t126)) % 1.11/1.31 (define @t130 () (forall @t35 @t126)) % 1.11/1.31 (define @t131 () (_ @t111 @t17 @t16 @t49)) % 1.11/1.31 (define @t132 () (_ @t113 @t17 @t16 @t49)) % 1.11/1.31 (define @t133 () (_ @t111 @t24 @t16 @t1)) % 1.11/1.31 (define @t134 () (_ @t113 @t24 @t16 @t1)) % 1.11/1.31 (define @t135 () (or @t134 @t133)) % 1.11/1.31 (define @t136 () (forall @t13 @t135)) % 1.11/1.31 (define @t137 () (not @t136)) % 1.11/1.31 (define @t138 () (_ @t111 @t17 @t24 @t1)) % 1.11/1.31 (define @t139 () (_ @t113 @t17 @t24 @t1)) % 1.11/1.31 (define @t140 () (or @t139 @t138)) % 1.11/1.31 (define @t141 () (forall @t13 @t140)) % 1.11/1.31 (define @t142 () (not @t141)) % 1.11/1.31 (define @t143 () (or @t142 @t137 @t132 @t131)) % 1.11/1.31 (define @t144 () (forall @t61 @t143)) % 1.11/1.31 (define @t145 () (not @t144)) % 1.11/1.31 (define @t146 () (_ @t111 @t17 @t17 @t1)) % 1.11/1.31 (define @t147 () (_ @t113 @t17 @t17 @t1)) % 1.11/1.31 (define @t148 () (or @t147 @t146)) % 1.11/1.31 (define @t149 () (forall @t40 @t148)) % 1.11/1.31 (define @t150 () (not @t149)) % 1.11/1.31 (define @t151 () (or @t150 @t145 @t114 @t112)) % 1.11/1.31 (assume @p1 @t45) % 1.11/1.31 (assume @p2 true) % 1.11/1.31 (step @p3 :rule bool-double-not-elim :args (@t70)) % 1.11/1.31 (step @p4 :rule aci_norm :args ((= @t72 @t68))) % 1.11/1.31 (step @p5 :rule cong :premises (@p4) :args (@t73)) % 1.11/1.31 (step @p6 :rule quant-merge-prenex :args ((= (forall @t43 @t75) @t73))) % 1.11/1.31 (step @p7 :rule alpha_equiv :args (@t76 (@list @t46) @t77)) % 1.11/1.31 (step @p8 :rule refl :args (@t63)) % 1.11/1.31 (step @p9 :rule refl :args (@t67)) % 1.11/1.31 (step @p10 :rule nary_cong :premises (@p9 @p8 @p7) :args (@t78)) % 1.11/1.31 (step @p11 :rule quant-miniscope-or :args ((= @t75 @t78))) % 1.11/1.31 (step @p12 :rule trans :premises (@p11 @p10)) % 1.11/1.31 (step @p13 :rule symm :premises (@p12)) % 1.11/1.31 (step @p14 :rule cong :premises (@p13) :args ((forall @t43 (or @t67 @t63 @t81)))) % 1.11/1.31 (step @p15 :rule trans :premises (@p14 @p6)) % 1.11/1.31 (step @p16 :rule trans :premises (@p15 @p5)) % 1.11/1.31 (step @p17 :rule bool-double-not-elim :args (@t81)) % 1.11/1.31 (step @p18 :rule nary_cong :premises (@p9 @p8 @p17) :args (@t84)) % 1.11/1.31 (step @p19 :rule aci_norm :args ((= (or @t67 (or @t63 @t83)) @t84))) % 1.11/1.31 (step @p20 :rule trans :premises (@p19 @p18)) % 1.11/1.31 (step @p21 :rule bool-and-de-morgan :args (@t62 @t82 true)) % 1.11/1.31 (step @p22 :rule nary_cong :premises (@p9 @p21) :args ((or @t67 (not (and @t62 @t82))))) % 1.11/1.31 (step @p23 :rule bool-and-de-morgan :args (@t66 @t62 (and @t82))) % 1.11/1.31 (step @p24 :rule trans :premises (@p23 @p22)) % 1.11/1.31 (step @p25 :rule trans :premises (@p24 @p20)) % 1.11/1.31 (step @p26 :rule cong :premises (@p25) :args (@t86)) % 1.11/1.31 (step @p27 :rule trans :premises (@p26 @p16)) % 1.11/1.31 (step @p28 :rule cong :premises (@p27) :args (@t87)) % 1.11/1.31 (step @p29 :rule exists-elim :args ((= (exists @t43 @t85) @t87))) % 1.11/1.31 (step @p30 :rule trans :premises (@p29 @p28)) % 1.11/1.31 (step @p31 :rule refl :args (@t79)) % 1.11/1.31 (step @p32 :rule refl :args (@t9)) % 1.11/1.31 (step @p33 :rule cong :premises (@p32 @p31) :args ((= @t9 @t79))) % 1.11/1.31 (step @p34 :rule symm :premises (@p33)) % 1.11/1.31 (step @p35 :rule eq_resolve :premises (@p32 @p34)) % 1.11/1.31 (step @p36 :rule refl :args (@t80)) % 1.11/1.31 (step @p37 :rule refl :args (@t11)) % 1.11/1.31 (step @p38 :rule cong :premises (@p37 @p36) :args ((= @t11 @t80))) % 1.11/1.31 (step @p39 :rule symm :premises (@p38)) % 1.11/1.31 (step @p40 :rule eq_resolve :premises (@p37 @p39)) % 1.11/1.31 (step @p41 :rule nary_cong :premises (@p40 @p35) :args (@t12)) % 1.11/1.31 (step @p42 :rule cong :premises (@p41) :args (@t14)) % 1.11/1.31 (step @p43 :rule cong :premises (@p42) :args (@t15)) % 1.11/1.31 (step @p44 :rule aci_norm :args ((= @t89 @t60))) % 1.11/1.31 (step @p45 :rule cong :premises (@p44) :args (@t90)) % 1.11/1.31 (step @p46 :rule quant-merge-prenex :args ((= (forall @t35 @t92) @t90))) % 1.11/1.31 (step @p47 :rule alpha_equiv :args (@t93 (@list @t49) @t77)) % 1.11/1.31 (step @p48 :rule refl :args (@t55)) % 1.11/1.31 (step @p49 :rule refl :args (@t59)) % 1.11/1.31 (step @p50 :rule nary_cong :premises (@p49 @p48 @p47) :args (@t94)) % 1.11/1.31 (step @p51 :rule quant-miniscope-or :args ((= @t92 @t94))) % 1.11/1.31 (step @p52 :rule trans :premises (@p51 @p50)) % 1.11/1.31 (step @p53 :rule symm :premises (@p52)) % 1.11/1.31 (step @p54 :rule cong :premises (@p53) :args ((forall @t35 @t98))) % 1.11/1.31 (step @p55 :rule trans :premises (@p54 @p46)) % 1.11/1.31 (step @p56 :rule trans :premises (@p55 @p45)) % 1.11/1.31 (step @p57 :rule aci_norm :args ((= (or (or @t59 @t55) @t97) @t98))) % 1.11/1.31 (step @p58 :rule refl :args (@t97)) % 1.11/1.31 (step @p59 :rule bool-and-de-morgan :args (@t58 @t54 true)) % 1.11/1.31 (step @p60 :rule nary_cong :premises (@p59 @p58) :args ((or (not @t99) @t97))) % 1.11/1.31 (step @p61 :rule trans :premises (@p60 @p57)) % 1.11/1.31 (step @p62 :rule bool-impl-elim :args (@t99 @t97)) % 1.11/1.31 (step @p63 :rule trans :premises (@p62 @p61)) % 1.11/1.31 (step @p64 :rule cong :premises (@p63) :args ((forall @t35 (=> @t99 @t97)))) % 1.11/1.31 (step @p65 :rule trans :premises (@p64 @p56)) % 1.11/1.31 (step @p66 :rule refl :args (@t95)) % 1.11/1.31 (step @p67 :rule refl :args (@t19)) % 1.11/1.31 (step @p68 :rule cong :premises (@p67 @p66) :args ((= @t19 @t95))) % 1.11/1.31 (step @p69 :rule symm :premises (@p68)) % 1.11/1.31 (step @p70 :rule eq_resolve :premises (@p67 @p69)) % 1.11/1.31 (step @p71 :rule refl :args (@t96)) % 1.11/1.31 (step @p72 :rule refl :args (@t21)) % 1.11/1.31 (step @p73 :rule cong :premises (@p72 @p71) :args ((= @t21 @t96))) % 1.11/1.31 (step @p74 :rule symm :premises (@p73)) % 1.11/1.31 (step @p75 :rule eq_resolve :premises (@p72 @p74)) % 1.11/1.31 (step @p76 :rule nary_cong :premises (@p75 @p70) :args (@t22)) % 1.11/1.31 (step @p77 :rule cong :premises (@p76) :args (@t23)) % 1.11/1.31 (step @p78 :rule refl :args (@t52)) % 1.11/1.31 (step @p79 :rule refl :args (@t25)) % 1.11/1.31 (step @p80 :rule cong :premises (@p79 @p78) :args ((= @t25 @t52))) % 1.11/1.31 (step @p81 :rule symm :premises (@p80)) % 1.11/1.31 (step @p82 :rule eq_resolve :premises (@p79 @p81)) % 1.11/1.31 (step @p83 :rule refl :args (@t53)) % 1.11/1.31 (step @p84 :rule refl :args (@t26)) % 1.11/1.31 (step @p85 :rule cong :premises (@p84 @p83) :args ((= @t26 @t53))) % 1.11/1.31 (step @p86 :rule symm :premises (@p85)) % 1.11/1.31 (step @p87 :rule eq_resolve :premises (@p84 @p86)) % 1.11/1.31 (step @p88 :rule nary_cong :premises (@p87 @p82) :args (@t27)) % 1.11/1.31 (step @p89 :rule cong :premises (@p88) :args (@t28)) % 1.11/1.31 (step @p90 :rule refl :args (@t56)) % 1.11/1.31 (step @p91 :rule refl :args (@t29)) % 1.11/1.31 (step @p92 :rule cong :premises (@p91 @p90) :args ((= @t29 @t56))) % 1.11/1.31 (step @p93 :rule symm :premises (@p92)) % 1.11/1.31 (step @p94 :rule eq_resolve :premises (@p91 @p93)) % 1.11/1.31 (step @p95 :rule refl :args (@t57)) % 1.11/1.31 (step @p96 :rule refl :args (@t30)) % 1.11/1.31 (step @p97 :rule cong :premises (@p96 @p95) :args ((= @t30 @t57))) % 1.11/1.31 (step @p98 :rule symm :premises (@p97)) % 1.11/1.31 (step @p99 :rule eq_resolve :premises (@p96 @p98)) % 1.11/1.31 (step @p100 :rule nary_cong :premises (@p99 @p94) :args (@t31)) % 1.11/1.31 (step @p101 :rule cong :premises (@p100) :args (@t32)) % 1.11/1.31 (step @p102 :rule nary_cong :premises (@p101 @p89) :args (@t33)) % 1.11/1.31 (step @p103 :rule cong :premises (@p102 @p77) :args (@t34)) % 1.11/1.31 (step @p104 :rule cong :premises (@p103) :args (@t36)) % 1.11/1.31 (step @p105 :rule trans :premises (@p104 @p65)) % 1.11/1.31 (step @p106 :rule refl :args (@t64)) % 1.11/1.31 (step @p107 :rule refl :args (@t37)) % 1.11/1.31 (step @p108 :rule cong :premises (@p107 @p106) :args ((= @t37 @t64))) % 1.11/1.31 (step @p109 :rule symm :premises (@p108)) % 1.11/1.31 (step @p110 :rule eq_resolve :premises (@p107 @p109)) % 1.11/1.31 (step @p111 :rule refl :args (@t65)) % 1.11/1.31 (step @p112 :rule refl :args (@t38)) % 1.11/1.31 (step @p113 :rule cong :premises (@p112 @p111) :args ((= @t38 @t65))) % 1.11/1.31 (step @p114 :rule symm :premises (@p113)) % 1.11/1.31 (step @p115 :rule eq_resolve :premises (@p112 @p114)) % 1.11/1.31 (step @p116 :rule nary_cong :premises (@p115 @p110) :args (@t39)) % 1.11/1.31 (step @p117 :rule cong :premises (@p116) :args (@t41)) % 1.11/1.31 (step @p118 :rule nary_cong :premises (@p117 @p105 @p43) :args (@t42)) % 1.11/1.31 (step @p119 :rule cong :premises (@p118) :args (@t44)) % 1.11/1.31 (step @p120 :rule trans :premises (@p119 @p30)) % 1.11/1.31 (step @p121 :rule cong :premises (@p120) :args (@t45)) % 1.11/1.31 (step @p122 :rule trans :premises (@p121 @p3)) % 1.11/1.31 (step @p123 :rule eq_resolve :premises (@p1 @p122)) % 1.11/1.31 (step @p124 :rule bool-impl-false1 :args (@t102)) % 1.11/1.31 (step @p125 :rule quant-unused-vars :args ((= (forall @t4 false) false))) % 1.11/1.31 (step @p126 :rule evaluate :args (@t103)) % 1.11/1.31 (step @p127 :rule cong :premises (@p126) :args ((forall @t4 @t103))) % 1.11/1.31 (step @p128 :rule trans :premises (@p127 @p125)) % 1.11/1.31 (step @p129 :rule bool-and-conf :args (true tptp.p true true)) % 1.11/1.31 (step @p130 :rule bool-or-taut :args (false tptp.p false false)) % 1.11/1.31 (step @p131 :rule cong :premises (@p130 @p129) :args (@t104)) % 1.11/1.31 (step @p132 :rule cong :premises (@p131) :args ((forall @t4 @t104))) % 1.11/1.31 (step @p133 :rule trans :premises (@p132 @p128)) % 1.11/1.31 (step @p134 :rule eq-symm :args (@t3 @t6)) % 1.11/1.31 (step @p135 :rule cong :premises (@p134) :args (@t105)) % 1.11/1.31 (step @p136 :rule trans :premises (@p135 @p133)) % 1.11/1.31 (step @p137 :rule refl :args (@t102)) % 1.11/1.31 (step @p138 :rule cong :premises (@p137 @p136) :args (@t106)) % 1.11/1.31 (step @p139 :rule trans :premises (@p138 @p124)) % 1.11/1.31 ; WARNING: add trust step for TRUST % 1.11/1.31 ; trust TRUST THEORY_LEMMA % 1.11/1.31 (step @p140 :rule trust :premises () :args (@t106)) % 1.11/1.31 (step @p141 :rule eq_resolve :premises (@p140 @p139)) % 1.11/1.31 (step @p142 :rule eq-symm :args (@t100 @t101)) % 1.11/1.31 (step @p143 :rule eq-refl :args (@t5)) % 1.11/1.31 (step @p144 :rule skolem_intro :args (@t101)) % 1.11/1.31 (step @p145 :rule refl :args (@t5)) % 1.11/1.31 (step @p146 :rule cong :premises (@p145 @p144) :args ((= @t5 @t101))) % 1.11/1.31 (step @p147 :rule trans :premises (@p146 @p143)) % 1.11/1.31 (step @p148 :rule true_elim :premises (@p147)) % 1.11/1.31 (step @p149 :rule eq-refl :args (@t7)) % 1.11/1.31 (step @p150 :rule skolem_intro :args (@t100)) % 1.11/1.31 (step @p151 :rule refl :args (@t7)) % 1.11/1.31 (step @p152 :rule cong :premises (@p151 @p150) :args ((= @t7 @t100))) % 1.11/1.31 (step @p153 :rule trans :premises (@p152 @p149)) % 1.11/1.31 (step @p154 :rule true_elim :premises (@p153)) % 1.11/1.31 (step @p155 :rule cong :premises (@p154 @p148) :args (@t107)) % 1.11/1.31 (step @p156 :rule trans :premises (@p155 @p142)) % 1.11/1.31 (step @p157 :rule refl :args (@t70)) % 1.11/1.31 (step @p158 :rule cong :premises (@p157 @p156) :args ((=> @t70 @t107))) % 1.11/1.31 (step @p159 :rule aci_norm :args ((= (or false false false @t107) @t107))) % 1.11/1.31 (step @p160 :rule beta-reduce :args ((= @t112 @t107))) % 1.11/1.31 (step @p161 :rule beta-reduce :args ((= @t114 false))) % 1.11/1.31 (step @p162 :rule evaluate :args ((not true))) % 1.11/1.31 (step @p163 :rule quant-unused-vars :args ((= (forall @t115 true) true))) % 1.11/1.31 (step @p164 :rule bool-or-taut2 :args (false @t116 false false)) % 1.11/1.31 (step @p165 :rule cong :premises (@p164) :args ((forall @t115 @t118))) % 1.11/1.31 (step @p166 :rule trans :premises (@p165 @p163)) % 1.11/1.31 (step @p167 :rule aci_norm :args ((= (or false @t117 @t116) @t118))) % 1.11/1.31 (step @p168 :rule refl :args (@t116)) % 1.11/1.31 (step @p169 :rule refl :args (@t117)) % 1.11/1.31 (step @p170 :rule eq-refl :args (@t24)) % 1.11/1.31 (step @p171 :rule cong :premises (@p170) :args (@t119)) % 1.11/1.31 (step @p172 :rule trans :premises (@p171 @p162)) % 1.11/1.31 (step @p173 :rule nary_cong :premises (@p172 @p169 @p168) :args (@t120)) % 1.11/1.31 (step @p174 :rule trans :premises (@p173 @p167)) % 1.11/1.31 (step @p175 :rule cong :premises (@p174) :args ((forall @t115 @t120))) % 1.11/1.31 (step @p176 :rule trans :premises (@p175 @p166)) % 1.11/1.31 (step @p177 :rule quant-var-elim-eq :args ((= (forall @t125 @t124) @t120))) % 1.11/1.31 (step @p178 :rule aci_norm :args ((= @t126 @t124))) % 1.11/1.31 (step @p179 :rule cong :premises (@p178) :args (@t127)) % 1.11/1.31 (step @p180 :rule trans :premises (@p179 @p177)) % 1.11/1.31 (step @p181 :rule cong :premises (@p180) :args (@t128)) % 1.11/1.31 (step @p182 :rule quant-merge-prenex :args ((= @t128 @t129))) % 1.11/1.31 (step @p183 :rule symm :premises (@p182)) % 1.11/1.31 (step @p184 :rule quant_var_reordering :args ((= @t130 @t129))) % 1.11/1.31 (step @p185 :rule trans :premises (@p184 @p183 @p181)) % 1.11/1.31 (step @p186 :rule trans :premises (@p185 @p176)) % 1.11/1.31 (step @p187 :rule quant-unused-vars :args ((= (forall @t61 @t126) @t130))) % 1.11/1.31 (step @p188 :rule trans :premises (@p187 @p186)) % 1.11/1.31 (step @p189 :rule aci_norm :args ((= (or @t123 @t117 false @t121) @t126))) % 1.11/1.31 (step @p190 :rule beta-reduce :args ((= @t131 @t121))) % 1.11/1.31 (step @p191 :rule beta-reduce :args ((= @t132 false))) % 1.11/1.31 (step @p192 :rule quant-unused-vars :args ((= (forall @t13 @t116) @t116))) % 1.11/1.31 (step @p193 :rule aci_norm :args ((= (or false @t116) @t116))) % 1.11/1.31 (step @p194 :rule beta-reduce :args ((= @t133 @t116))) % 1.11/1.31 (step @p195 :rule beta-reduce :args ((= @t134 false))) % 1.11/1.31 (step @p196 :rule nary_cong :premises (@p195 @p194) :args (@t135)) % 1.11/1.31 (step @p197 :rule trans :premises (@p196 @p193)) % 1.11/1.31 (step @p198 :rule cong :premises (@p197) :args (@t136)) % 1.11/1.31 (step @p199 :rule trans :premises (@p198 @p192)) % 1.11/1.31 (step @p200 :rule cong :premises (@p199) :args (@t137)) % 1.11/1.31 (step @p201 :rule quant-unused-vars :args ((= (forall @t13 @t122) @t122))) % 1.11/1.31 (step @p202 :rule aci_norm :args ((= (or false @t122) @t122))) % 1.11/1.31 (step @p203 :rule beta-reduce :args ((= @t138 @t122))) % 1.11/1.31 (step @p204 :rule beta-reduce :args ((= @t139 false))) % 1.11/1.31 (step @p205 :rule nary_cong :premises (@p204 @p203) :args (@t140)) % 1.11/1.31 (step @p206 :rule trans :premises (@p205 @p202)) % 1.11/1.31 (step @p207 :rule cong :premises (@p206) :args (@t141)) % 1.11/1.31 (step @p208 :rule trans :premises (@p207 @p201)) % 1.11/1.31 (step @p209 :rule cong :premises (@p208) :args (@t142)) % 1.11/1.31 (step @p210 :rule nary_cong :premises (@p209 @p200 @p191 @p190) :args (@t143)) % 1.11/1.31 (step @p211 :rule trans :premises (@p210 @p189)) % 1.11/1.31 (step @p212 :rule cong :premises (@p211) :args (@t144)) % 1.11/1.31 (step @p213 :rule trans :premises (@p212 @p188)) % 1.11/1.31 (step @p214 :rule cong :premises (@p213) :args (@t145)) % 1.11/1.31 (step @p215 :rule trans :premises (@p214 @p162)) % 1.11/1.31 (step @p216 :rule quant-unused-vars :args ((= (forall @t40 true) true))) % 1.11/1.31 (step @p217 :rule evaluate :args ((or false true))) % 1.11/1.31 (step @p218 :rule eq-refl :args (@t17)) % 1.11/1.31 (step @p219 :rule beta-reduce :args ((= @t146 (= @t17 @t17)))) % 1.11/1.31 (step @p220 :rule trans :premises (@p219 @p218)) % 1.11/1.31 (step @p221 :rule beta-reduce :args ((= @t147 false))) % 1.11/1.31 (step @p222 :rule nary_cong :premises (@p221 @p220) :args (@t148)) % 1.11/1.31 (step @p223 :rule trans :premises (@p222 @p217)) % 1.11/1.31 (step @p224 :rule cong :premises (@p223) :args (@t149)) % 1.11/1.31 (step @p225 :rule trans :premises (@p224 @p216)) % 1.11/1.31 (step @p226 :rule cong :premises (@p225) :args (@t150)) % 1.11/1.31 (step @p227 :rule trans :premises (@p226 @p162)) % 1.11/1.31 (step @p228 :rule nary_cong :premises (@p227 @p215 @p161 @p160) :args (@t151)) % 1.11/1.31 (step @p229 :rule trans :premises (@p228 @p159)) % 1.11/1.31 (step @p230 :rule cong :premises (@p157 @p229) :args ((=> @t70 @t151))) % 1.11/1.31 (assume-push @p239 @t70) % 1.11/1.31 (step @p232 :rule instantiate :premises (@p123) :args ((@list @t111 @t113 @t108))) % 1.11/1.31 (step-pop @p240 :rule scope :premises (@p232)) % 1.11/1.31 (step @p233 :rule process_scope :premises (@p240) :args (@t151)) % 1.11/1.31 (step @p235 :rule eq_resolve :premises (@p233 @p230)) % 1.11/1.31 (step @p236 :rule eq_resolve :premises (@p235 @p158)) % 1.11/1.31 (step @p237 :rule implies_elim :premises (@p236)) % 1.11/1.31 (step @p238 false :rule chain_m_resolution :premises (@p237 @p141 @p123) :args (false (@list true false) (@list @t102 @t70))) % 1.11/1.31 ) % 1.11/1.31 % SZS output end Proof % 1.11/1.31 % cvc5 exiting %------------------------------------------------------------------------------