%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV080^5 : 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 : n008.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 08:55:25 AM UTC 2026 % Result : Theorem 1.74s 1.93s % Output : Proof 1.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV080^5 : 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 : n008.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 18:12:03 EDT 2026 % 0.17/0.35 % CPUTime : % 0.30/0.50 %----Proving TH0 % 1.74/1.93 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 1.74/1.93 % SZS status Theorem % 1.74/1.93 % SZS output start Proof % 1.74/1.93 ( % 1.74/1.93 (declare-sort tptp.a 0) % 1.74/1.93 (define @t1 () (@var "Xy_28" tptp.a)) % 1.74/1.93 (define @t2 () (@var "Xy" tptp.a)) % 1.74/1.93 (define @t3 () (@var "Xx" tptp.a)) % 1.74/1.93 (define @t4 () (@list @t3 @t2)) % 1.74/1.93 (define @t5 () (lambda @t4 (= @t3 @t2))) % 1.74/1.93 (define @t6 () (@var "Xx0" tptp.a)) % 1.74/1.93 (define @t7 () (@var "Xs" (-> tptp.a tptp.a))) % 1.74/1.93 (define @t8 () (_ @t7 @t6)) % 1.74/1.93 (define @t9 () (@var "Xx" (-> tptp.a Bool))) % 1.74/1.93 (define @t10 () (_ @t9 @t6)) % 1.74/1.93 (define @t11 () (and @t10 (= @t2 @t8))) % 1.74/1.93 (define @t12 () (@list @t6)) % 1.74/1.93 (define @t13 () (lambda @t12 @t11)) % 1.74/1.93 (define @t14 () (= @t13 (_ @t5 @t1))) % 1.74/1.93 (define @t15 () (@list @t1)) % 1.74/1.93 (define @t16 () (exists @t15 @t14)) % 1.74/1.93 (define @t17 () (_ @t9 @t2)) % 1.74/1.93 (define @t18 () (=> @t17 @t16)) % 1.74/1.93 (define @t19 () (@list @t2)) % 1.74/1.93 (define @t20 () (forall @t19 @t18)) % 1.74/1.93 (define @t21 () (_ @t9 @t8)) % 1.74/1.93 (define @t22 () (forall @t12 (=> @t10 @t21))) % 1.74/1.93 (define @t23 () (and @t22 @t20)) % 1.74/1.93 (define @t24 () (@list @t7)) % 1.74/1.93 (define @t25 () (exists @t24 @t23)) % 1.74/1.93 (define @t26 () (@list @t9)) % 1.74/1.93 (define @t27 () (forall @t26 @t25)) % 1.74/1.93 (define @t28 () (not @t27)) % 1.74/1.93 (define @t29 () (_ @t7 @t6)) % 1.74/1.93 (define @t30 () (_ @t9 @t29)) % 1.74/1.93 (define @t31 () (_ @t9 @t6)) % 1.74/1.93 (define @t32 () (forall @t12 (or (not @t31) @t30))) % 1.74/1.93 (define @t33 () (@var "BOUND_VARIABLE_7485" tptp.a)) % 1.74/1.93 (define @t34 () (@list @t33)) % 1.74/1.93 (define @t35 () (lambda @t34 (= @t1 @t33))) % 1.74/1.93 (define @t36 () (= @t2 @t29)) % 1.74/1.93 (define @t37 () (lambda @t12 (and @t31 @t36))) % 1.74/1.93 (define @t38 () (not (forall @t15 (not (= @t37 @t35))))) % 1.74/1.93 (define @t39 () (_ @t9 @t2)) % 1.74/1.93 (define @t40 () (forall @t19 (or (not @t39) @t38))) % 1.74/1.93 (define @t41 () (and @t32 @t40)) % 1.74/1.93 (define @t42 () (forall @t24 (not @t41))) % 1.74/1.93 (define @t43 () (not @t42)) % 1.74/1.93 (define @t44 () (not @t17)) % 1.74/1.93 (define @t45 () (or @t44 @t38)) % 1.74/1.93 (define @t46 () (lambda @t34 (= @t33 @t1))) % 1.74/1.93 (define @t47 () (= @t46 @t37)) % 1.74/1.93 (define @t48 () (not @t47)) % 1.74/1.93 (define @t49 () (forall @t15 @t48)) % 1.74/1.93 (define @t50 () (not @t49)) % 1.74/1.93 (define @t51 () (=> @t17 @t50)) % 1.74/1.93 (define @t52 () (lambda @t19 (= @t2 @t1))) % 1.74/1.93 (define @t53 () (= @t52 @t37)) % 1.74/1.93 (define @t54 () (not @t53)) % 1.74/1.93 (define @t55 () (forall @t15 @t54)) % 1.74/1.93 (define @t56 () (not @t55)) % 1.74/1.93 (define @t57 () (=> @t17 @t56)) % 1.74/1.93 (define @t58 () (and @t31 (= @t29 @t2))) % 1.74/1.93 (define @t59 () (lambda @t12 @t58)) % 1.74/1.93 (define @t60 () (= @t59 @t52)) % 1.74/1.93 (define @t61 () (not @t60)) % 1.74/1.93 (define @t62 () (= @t8 @t2)) % 1.74/1.93 (define @t63 () (and @t10 @t62)) % 1.74/1.93 (define @t64 () (lambda @t12 @t63)) % 1.74/1.93 (define @t65 () (= @t64 @t52)) % 1.74/1.93 (define @t66 () (not @t65)) % 1.74/1.93 (define @t67 () (forall @t15 @t66)) % 1.74/1.93 (define @t68 () (not @t67)) % 1.74/1.93 (define @t69 () (not @t10)) % 1.74/1.93 (define @t70 () (or @t69 @t21)) % 1.74/1.93 (define @t71 () (forall @t26 (not (forall @t24 (or (not @t32) (not @t40)))))) % 1.74/1.93 (define @t72 () (@quantifiers_skolemize @t71 0)) % 1.74/1.93 (define @t73 () (_ @t72 @t6)) % 1.74/1.93 (define @t74 () (lambda @t12 (and @t73 @t36))) % 1.74/1.93 (define @t75 () (not (_ @t72 @t2))) % 1.74/1.93 (define @t76 () (not @t73)) % 1.74/1.93 (define @t77 () (not (forall @t12 (or @t76 (_ @t72 @t29))))) % 1.74/1.93 (define @t78 () (forall @t24 (or @t77 (not (forall @t19 (or @t75 (not (forall @t15 (not (= @t35 @t74)))))))))) % 1.74/1.93 (define @t79 () (not @t71)) % 1.74/1.93 (define @t80 () (not (= @t74 @t35))) % 1.74/1.93 (define @t81 () (forall @t15 @t80)) % 1.74/1.93 (define @t82 () (not @t81)) % 1.74/1.93 (define @t83 () (or @t75 @t82)) % 1.74/1.93 (define @t84 () (forall @t19 @t83)) % 1.74/1.93 (define @t85 () (not @t84)) % 1.74/1.93 (define @t86 () (or @t77 @t85)) % 1.74/1.93 (define @t87 () (forall @t24 @t86)) % 1.74/1.93 (define @t88 () (not (not @t87))) % 1.74/1.93 (define @t89 () (@list true)) % 1.74/1.93 (define @t90 () (forall @t19 (or @t75 (not (forall @t15 (not (= @t35 (lambda @t12 (and @t73 (= @t6 @t2)))))))))) % 1.74/1.93 (define @t91 () (not @t90)) % 1.74/1.93 (define @t92 () (@var "BOUND_VARIABLE_14670" tptp.a)) % 1.74/1.93 (define @t93 () (lambda (@list @t92) @t92)) % 1.74/1.93 (define @t94 () (_ @t93 @t6)) % 1.74/1.93 (define @t95 () (= @t2 @t94)) % 1.74/1.93 (define @t96 () (and @t73 @t95)) % 1.74/1.93 (define @t97 () (lambda @t12 @t96)) % 1.74/1.93 (define @t98 () (= @t35 @t97)) % 1.74/1.93 (define @t99 () (not @t98)) % 1.74/1.93 (define @t100 () (forall @t15 @t99)) % 1.74/1.93 (define @t101 () (not @t100)) % 1.74/1.93 (define @t102 () (or @t75 @t101)) % 1.74/1.93 (define @t103 () (forall @t19 @t102)) % 1.74/1.93 (define @t104 () (not @t103)) % 1.74/1.93 (define @t105 () (_ @t72 @t94)) % 1.74/1.93 (define @t106 () (or @t76 @t105)) % 1.74/1.93 (define @t107 () (forall @t12 @t106)) % 1.74/1.93 (define @t108 () (not @t107)) % 1.74/1.93 (define @t109 () (or @t108 @t104)) % 1.74/1.93 (define @t110 () (@list false)) % 1.74/1.93 (define @t111 () (@quantifiers_skolemize @t90 0)) % 1.74/1.93 (define @t112 () (lambda @t12 (and @t73 (= @t6 @t111)))) % 1.74/1.93 (define @t113 () (forall @t15 (not (= @t35 @t112)))) % 1.74/1.93 (define @t114 () (not @t113)) % 1.74/1.93 (define @t115 () (_ @t72 @t111)) % 1.74/1.93 (define @t116 () (not @t115)) % 1.74/1.93 (define @t117 () (or @t116 @t114)) % 1.74/1.93 (define @t118 () (@list @t117)) % 1.74/1.93 (define @t119 () (lambda @t34 (= @t33 @t111))) % 1.74/1.93 (define @t120 () (@purify @t119)) % 1.74/1.93 (define @t121 () (@purify @t112)) % 1.74/1.93 (define @t122 () (= @t112 @t119)) % 1.74/1.93 (define @t123 () (not @t122)) % 1.74/1.93 (define @t124 () (lambda @t34 (= @t111 @t33))) % 1.74/1.93 (define @t125 () (= @t124 @t112)) % 1.74/1.93 (define @t126 () (not @t125)) % 1.74/1.93 (define @t127 () (= @t121 @t120)) % 1.74/1.93 (define @t128 () (@const 0 tptp.a)) % 1.74/1.93 (define @t129 () (= @t111 @t128)) % 1.74/1.93 (define @t130 () (_ @t72 @t128)) % 1.74/1.93 (define @t131 () (and @t130 @t129)) % 1.74/1.93 (define @t132 () (= @t128 @t111)) % 1.74/1.93 (define @t133 () (_ @t119 @t128)) % 1.74/1.93 (define @t134 () (_ @t120 @t128)) % 1.74/1.93 (define @t135 () (and @t130 @t132)) % 1.74/1.93 (define @t136 () (_ @t112 @t128)) % 1.74/1.93 (define @t137 () (_ @t121 @t128)) % 1.74/1.93 (define @t138 () (= @t137 @t134)) % 1.74/1.93 (define @t139 () (not @t138)) % 1.74/1.93 (define @t140 () (or @t127 @t139)) % 1.74/1.93 (define @t141 () (= @t129 @t131)) % 1.74/1.93 (define @t142 () (not @t129)) % 1.74/1.93 (define @t143 () (and @t115 @t129)) % 1.74/1.93 (define @t144 () (not @t131)) % 1.74/1.93 (assume @p1 @t28) % 1.74/1.93 (assume @p2 true) % 1.74/1.93 (step @p3 :rule bool-and-de-morgan :args (@t32 @t40 true)) % 1.74/1.93 (step @p4 :rule cong :premises (@p3) :args (@t42)) % 1.74/1.93 (step @p5 :rule cong :premises (@p4) :args (@t43)) % 1.74/1.93 (step @p6 :rule exists-elim :args ((= (exists @t24 @t41) @t43))) % 1.74/1.93 (step @p7 :rule trans :premises (@p6 @p5)) % 1.74/1.93 (step @p8 :rule refl :args (@t38)) % 1.74/1.93 (step @p9 :rule refl :args (@t39)) % 1.74/1.93 (step @p10 :rule refl :args (@t17)) % 1.74/1.93 (step @p11 :rule cong :premises (@p10 @p9) :args ((= @t17 @t39))) % 1.74/1.93 (step @p12 :rule symm :premises (@p11)) % 1.74/1.93 (step @p13 :rule eq_resolve :premises (@p10 @p12)) % 1.74/1.93 (step @p14 :rule cong :premises (@p13) :args (@t44)) % 1.74/1.93 (step @p15 :rule nary_cong :premises (@p14 @p8) :args (@t45)) % 1.74/1.93 (step @p16 :rule cong :premises (@p15) :args ((forall @t19 @t45))) % 1.74/1.93 (step @p17 :rule bool-impl-elim :args (@t17 @t38)) % 1.74/1.93 (step @p18 :rule cong :premises (@p17) :args ((forall @t19 (=> @t17 @t38)))) % 1.74/1.93 (step @p19 :rule trans :premises (@p18 @p16)) % 1.74/1.93 (step @p20 :rule eq-symm :args (@t35 @t37)) % 1.74/1.93 (step @p21 :rule refl :args (@t37)) % 1.74/1.93 (step @p22 :rule eq-symm :args (@t33 @t1)) % 1.74/1.93 (step @p23 :rule cong :premises (@p22) :args (@t46)) % 1.74/1.93 (step @p24 :rule cong :premises (@p23 @p21) :args (@t47)) % 1.74/1.93 (step @p25 :rule trans :premises (@p24 @p20)) % 1.74/1.93 (step @p26 :rule cong :premises (@p25) :args (@t48)) % 1.74/1.93 (step @p27 :rule cong :premises (@p26) :args (@t49)) % 1.74/1.93 (step @p28 :rule cong :premises (@p27) :args (@t50)) % 1.74/1.93 (step @p29 :rule refl :args (@t17)) % 1.74/1.93 (step @p30 :rule cong :premises (@p29 @p28) :args (@t51)) % 1.74/1.93 (step @p31 :rule cong :premises (@p30) :args ((forall @t19 @t51))) % 1.74/1.93 (step @p32 :rule trans :premises (@p31 @p19)) % 1.74/1.93 (step @p33 :rule refl :args (@t37)) % 1.74/1.93 (step @p34 :rule alpha_equiv :args (@t52 (@list @t2) (@list @t33))) % 1.74/1.93 (step @p35 :rule cong :premises (@p34 @p33) :args (@t53)) % 1.74/1.93 (step @p36 :rule cong :premises (@p35) :args (@t54)) % 1.74/1.93 (step @p37 :rule cong :premises (@p36) :args (@t55)) % 1.74/1.93 (step @p38 :rule cong :premises (@p37) :args (@t56)) % 1.74/1.93 (step @p39 :rule cong :premises (@p10 @p38) :args (@t57)) % 1.74/1.93 (step @p40 :rule cong :premises (@p39) :args ((forall @t19 @t57))) % 1.74/1.93 (step @p41 :rule trans :premises (@p40 @p32)) % 1.74/1.93 (step @p42 :rule eq-symm :args (@t37 @t52)) % 1.74/1.93 (step @p43 :rule refl :args (@t52)) % 1.74/1.93 (step @p44 :rule eq-symm :args (@t29 @t2)) % 1.74/1.93 (step @p45 :rule refl :args (@t31)) % 1.74/1.93 (step @p46 :rule nary_cong :premises (@p45 @p44) :args (@t58)) % 1.74/1.93 (step @p47 :rule cong :premises (@p46) :args (@t59)) % 1.74/1.93 (step @p48 :rule cong :premises (@p47 @p43) :args (@t60)) % 1.74/1.93 (step @p49 :rule trans :premises (@p48 @p42)) % 1.74/1.93 (step @p50 :rule cong :premises (@p49) :args (@t61)) % 1.74/1.93 (step @p51 :rule cong :premises (@p50) :args ((forall @t15 @t61))) % 1.74/1.93 (step @p52 :rule refl :args (@t52)) % 1.74/1.93 (step @p53 :rule refl :args (@t2)) % 1.74/1.93 (step @p54 :rule refl :args (@t29)) % 1.74/1.93 (step @p55 :rule refl :args (@t8)) % 1.74/1.93 (step @p56 :rule cong :premises (@p55 @p54) :args ((= @t8 @t29))) % 1.74/1.93 (step @p57 :rule symm :premises (@p56)) % 1.74/1.93 (step @p58 :rule eq_resolve :premises (@p55 @p57)) % 1.74/1.93 (step @p59 :rule cong :premises (@p58 @p53) :args (@t62)) % 1.74/1.93 (step @p60 :rule refl :args (@t31)) % 1.74/1.93 (step @p61 :rule refl :args (@t10)) % 1.74/1.93 (step @p62 :rule cong :premises (@p61 @p60) :args ((= @t10 @t31))) % 1.74/1.93 (step @p63 :rule symm :premises (@p62)) % 1.74/1.93 (step @p64 :rule eq_resolve :premises (@p61 @p63)) % 1.74/1.93 (step @p65 :rule nary_cong :premises (@p64 @p59) :args (@t63)) % 1.74/1.93 (step @p66 :rule cong :premises (@p65) :args (@t64)) % 1.74/1.93 (step @p67 :rule cong :premises (@p66 @p52) :args (@t65)) % 1.74/1.93 (step @p68 :rule cong :premises (@p67) :args (@t66)) % 1.74/1.93 (step @p69 :rule cong :premises (@p68) :args (@t67)) % 1.74/1.93 (step @p70 :rule trans :premises (@p69 @p51)) % 1.74/1.93 (step @p71 :rule cong :premises (@p70) :args (@t68)) % 1.74/1.93 (step @p72 :rule exists-elim :args ((= (exists @t15 @t65) @t68))) % 1.74/1.93 (step @p73 :rule trans :premises (@p72 @p71)) % 1.74/1.93 (step @p74 :rule beta-reduce :args ((= (_ (lambda @t4 (= @t2 @t3)) @t1) @t52))) % 1.74/1.93 (step @p75 :rule refl :args (@t1)) % 1.74/1.93 (step @p76 :rule eq-symm :args (@t3 @t2)) % 1.74/1.93 (step @p77 :rule cong :premises (@p76) :args (@t5)) % 1.74/1.93 (step @p78 :rule ho_cong :premises (@p77 @p75)) % 1.74/1.93 (step @p79 :rule trans :premises (@p78 @p74)) % 1.74/1.93 (step @p80 :rule eq-symm :args (@t2 @t8)) % 1.74/1.93 (step @p81 :rule refl :args (@t10)) % 1.74/1.93 (step @p82 :rule nary_cong :premises (@p81 @p80) :args (@t11)) % 1.74/1.93 (step @p83 :rule cong :premises (@p82) :args (@t13)) % 1.74/1.93 (step @p84 :rule cong :premises (@p83 @p79) :args (@t14)) % 1.74/1.93 (step @p85 :rule cong :premises (@p84) :args (@t16)) % 1.74/1.93 (step @p86 :rule trans :premises (@p85 @p73)) % 1.74/1.93 (step @p87 :rule cong :premises (@p29 @p86) :args (@t18)) % 1.74/1.93 (step @p88 :rule cong :premises (@p87) :args (@t20)) % 1.74/1.93 (step @p89 :rule trans :premises (@p88 @p41)) % 1.74/1.93 (step @p90 :rule refl :args ((_ @t9 @t8))) % 1.74/1.93 (step @p91 :rule cong :premises (@p54) :args (@t30)) % 1.74/1.93 (step @p92 :rule trans :premises (@p91 @p90)) % 1.74/1.93 (step @p93 :rule refl :args (@t9)) % 1.74/1.93 (step @p94 :rule ho_cong :premises (@p93 @p54)) % 1.74/1.93 (step @p95 :rule cong :premises (@p94 @p92) :args ((= (_ @t9 @t29) @t30))) % 1.74/1.93 (step @p96 :rule symm :premises (@p95)) % 1.74/1.93 (step @p97 :rule refl :args (@t21)) % 1.74/1.93 (step @p98 :rule eq_resolve :premises (@p97 @p96)) % 1.74/1.93 (step @p99 :rule ho_cong :premises (@p93 @p58)) % 1.74/1.93 (step @p100 :rule trans :premises (@p99 @p98)) % 1.74/1.93 (step @p101 :rule cong :premises (@p64) :args (@t69)) % 1.74/1.93 (step @p102 :rule nary_cong :premises (@p101 @p100) :args (@t70)) % 1.74/1.93 (step @p103 :rule cong :premises (@p102) :args ((forall @t12 @t70))) % 1.74/1.93 (step @p104 :rule bool-impl-elim :args (@t10 @t21)) % 1.74/1.93 (step @p105 :rule cong :premises (@p104) :args (@t22)) % 1.74/1.93 (step @p106 :rule trans :premises (@p105 @p103)) % 1.74/1.93 (step @p107 :rule nary_cong :premises (@p106 @p89) :args (@t23)) % 1.74/1.93 (step @p108 :rule cong :premises (@p107) :args (@t25)) % 1.74/1.93 (step @p109 :rule trans :premises (@p108 @p7)) % 1.74/1.93 (step @p110 :rule cong :premises (@p109) :args (@t27)) % 1.74/1.93 (step @p111 :rule cong :premises (@p110) :args (@t28)) % 1.74/1.93 (step @p112 :rule eq_resolve :premises (@p1 @p111)) % 1.74/1.93 (step @p113 :rule refl :args (@t78)) % 1.74/1.93 (step @p114 :rule bool-double-not-elim :args (@t71)) % 1.74/1.93 (step @p115 :rule nary_cong :premises (@p114 @p113) :args ((or (not @t79) @t78))) % 1.74/1.93 (step @p116 :rule eq-symm :args (@t74 @t35)) % 1.74/1.93 (step @p117 :rule cong :premises (@p116) :args (@t80)) % 1.74/1.93 (step @p118 :rule cong :premises (@p117) :args (@t81)) % 1.74/1.93 (step @p119 :rule cong :premises (@p118) :args (@t82)) % 1.74/1.93 (step @p120 :rule refl :args (@t75)) % 1.74/1.93 (step @p121 :rule nary_cong :premises (@p120 @p119) :args (@t83)) % 1.74/1.93 (step @p122 :rule cong :premises (@p121) :args (@t84)) % 1.74/1.93 (step @p123 :rule cong :premises (@p122) :args (@t85)) % 1.74/1.93 (step @p124 :rule refl :args (@t77)) % 1.74/1.93 (step @p125 :rule nary_cong :premises (@p124 @p123) :args (@t86)) % 1.74/1.93 (step @p126 :rule cong :premises (@p125) :args (@t87)) % 1.74/1.93 (step @p127 :rule bool-double-not-elim :args (@t87)) % 1.74/1.93 (step @p128 :rule trans :premises (@p127 @p126)) % 1.74/1.93 (step @p129 :rule refl :args (@t79)) % 1.74/1.93 (step @p130 :rule cong :premises (@p129 @p128) :args ((=> @t79 @t88))) % 1.74/1.93 (assume-push @p291 @t79) % 1.74/1.93 (step @p132 :rule skolemize :premises (@p112)) % 1.74/1.93 (step-pop @p292 :rule scope :premises (@p132)) % 1.74/1.93 (step @p133 :rule process_scope :premises (@p292) :args (@t88)) % 1.74/1.93 (step @p135 :rule eq_resolve :premises (@p133 @p130)) % 1.74/1.93 (step @p136 :rule implies_elim :premises (@p135)) % 1.74/1.93 (step @p137 :rule eq_resolve :premises (@p136 @p115)) % 1.74/1.93 (step @p138 :rule chain_m_resolution :premises (@p137 @p112) :args (@t78 @t89 (@list @t71))) % 1.74/1.93 (step @p139 :rule aci_norm :args ((= (or false @t91) @t91))) % 1.74/1.93 (step @p140 :rule eq-symm :args (@t2 @t6)) % 1.74/1.93 (step @p141 :rule beta-reduce :args ((= @t94 @t6))) % 1.74/1.93 (step @p142 :rule refl :args (@t2)) % 1.74/1.93 (step @p143 :rule cong :premises (@p142 @p141) :args (@t95)) % 1.74/1.93 (step @p144 :rule trans :premises (@p143 @p140)) % 1.74/1.93 (step @p145 :rule refl :args (@t73)) % 1.74/1.93 (step @p146 :rule nary_cong :premises (@p145 @p144) :args (@t96)) % 1.74/1.93 (step @p147 :rule cong :premises (@p146) :args (@t97)) % 1.74/1.93 (step @p148 :rule refl :args (@t35)) % 1.74/1.93 (step @p149 :rule cong :premises (@p148 @p147) :args (@t98)) % 1.74/1.93 (step @p150 :rule cong :premises (@p149) :args (@t99)) % 1.74/1.93 (step @p151 :rule cong :premises (@p150) :args (@t100)) % 1.74/1.93 (step @p152 :rule cong :premises (@p151) :args (@t101)) % 1.74/1.93 (step @p153 :rule nary_cong :premises (@p120 @p152) :args (@t102)) % 1.74/1.93 (step @p154 :rule cong :premises (@p153) :args (@t103)) % 1.74/1.93 (step @p155 :rule cong :premises (@p154) :args (@t104)) % 1.74/1.93 (step @p156 :rule evaluate :args ((not true))) % 1.74/1.93 (step @p157 :rule quant-unused-vars :args ((= (forall @t12 true) true))) % 1.74/1.93 (step @p158 :rule bool-or-taut2 :args (false @t73 false false)) % 1.74/1.93 (step @p159 :rule cong :premises (@p158) :args ((forall @t12 (or @t76 @t73)))) % 1.74/1.93 (step @p160 :rule trans :premises (@p159 @p157)) % 1.74/1.93 (step @p161 :rule cong :premises (@p141) :args (@t105)) % 1.74/1.93 (step @p162 :rule refl :args (@t76)) % 1.74/1.93 (step @p163 :rule nary_cong :premises (@p162 @p161) :args (@t106)) % 1.74/1.93 (step @p164 :rule cong :premises (@p163) :args (@t107)) % 1.74/1.93 (step @p165 :rule trans :premises (@p164 @p160)) % 1.74/1.93 (step @p166 :rule cong :premises (@p165) :args (@t108)) % 1.74/1.93 (step @p167 :rule trans :premises (@p166 @p156)) % 1.74/1.93 (step @p168 :rule nary_cong :premises (@p167 @p155) :args (@t109)) % 1.74/1.93 (step @p169 :rule trans :premises (@p168 @p139)) % 1.74/1.93 (step @p170 :rule cong :premises (@p113 @p169) :args ((=> @t78 @t109))) % 1.74/1.93 (assume-push @p293 @t78) % 1.74/1.93 (step @p172 :rule instantiate :premises (@p138) :args ((@list @t93))) % 1.74/1.93 (step-pop @p294 :rule scope :premises (@p172)) % 1.74/1.93 (step @p173 :rule process_scope :premises (@p294) :args (@t109)) % 1.74/1.93 (step @p175 :rule eq_resolve :premises (@p173 @p170)) % 1.74/1.93 (step @p176 :rule implies_elim :premises (@p175)) % 1.74/1.93 (step @p177 :rule chain_m_resolution :premises (@p176 @p138) :args (@t91 @t110 (@list @t78))) % 1.74/1.93 (step @p178 :rule skolemize :premises (@p177)) % 1.74/1.93 (step @p179 :rule bool-double-not-elim :args (@t113)) % 1.74/1.93 (step @p180 :rule refl :args (@t117)) % 1.74/1.93 (step @p181 :rule nary_cong :premises (@p180 @p179) :args ((or @t117 (not @t114)))) % 1.74/1.93 (step @p182 :rule cnf_or_neg :args (@t117 1)) % 1.74/1.93 (step @p183 :rule eq_resolve :premises (@p182 @p181)) % 1.74/1.93 (step @p184 :rule reordering :premises (@p183) :args ((or @t113 @t117))) % 1.74/1.93 (step @p185 :rule chain_m_resolution :premises (@p184 @p178) :args (@t113 @t89 @t118)) % 1.74/1.93 (step @p186 :rule eq-refl :args (@t119)) % 1.74/1.93 (step @p187 :rule skolem_intro :args (@t120)) % 1.74/1.93 (step @p188 :rule refl :args (@t119)) % 1.74/1.93 (step @p189 :rule cong :premises (@p188 @p187) :args ((= @t119 @t120))) % 1.74/1.93 (step @p190 :rule trans :premises (@p189 @p186)) % 1.74/1.93 (step @p191 :rule true_elim :premises (@p190)) % 1.74/1.93 (step @p192 :rule eq-refl :args (@t112)) % 1.74/1.93 (step @p193 :rule skolem_intro :args (@t121)) % 1.74/1.93 (step @p194 :rule refl :args (@t112)) % 1.74/1.93 (step @p195 :rule cong :premises (@p194 @p193) :args ((= @t112 @t121))) % 1.74/1.93 (step @p196 :rule trans :premises (@p195 @p192)) % 1.74/1.93 (step @p197 :rule true_elim :premises (@p196)) % 1.74/1.93 (step @p198 :rule cong :premises (@p197 @p191) :args (@t122)) % 1.74/1.93 (step @p199 :rule cong :premises (@p198) :args (@t123)) % 1.74/1.93 (step @p200 :rule refl :args (@t113)) % 1.74/1.93 (step @p201 :rule cong :premises (@p200 @p199) :args ((=> @t113 @t123))) % 1.74/1.93 (step @p202 :rule eq-symm :args (@t119 @t112)) % 1.74/1.93 (step @p203 :rule eq-symm :args (@t111 @t33)) % 1.74/1.93 (step @p204 :rule cong :premises (@p203) :args (@t124)) % 1.74/1.93 (step @p205 :rule cong :premises (@p204 @p194) :args (@t125)) % 1.74/1.93 (step @p206 :rule trans :premises (@p205 @p202)) % 1.74/1.93 (step @p207 :rule cong :premises (@p206) :args (@t126)) % 1.74/1.93 (step @p208 :rule cong :premises (@p200 @p207) :args ((=> @t113 @t126))) % 1.74/1.93 (assume-push @p295 @t113) % 1.74/1.93 (step @p210 :rule instantiate :premises (@p185) :args ((@list @t111))) % 1.74/1.93 (step-pop @p296 :rule scope :premises (@p210)) % 1.74/1.93 (step @p211 :rule process_scope :premises (@p296) :args (@t126)) % 1.74/1.93 (step @p213 :rule eq_resolve :premises (@p211 @p208)) % 1.74/1.93 (step @p214 :rule eq_resolve :premises (@p213 @p201)) % 1.74/1.93 (step @p215 :rule implies_elim :premises (@p214)) % 1.74/1.93 (step @p216 :rule chain_m_resolution :premises (@p215 @p185) :args ((not @t127) @t110 (@list @t113))) % 1.74/1.93 (step @p217 :rule eq-symm :args (@t131 @t129)) % 1.74/1.93 (step @p218 :rule eq-refl :args (@t129)) % 1.74/1.93 (step @p219 :rule eq-symm :args (@t128 @t111)) % 1.74/1.93 (step @p220 :rule beta-reduce :args ((= @t133 @t132))) % 1.74/1.93 (step @p221 :rule trans :premises (@p220 @p219)) % 1.74/1.93 (step @p222 :rule refl :args (@t129)) % 1.74/1.93 (step @p223 :rule cong :premises (@p222 @p221) :args ((= @t129 @t133))) % 1.74/1.93 (step @p224 :rule trans :premises (@p223 @p218)) % 1.74/1.93 (step @p225 :rule eq-symm :args (@t133 @t129)) % 1.74/1.93 (step @p226 :rule trans :premises (@p225 @p224)) % 1.74/1.93 (step @p227 :rule refl :args (@t128)) % 1.74/1.93 (step @p228 :rule ho_cong :premises (@p187 @p227)) % 1.74/1.93 (step @p229 :rule cong :premises (@p228 @p222) :args ((= @t134 @t129))) % 1.74/1.93 (step @p230 :rule trans :premises (@p229 @p226)) % 1.74/1.93 (step @p231 :rule true_elim :premises (@p230)) % 1.74/1.93 (step @p232 :rule eq-refl :args (@t131)) % 1.74/1.93 (step @p233 :rule refl :args (@t130)) % 1.74/1.93 (step @p234 :rule nary_cong :premises (@p233 @p219) :args (@t135)) % 1.74/1.93 (step @p235 :rule beta-reduce :args ((= @t136 @t135))) % 1.74/1.93 (step @p236 :rule trans :premises (@p235 @p234)) % 1.74/1.93 (step @p237 :rule refl :args (@t131)) % 1.74/1.93 (step @p238 :rule cong :premises (@p237 @p236) :args ((= @t131 @t136))) % 1.74/1.93 (step @p239 :rule trans :premises (@p238 @p232)) % 1.74/1.93 (step @p240 :rule eq-symm :args (@t136 @t131)) % 1.74/1.93 (step @p241 :rule trans :premises (@p240 @p239)) % 1.74/1.93 (step @p242 :rule ho_cong :premises (@p193 @p227)) % 1.74/1.93 (step @p243 :rule cong :premises (@p242 @p237) :args ((= @t137 @t131))) % 1.74/1.93 (step @p244 :rule trans :premises (@p243 @p241)) % 1.74/1.93 (step @p245 :rule true_elim :premises (@p244)) % 1.74/1.93 (step @p246 :rule cong :premises (@p245 @p231) :args (@t138)) % 1.74/1.93 (step @p247 :rule trans :premises (@p246 @p217)) % 1.74/1.93 (step @p248 :rule cong :premises (@p247) :args (@t139)) % 1.74/1.93 (step @p249 :rule refl :args (@t127)) % 1.74/1.93 (step @p250 :rule nary_cong :premises (@p249 @p248) :args (@t140)) % 1.74/1.93 ; WARNING: add trust step for TRUST % 1.74/1.93 ; trust TRUST THEORY_LEMMA % 1.74/1.93 (step @p251 :rule trust :premises () :args (@t140)) % 1.74/1.93 (step @p252 :rule eq_resolve :premises (@p251 @p250)) % 1.74/1.93 (step @p253 :rule chain_m_resolution :premises (@p252 @p216) :args ((not @t141) @t89 (@list @t127))) % 1.74/1.93 (step @p254 :rule cnf_equiv_neg2 :args (@t141)) % 1.74/1.93 (step @p255 :rule cnf_and_neg :args (@t131)) % 1.74/1.93 (step @p256 :rule reordering :premises (@p255) :args ((or @t131 @t142 (not @t130)))) % 1.74/1.93 (step @p257 :rule bool-double-not-elim :args (@t115)) % 1.74/1.93 (step @p258 :rule nary_cong :premises (@p180 @p257) :args ((or @t117 (not @t116)))) % 1.74/1.93 (step @p259 :rule cnf_or_neg :args (@t117 0)) % 1.74/1.93 (step @p260 :rule eq_resolve :premises (@p259 @p258)) % 1.74/1.93 (step @p261 :rule reordering :premises (@p260) :args ((or @t115 @t117))) % 1.74/1.93 (step @p262 :rule chain_m_resolution :premises (@p261 @p178) :args (@t115 @t89 @t118)) % 1.74/1.93 (assume-push @p297 @t115) % 1.74/1.93 (assume-push @p298 @t129) % 1.74/1.93 (assume-push @p299 @t115) % 1.74/1.93 (assume-push @p300 @t129) % 1.74/1.93 (step @p267 :rule true_intro :premises (@p262)) % 1.74/1.93 (step @p268 :rule symm :premises (@p298)) % 1.74/1.93 (step @p269 :rule cong :premises (@p268) :args (@t130)) % 1.74/1.93 (step @p270 :rule trans :premises (@p269 @p267)) % 1.74/1.93 (step @p271 :rule true_elim :premises (@p270)) % 1.74/1.93 (step-pop @p301 :rule scope :premises (@p271)) % 1.74/1.93 (step-pop @p302 :rule scope :premises (@p301)) % 1.74/1.93 (step @p272 :rule process_scope :premises (@p302) :args (@t130)) % 1.74/1.93 (step @p275 :rule and_intro :premises (@p262 @p298)) % 1.74/1.93 (step @p276 :rule modus_ponens :premises (@p275 @p272)) % 1.74/1.93 (step-pop @p303 :rule scope :premises (@p276)) % 1.74/1.93 (step-pop @p304 :rule scope :premises (@p303)) % 1.74/1.93 (step @p277 :rule process_scope :premises (@p304) :args (@t130)) % 1.74/1.93 (step @p280 :rule implies_elim :premises (@p277)) % 1.74/1.93 (step @p281 :rule cnf_and_neg :args (@t143)) % 1.74/1.93 (step @p282 :rule resolution :premises (@p281 @p280) :args (true @t143)) % 1.74/1.93 (step @p283 :rule reordering :premises (@p282) :args ((or @t116 @t130 @t142))) % 1.74/1.93 (step @p284 :rule chain_m_resolution :premises (@p283 @p262 @p256 @p254 @p253) :args (@t142 (@list false true true true) (@list @t115 @t130 @t131 @t141))) % 1.74/1.93 (step @p285 :rule cnf_and_pos :args (@t131 1)) % 1.74/1.93 (step @p286 :rule reordering :premises (@p285) :args ((or @t129 @t144))) % 1.74/1.93 (step @p287 :rule chain_m_resolution :premises (@p286 @p284) :args (@t144 @t89 (@list @t129))) % 1.74/1.93 (step @p288 :rule cnf_equiv_neg1 :args (@t141)) % 1.74/1.93 (step @p289 :rule reordering :premises (@p288) :args ((or @t129 @t131 @t141))) % 1.74/1.93 (step @p290 false :rule chain_m_resolution :premises (@p289 @p287 @p284 @p253) :args (false (@list true true true) (@list @t131 @t129 @t141))) % 1.74/1.93 ) % 1.74/1.93 % SZS output end Proof % 1.74/1.93 % cvc5 exiting %------------------------------------------------------------------------------