%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU894^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n028.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 08:53:29 AM UTC 2026 % Result : Theorem 2.72s 2.91s % Output : Proof 2.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU894^5 : TPTP v9.2.1. Released v4.0.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n028.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 17:58:05 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.48 %----Proving TH0 % 2.72/2.91 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 2.72/2.91 % SZS status Theorem % 2.72/2.91 % SZS output start Proof % 2.72/2.91 ( % 2.72/2.91 (declare-sort $$unsorted 0) % 2.72/2.91 (define @t1 () (@var "Y" $$unsorted)) % 2.72/2.91 (define @t2 () (@var "F" (-> $$unsorted $$unsorted))) % 2.72/2.91 (define @t3 () (_ @t2 @t1)) % 2.72/2.91 (define @t4 () (@list @t1)) % 2.72/2.91 (define @t5 () (exists @t4 (= @t3 @t1))) % 2.72/2.91 (define @t6 () (@var "X" $$unsorted)) % 2.72/2.91 (define @t7 () (= @t6 @t1)) % 2.72/2.91 (define @t8 () (@var "G" (-> $$unsorted $$unsorted))) % 2.72/2.91 (define @t9 () (_ @t8 @t1)) % 2.72/2.91 (define @t10 () (=> (= @t9 @t1) @t7)) % 2.72/2.91 (define @t11 () (forall @t4 @t10)) % 2.72/2.91 (define @t12 () (_ @t8 @t6)) % 2.72/2.91 (define @t13 () (and (= @t12 @t6) @t11)) % 2.72/2.91 (define @t14 () (@list @t6)) % 2.72/2.91 (define @t15 () (exists @t14 @t13)) % 2.72/2.91 (define @t16 () (@var "P" (-> (-> $$unsorted $$unsorted) Bool))) % 2.72/2.91 (define @t17 () (_ @t16 @t8)) % 2.72/2.91 (define @t18 () (@var "T" $$unsorted)) % 2.72/2.91 (define @t19 () (@var "H" (-> $$unsorted $$unsorted))) % 2.72/2.91 (define @t20 () (_ @t19 @t18)) % 2.72/2.91 (define @t21 () (_ @t2 @t20)) % 2.72/2.91 (define @t22 () (@list @t18)) % 2.72/2.91 (define @t23 () (lambda @t22 @t21)) % 2.72/2.91 (define @t24 () (_ @t16 @t23)) % 2.72/2.91 (define @t25 () (_ @t16 @t19)) % 2.72/2.91 (define @t26 () (@list @t19)) % 2.72/2.91 (define @t27 () (forall @t26 (=> @t25 @t24))) % 2.72/2.91 (define @t28 () (_ @t16 @t2)) % 2.72/2.91 (define @t29 () (and @t28 @t27)) % 2.72/2.91 (define @t30 () (=> @t29 @t17)) % 2.72/2.91 (define @t31 () (@list @t16)) % 2.72/2.91 (define @t32 () (forall @t31 @t30)) % 2.72/2.91 (define @t33 () (and @t32 @t15)) % 2.72/2.91 (define @t34 () (=> @t33 @t5)) % 2.72/2.91 (define @t35 () (@list @t8)) % 2.72/2.91 (define @t36 () (exists @t35 @t34)) % 2.72/2.91 (define @t37 () (@list @t2)) % 2.72/2.91 (define @t38 () (forall @t37 @t36)) % 2.72/2.91 (define @t39 () (not @t38)) % 2.72/2.91 (define @t40 () (_ @t2 @t1)) % 2.72/2.91 (define @t41 () (forall @t4 (not (= @t1 @t40)))) % 2.72/2.91 (define @t42 () (not @t41)) % 2.72/2.91 (define @t43 () (@var "BOUND_VARIABLE_7523" (-> $$unsorted $$unsorted))) % 2.72/2.91 (define @t44 () (_ @t16 @t43)) % 2.72/2.91 (define @t45 () (_ @t19 @t18)) % 2.72/2.91 (define @t46 () (_ @t2 @t45)) % 2.72/2.91 (define @t47 () (lambda @t22 @t46)) % 2.72/2.91 (define @t48 () (_ @t16 @t47)) % 2.72/2.91 (define @t49 () (_ @t16 @t19)) % 2.72/2.91 (define @t50 () (not @t49)) % 2.72/2.91 (define @t51 () (forall @t26 (or @t50 @t48))) % 2.72/2.91 (define @t52 () (not @t51)) % 2.72/2.91 (define @t53 () (_ @t16 @t2)) % 2.72/2.91 (define @t54 () (not @t53)) % 2.72/2.91 (define @t55 () (or @t54 @t52 @t44)) % 2.72/2.91 (define @t56 () (@list @t43 @t16)) % 2.72/2.91 (define @t57 () (forall @t56 @t55)) % 2.72/2.91 (define @t58 () (not @t57)) % 2.72/2.91 (define @t59 () (or @t58 @t42)) % 2.72/2.91 (define @t60 () (forall @t37 @t59)) % 2.72/2.91 (define @t61 () (@var "BOUND_VARIABLE_7530" (-> $$unsorted $$unsorted))) % 2.72/2.91 (define @t62 () (forall (@list @t61) (not (forall @t14 (or (not (= @t6 (_ @t61 @t6))) (not (forall @t4 (or (not (= @t1 (_ @t61 @t1))) @t7)))))))) % 2.72/2.91 (define @t63 () (not @t62)) % 2.72/2.91 (define @t64 () (or @t63 @t59)) % 2.72/2.91 (define @t65 () (or @t58 @t63 @t42)) % 2.72/2.91 (define @t66 () (forall (@list @t43) (forall @t31 @t55))) % 2.72/2.91 (define @t67 () (forall @t35 @t41)) % 2.72/2.91 (define @t68 () (_ @t8 @t1)) % 2.72/2.91 (define @t69 () (forall @t4 (or (not (= @t1 @t68)) @t7))) % 2.72/2.91 (define @t70 () (not @t69)) % 2.72/2.91 (define @t71 () (_ @t8 @t6)) % 2.72/2.91 (define @t72 () (not (forall @t14 (or (not (= @t6 @t71)) @t70)))) % 2.72/2.91 (define @t73 () (forall @t35 @t72)) % 2.72/2.91 (define @t74 () (@list @t8)) % 2.72/2.91 (define @t75 () (_ @t16 @t8)) % 2.72/2.91 (define @t76 () (forall @t31 (or @t54 @t52 @t75))) % 2.72/2.91 (define @t77 () (forall @t35 @t76)) % 2.72/2.91 (define @t78 () (and @t77 @t73 @t67)) % 2.72/2.91 (define @t79 () (and @t76 @t72 @t41)) % 2.72/2.91 (define @t80 () (and @t76 @t72)) % 2.72/2.91 (define @t81 () (=> @t80 @t42)) % 2.72/2.91 (define @t82 () (forall @t35 (not @t81))) % 2.72/2.91 (define @t83 () (not @t82)) % 2.72/2.91 (define @t84 () (= @t1 @t3)) % 2.72/2.91 (define @t85 () (not @t84)) % 2.72/2.91 (define @t86 () (forall @t4 @t85)) % 2.72/2.91 (define @t87 () (not @t86)) % 2.72/2.91 (define @t88 () (= @t6 @t12)) % 2.72/2.91 (define @t89 () (not @t88)) % 2.72/2.91 (define @t90 () (or @t89 @t70)) % 2.72/2.91 (define @t91 () (and @t88 @t69)) % 2.72/2.91 (define @t92 () (forall @t14 (not @t91))) % 2.72/2.91 (define @t93 () (not @t92)) % 2.72/2.91 (define @t94 () (= @t1 @t9)) % 2.72/2.91 (define @t95 () (not @t94)) % 2.72/2.91 (define @t96 () (or @t95 @t7)) % 2.72/2.91 (define @t97 () (not @t28)) % 2.72/2.91 (define @t98 () (or @t97 @t52 @t17)) % 2.72/2.91 (define @t99 () (and @t28 @t51)) % 2.72/2.91 (define @t100 () (not @t25)) % 2.72/2.91 (define @t101 () (or @t100 @t24)) % 2.72/2.91 (define @t102 () (not (forall @t4 @t7))) % 2.72/2.91 (define @t103 () (@var "BOUND_VARIABLE_28857" $$unsorted)) % 2.72/2.91 (define @t104 () (lambda (@list @t103) @t103)) % 2.72/2.91 (define @t105 () (_ @t104 @t1)) % 2.72/2.91 (define @t106 () (= @t1 @t105)) % 2.72/2.91 (define @t107 () (not @t106)) % 2.72/2.91 (define @t108 () (or @t107 @t7)) % 2.72/2.91 (define @t109 () (forall @t4 @t108)) % 2.72/2.91 (define @t110 () (not @t109)) % 2.72/2.91 (define @t111 () (_ @t104 @t6)) % 2.72/2.91 (define @t112 () (= @t6 @t111)) % 2.72/2.91 (define @t113 () (not @t112)) % 2.72/2.91 (define @t114 () (or @t113 @t110)) % 2.72/2.91 (define @t115 () (forall @t14 @t114)) % 2.72/2.91 (define @t116 () (not @t115)) % 2.72/2.91 (define @t117 () (forall @t14 @t102)) % 2.72/2.91 (define @t118 () (not @t117)) % 2.72/2.91 (define @t119 () (@list false)) % 2.72/2.91 (define @t120 () (@quantifiers_skolemize @t117 0)) % 2.72/2.91 (define @t121 () (forall @t4 (= @t1 @t120))) % 2.72/2.91 (define @t122 () (forall @t4 (= @t120 @t1))) % 2.72/2.91 (define @t123 () (not (not @t122))) % 2.72/2.91 (define @t124 () (@list true)) % 2.72/2.91 (define @t125 () (@const 0 $$unsorted)) % 2.72/2.91 (define @t126 () (@quantifiers_skolemize @t60 0)) % 2.72/2.91 (define @t127 () (_ @t126 @t125)) % 2.72/2.91 (define @t128 () (= @t127 @t120)) % 2.72/2.91 (define @t129 () (@list @t125)) % 2.72/2.91 (define @t130 () (forall @t4 (not (= @t1 (_ @t126 @t1))))) % 2.72/2.91 (define @t131 () (not @t130)) % 2.72/2.91 (define @t132 () (or (not (forall @t56 (or (not (_ @t16 @t126)) (not (forall @t26 (or @t50 (_ @t16 (lambda @t22 (_ @t126 @t45)))))) @t44))) @t131)) % 2.72/2.91 (assume @p1 @t39) % 2.72/2.91 (assume @p2 true) % 2.72/2.91 (step @p3 :rule evaluate :args ((= false true))) % 2.72/2.91 (step @p4 :rule quant-miniscope-or :args ((= (forall @t37 @t64) (or @t63 @t60)))) % 2.72/2.91 (step @p5 :rule aci_norm :args ((= @t65 @t64))) % 2.72/2.91 (step @p6 :rule cong :premises (@p5) :args ((forall @t37 @t65))) % 2.72/2.91 (step @p7 :rule trans :premises (@p6 @p4)) % 2.72/2.91 (step @p8 :rule aci_norm :args ((= (or @t58 (or @t63 @t42)) @t65))) % 2.72/2.91 (step @p9 :rule bool-and-de-morgan :args (@t62 @t41 true)) % 2.72/2.91 (step @p10 :rule refl :args (@t58)) % 2.72/2.91 (step @p11 :rule nary_cong :premises (@p10 @p9) :args ((or @t58 (not (and @t62 @t41))))) % 2.72/2.91 (step @p12 :rule bool-and-de-morgan :args (@t57 @t62 (and @t41))) % 2.72/2.91 (step @p13 :rule trans :premises (@p12 @p11)) % 2.72/2.91 (step @p14 :rule trans :premises (@p13 @p8)) % 2.72/2.91 (step @p15 :rule cong :premises (@p14) :args ((forall @t37 (not (and @t57 @t62 @t41))))) % 2.72/2.91 (step @p16 :rule trans :premises (@p15 @p7)) % 2.72/2.91 (step @p17 :rule refl :args (@t41)) % 2.72/2.91 (step @p18 :rule refl :args (@t62)) % 2.72/2.91 (step @p19 :rule quant-merge-prenex :args ((= @t66 @t57))) % 2.72/2.91 (step @p20 :rule nary_cong :premises (@p19 @p18 @p17) :args ((and @t66 @t62 @t41))) % 2.72/2.91 (step @p21 :rule quant-unused-vars :args ((= @t67 @t41))) % 2.72/2.91 (step @p22 :rule alpha_equiv :args (@t73 @t74 (@list @t61))) % 2.72/2.91 (step @p23 :rule alpha_equiv :args (@t77 @t74 (@list @t43))) % 2.72/2.91 (step @p24 :rule nary_cong :premises (@p23 @p22 @p21) :args (@t78)) % 2.72/2.91 (step @p25 :rule quant-miniscope-and :args ((= (forall @t35 @t79) @t78))) % 2.72/2.91 (step @p26 :rule trans :premises (@p25 @p24)) % 2.72/2.91 (step @p27 :rule trans :premises (@p26 @p20)) % 2.72/2.91 (step @p28 :rule aci_norm :args ((= (and @t80 @t41) @t79))) % 2.72/2.91 (step @p29 :rule bool-double-not-elim :args (@t41)) % 2.72/2.91 (step @p30 :rule refl :args (@t80)) % 2.72/2.91 (step @p31 :rule nary_cong :premises (@p30 @p29) :args ((and @t80 (not @t42)))) % 2.72/2.91 (step @p32 :rule bool-implies-de-morgan :args (@t80 @t42)) % 2.72/2.91 (step @p33 :rule trans :premises (@p32 @p31)) % 2.72/2.91 (step @p34 :rule trans :premises (@p33 @p28)) % 2.72/2.91 (step @p35 :rule cong :premises (@p34) :args (@t82)) % 2.72/2.91 (step @p36 :rule trans :premises (@p35 @p27)) % 2.72/2.91 (step @p37 :rule cong :premises (@p36) :args (@t83)) % 2.72/2.91 (step @p38 :rule exists-elim :args ((= (exists @t35 @t81) @t83))) % 2.72/2.91 (step @p39 :rule trans :premises (@p38 @p37)) % 2.72/2.91 (step @p40 :rule refl :args (@t40)) % 2.72/2.91 (step @p41 :rule refl :args (@t3)) % 2.72/2.91 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t3 @t40))) % 2.72/2.91 (step @p43 :rule symm :premises (@p42)) % 2.72/2.91 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 2.72/2.91 (step @p45 :rule refl :args (@t1)) % 2.72/2.91 (step @p46 :rule cong :premises (@p45 @p44) :args (@t84)) % 2.72/2.91 (step @p47 :rule cong :premises (@p46) :args (@t85)) % 2.72/2.91 (step @p48 :rule cong :premises (@p47) :args (@t86)) % 2.72/2.91 (step @p49 :rule cong :premises (@p48) :args (@t87)) % 2.72/2.91 (step @p50 :rule exists-elim :args ((= (exists @t4 @t84) @t87))) % 2.72/2.91 (step @p51 :rule trans :premises (@p50 @p49)) % 2.72/2.91 (step @p52 :rule eq-symm :args (@t3 @t1)) % 2.72/2.91 (step @p53 :rule cong :premises (@p52) :args (@t5)) % 2.72/2.91 (step @p54 :rule trans :premises (@p53 @p51)) % 2.72/2.91 (step @p55 :rule refl :args (@t70)) % 2.72/2.91 (step @p56 :rule refl :args (@t71)) % 2.72/2.91 (step @p57 :rule refl :args (@t12)) % 2.72/2.91 (step @p58 :rule cong :premises (@p57 @p56) :args ((= @t12 @t71))) % 2.72/2.91 (step @p59 :rule symm :premises (@p58)) % 2.72/2.91 (step @p60 :rule eq_resolve :premises (@p57 @p59)) % 2.72/2.91 (step @p61 :rule refl :args (@t6)) % 2.72/2.91 (step @p62 :rule cong :premises (@p61 @p60) :args (@t88)) % 2.72/2.91 (step @p63 :rule cong :premises (@p62) :args (@t89)) % 2.72/2.91 (step @p64 :rule nary_cong :premises (@p63 @p55) :args (@t90)) % 2.72/2.91 (step @p65 :rule cong :premises (@p64) :args ((forall @t14 @t90))) % 2.72/2.91 (step @p66 :rule bool-and-de-morgan :args (@t88 @t69 true)) % 2.72/2.91 (step @p67 :rule cong :premises (@p66) :args (@t92)) % 2.72/2.91 (step @p68 :rule trans :premises (@p67 @p65)) % 2.72/2.91 (step @p69 :rule cong :premises (@p68) :args (@t93)) % 2.72/2.91 (step @p70 :rule exists-elim :args ((= (exists @t14 @t91) @t93))) % 2.72/2.91 (step @p71 :rule trans :premises (@p70 @p69)) % 2.72/2.91 (step @p72 :rule refl :args (@t7)) % 2.72/2.91 (step @p73 :rule refl :args (@t68)) % 2.72/2.91 (step @p74 :rule refl :args (@t9)) % 2.72/2.91 (step @p75 :rule cong :premises (@p74 @p73) :args ((= @t9 @t68))) % 2.72/2.91 (step @p76 :rule symm :premises (@p75)) % 2.72/2.91 (step @p77 :rule eq_resolve :premises (@p74 @p76)) % 2.72/2.91 (step @p78 :rule cong :premises (@p45 @p77) :args (@t94)) % 2.72/2.91 (step @p79 :rule cong :premises (@p78) :args (@t95)) % 2.72/2.91 (step @p80 :rule nary_cong :premises (@p79 @p72) :args (@t96)) % 2.72/2.91 (step @p81 :rule cong :premises (@p80) :args ((forall @t4 @t96))) % 2.72/2.91 (step @p82 :rule bool-impl-elim :args (@t94 @t7)) % 2.72/2.91 (step @p83 :rule cong :premises (@p82) :args ((forall @t4 (=> @t94 @t7)))) % 2.72/2.91 (step @p84 :rule trans :premises (@p83 @p81)) % 2.72/2.91 (step @p85 :rule refl :args (@t7)) % 2.72/2.91 (step @p86 :rule eq-symm :args (@t9 @t1)) % 2.72/2.91 (step @p87 :rule cong :premises (@p86 @p85) :args (@t10)) % 2.72/2.91 (step @p88 :rule cong :premises (@p87) :args (@t11)) % 2.72/2.91 (step @p89 :rule trans :premises (@p88 @p84)) % 2.72/2.91 (step @p90 :rule eq-symm :args (@t12 @t6)) % 2.72/2.91 (step @p91 :rule nary_cong :premises (@p90 @p89) :args (@t13)) % 2.72/2.91 (step @p92 :rule cong :premises (@p91) :args (@t15)) % 2.72/2.91 (step @p93 :rule trans :premises (@p92 @p71)) % 2.72/2.91 (step @p94 :rule refl :args (@t75)) % 2.72/2.91 (step @p95 :rule refl :args (@t17)) % 2.72/2.91 (step @p96 :rule cong :premises (@p95 @p94) :args ((= @t17 @t75))) % 2.72/2.91 (step @p97 :rule symm :premises (@p96)) % 2.72/2.91 (step @p98 :rule eq_resolve :premises (@p95 @p97)) % 2.72/2.91 (step @p99 :rule refl :args (@t52)) % 2.72/2.91 (step @p100 :rule refl :args (@t53)) % 2.72/2.91 (step @p101 :rule refl :args (@t28)) % 2.72/2.91 (step @p102 :rule cong :premises (@p101 @p100) :args ((= @t28 @t53))) % 2.72/2.91 (step @p103 :rule symm :premises (@p102)) % 2.72/2.91 (step @p104 :rule eq_resolve :premises (@p101 @p103)) % 2.72/2.91 (step @p105 :rule cong :premises (@p104) :args (@t97)) % 2.72/2.91 (step @p106 :rule nary_cong :premises (@p105 @p99 @p98) :args (@t98)) % 2.72/2.91 (step @p107 :rule cong :premises (@p106) :args ((forall @t31 @t98))) % 2.72/2.91 (step @p108 :rule aci_norm :args ((= (or (or @t97 @t52) @t17) @t98))) % 2.72/2.91 (step @p109 :rule bool-and-de-morgan :args (@t28 @t51 true)) % 2.72/2.91 (step @p110 :rule nary_cong :premises (@p109 @p95) :args ((or (not @t99) @t17))) % 2.72/2.91 (step @p111 :rule trans :premises (@p110 @p108)) % 2.72/2.91 (step @p112 :rule bool-impl-elim :args (@t99 @t17)) % 2.72/2.91 (step @p113 :rule trans :premises (@p112 @p111)) % 2.72/2.91 (step @p114 :rule cong :premises (@p113) :args ((forall @t31 (=> @t99 @t17)))) % 2.72/2.91 (step @p115 :rule trans :premises (@p114 @p107)) % 2.72/2.91 (step @p116 :rule refl :args (@t17)) % 2.72/2.91 (step @p117 :rule refl :args ((_ @t16 @t23))) % 2.72/2.91 (step @p118 :rule refl :args ((_ @t2 @t20))) % 2.72/2.91 (step @p119 :rule refl :args (@t45)) % 2.72/2.91 (step @p120 :rule cong :premises (@p119) :args (@t46)) % 2.72/2.91 (step @p121 :rule trans :premises (@p120 @p118)) % 2.72/2.91 (step @p122 :rule cong :premises (@p121) :args (@t47)) % 2.72/2.91 (step @p123 :rule cong :premises (@p122) :args (@t48)) % 2.72/2.91 (step @p124 :rule trans :premises (@p123 @p117)) % 2.72/2.91 (step @p125 :rule refl :args (@t16)) % 2.72/2.91 (step @p126 :rule ho_cong :premises (@p125 @p122)) % 2.72/2.91 (step @p127 :rule cong :premises (@p126 @p124) :args ((= (_ @t16 @t47) @t48))) % 2.72/2.91 (step @p128 :rule symm :premises (@p127)) % 2.72/2.91 (step @p129 :rule refl :args (@t24)) % 2.72/2.91 (step @p130 :rule eq_resolve :premises (@p129 @p128)) % 2.72/2.91 (step @p131 :rule refl :args (@t2)) % 2.72/2.91 (step @p132 :rule ho_cong :premises (@p131 @p119)) % 2.72/2.91 (step @p133 :rule cong :premises (@p132 @p121) :args ((= (_ @t2 @t45) @t46))) % 2.72/2.91 (step @p134 :rule symm :premises (@p133)) % 2.72/2.91 (step @p135 :rule refl :args (@t21)) % 2.72/2.91 (step @p136 :rule eq_resolve :premises (@p135 @p134)) % 2.72/2.91 (step @p137 :rule refl :args (@t20)) % 2.72/2.91 (step @p138 :rule cong :premises (@p137 @p119) :args ((= @t20 @t45))) % 2.72/2.91 (step @p139 :rule symm :premises (@p138)) % 2.72/2.91 (step @p140 :rule eq_resolve :premises (@p137 @p139)) % 2.72/2.91 (step @p141 :rule ho_cong :premises (@p131 @p140)) % 2.72/2.91 (step @p142 :rule trans :premises (@p141 @p136)) % 2.72/2.91 (step @p143 :rule cong :premises (@p142) :args (@t23)) % 2.72/2.91 (step @p144 :rule ho_cong :premises (@p125 @p143)) % 2.72/2.91 (step @p145 :rule trans :premises (@p144 @p130)) % 2.72/2.91 (step @p146 :rule refl :args (@t49)) % 2.72/2.91 (step @p147 :rule refl :args (@t25)) % 2.72/2.91 (step @p148 :rule cong :premises (@p147 @p146) :args ((= @t25 @t49))) % 2.72/2.91 (step @p149 :rule symm :premises (@p148)) % 2.72/2.91 (step @p150 :rule eq_resolve :premises (@p147 @p149)) % 2.72/2.91 (step @p151 :rule cong :premises (@p150) :args (@t100)) % 2.72/2.91 (step @p152 :rule nary_cong :premises (@p151 @p145) :args (@t101)) % 2.72/2.91 (step @p153 :rule cong :premises (@p152) :args ((forall @t26 @t101))) % 2.72/2.91 (step @p154 :rule bool-impl-elim :args (@t25 @t24)) % 2.72/2.91 (step @p155 :rule cong :premises (@p154) :args (@t27)) % 2.72/2.91 (step @p156 :rule trans :premises (@p155 @p153)) % 2.72/2.91 (step @p157 :rule refl :args (@t28)) % 2.72/2.91 (step @p158 :rule nary_cong :premises (@p157 @p156) :args (@t29)) % 2.72/2.91 (step @p159 :rule cong :premises (@p158 @p116) :args (@t30)) % 2.72/2.91 (step @p160 :rule cong :premises (@p159) :args (@t32)) % 2.72/2.91 (step @p161 :rule trans :premises (@p160 @p115)) % 2.72/2.91 (step @p162 :rule nary_cong :premises (@p161 @p93) :args (@t33)) % 2.72/2.91 (step @p163 :rule cong :premises (@p162 @p54) :args (@t34)) % 2.72/2.91 (step @p164 :rule cong :premises (@p163) :args (@t36)) % 2.72/2.91 (step @p165 :rule trans :premises (@p164 @p39)) % 2.72/2.91 (step @p166 :rule cong :premises (@p165) :args (@t38)) % 2.72/2.91 (step @p167 :rule trans :premises (@p166 @p16)) % 2.72/2.91 (step @p168 :rule cong :premises (@p167) :args (@t39)) % 2.72/2.91 (step @p169 :rule eq_resolve :premises (@p1 @p168)) % 2.72/2.91 (step @p170 :rule not_or_elim :premises (@p169) :args (0)) % 2.72/2.91 (step @p171 :rule not_not_elim :premises (@p170)) % 2.72/2.91 (step @p172 :rule aci_norm :args ((= (or false @t102) @t102))) % 2.72/2.91 (step @p173 :rule aci_norm :args ((= (or false @t7) @t7))) % 2.72/2.91 (step @p174 :rule evaluate :args ((not true))) % 2.72/2.91 (step @p175 :rule eq-refl :args (@t1)) % 2.72/2.91 (step @p176 :rule beta-reduce :args ((= @t105 @t1))) % 2.72/2.91 (step @p177 :rule refl :args (@t1)) % 2.72/2.91 (step @p178 :rule cong :premises (@p177 @p176) :args (@t106)) % 2.72/2.91 (step @p179 :rule trans :premises (@p178 @p175)) % 2.72/2.91 (step @p180 :rule cong :premises (@p179) :args (@t107)) % 2.72/2.91 (step @p181 :rule trans :premises (@p180 @p174)) % 2.72/2.91 (step @p182 :rule nary_cong :premises (@p181 @p85) :args (@t108)) % 2.72/2.91 (step @p183 :rule trans :premises (@p182 @p173)) % 2.72/2.91 (step @p184 :rule cong :premises (@p183) :args (@t109)) % 2.72/2.91 (step @p185 :rule cong :premises (@p184) :args (@t110)) % 2.72/2.91 (step @p186 :rule eq-refl :args (@t6)) % 2.72/2.91 (step @p187 :rule beta-reduce :args ((= @t111 @t6))) % 2.72/2.91 (step @p188 :rule refl :args (@t6)) % 2.72/2.91 (step @p189 :rule cong :premises (@p188 @p187) :args (@t112)) % 2.72/2.91 (step @p190 :rule trans :premises (@p189 @p186)) % 2.72/2.91 (step @p191 :rule cong :premises (@p190) :args (@t113)) % 2.72/2.91 (step @p192 :rule trans :premises (@p191 @p174)) % 2.72/2.91 (step @p193 :rule nary_cong :premises (@p192 @p185) :args (@t114)) % 2.72/2.91 (step @p194 :rule trans :premises (@p193 @p172)) % 2.72/2.91 (step @p195 :rule cong :premises (@p194) :args (@t115)) % 2.72/2.91 (step @p196 :rule cong :premises (@p195) :args (@t116)) % 2.72/2.91 (step @p197 :rule cong :premises (@p18 @p196) :args ((=> @t62 @t116))) % 2.72/2.91 (assume-push @p248 @t62) % 2.72/2.91 (step @p199 :rule instantiate :premises (@p171) :args ((@list @t104))) % 2.72/2.91 (step-pop @p249 :rule scope :premises (@p199)) % 2.72/2.91 (step @p200 :rule process_scope :premises (@p249) :args (@t116)) % 2.72/2.91 (step @p202 :rule eq_resolve :premises (@p200 @p197)) % 2.72/2.91 (step @p203 :rule implies_elim :premises (@p202)) % 2.72/2.91 (step @p204 :rule chain_m_resolution :premises (@p203 @p171) :args (@t118 @t119 (@list @t62))) % 2.72/2.91 (step @p205 :rule refl :args (@t121)) % 2.72/2.91 (step @p206 :rule bool-double-not-elim :args (@t117)) % 2.72/2.91 (step @p207 :rule nary_cong :premises (@p206 @p205) :args ((or (not @t118) @t121))) % 2.72/2.91 (step @p208 :rule eq-symm :args (@t120 @t1)) % 2.72/2.91 (step @p209 :rule cong :premises (@p208) :args (@t122)) % 2.72/2.91 (step @p210 :rule bool-double-not-elim :args (@t122)) % 2.72/2.91 (step @p211 :rule trans :premises (@p210 @p209)) % 2.72/2.91 (step @p212 :rule refl :args (@t118)) % 2.72/2.91 (step @p213 :rule cong :premises (@p212 @p211) :args ((=> @t118 @t123))) % 2.72/2.92 (assume-push @p250 @t118) % 2.72/2.92 (step @p215 :rule skolemize :premises (@p204)) % 2.72/2.92 (step-pop @p251 :rule scope :premises (@p215)) % 2.72/2.92 (step @p216 :rule process_scope :premises (@p251) :args (@t123)) % 2.72/2.92 (step @p218 :rule eq_resolve :premises (@p216 @p213)) % 2.72/2.92 (step @p219 :rule implies_elim :premises (@p218)) % 2.72/2.92 (step @p220 :rule eq_resolve :premises (@p219 @p207)) % 2.72/2.92 (step @p221 :rule chain_m_resolution :premises (@p220 @p204) :args (@t121 @t124 (@list @t117))) % 2.72/2.92 (step @p222 :rule eq-symm :args (@t127 @t120)) % 2.72/2.92 (step @p223 :rule cong :premises (@p205 @p222) :args ((=> @t121 @t128))) % 2.72/2.92 (assume-push @p252 @t121) % 2.72/2.92 (step @p225 :rule instantiate :premises (@p221) :args ((@list @t127))) % 2.72/2.92 (step-pop @p253 :rule scope :premises (@p225)) % 2.72/2.92 (step @p226 :rule process_scope :premises (@p253) :args (@t128)) % 2.72/2.92 (step @p228 :rule eq_resolve :premises (@p226 @p223)) % 2.72/2.92 (step @p229 :rule implies_elim :premises (@p228)) % 2.72/2.92 (step @p230 :rule chain_m_resolution :premises (@p229 @p221) :args ((= @t120 @t127) @t119 (@list @t121))) % 2.72/2.92 (step @p231 :rule instantiate :premises (@p221) :args (@t129)) % 2.72/2.92 (step @p232 :rule trans :premises (@p231 @p230)) % 2.72/2.92 (step @p233 :rule true_intro :premises (@p232)) % 2.72/2.92 (step @p234 :rule not_or_elim :premises (@p169) :args (1)) % 2.72/2.92 (step @p235 :rule skolemize :premises (@p234)) % 2.72/2.92 (step @p236 :rule bool-double-not-elim :args (@t130)) % 2.72/2.92 (step @p237 :rule refl :args (@t132)) % 2.72/2.92 (step @p238 :rule nary_cong :premises (@p237 @p236) :args ((or @t132 (not @t131)))) % 2.72/2.92 (step @p239 :rule cnf_or_neg :args (@t132 1)) % 2.72/2.92 (step @p240 :rule eq_resolve :premises (@p239 @p238)) % 2.72/2.92 (step @p241 :rule reordering :premises (@p240) :args ((or @t130 @t132))) % 2.72/2.92 (step @p242 :rule chain_m_resolution :premises (@p241 @p235) :args (@t130 @t124 (@list @t132))) % 2.72/2.92 (step @p243 :rule instantiate :premises (@p242) :args (@t129)) % 2.72/2.92 (step @p244 :rule false_intro :premises (@p243)) % 2.72/2.92 (step @p245 :rule symm :premises (@p244)) % 2.72/2.92 (step @p246 :rule trans :premises (@p245 @p233)) % 2.72/2.92 (step @p247 false :rule eq_resolve :premises (@p246 @p3)) % 2.72/2.92 ) % 2.72/2.92 % SZS output end Proof % 2.72/2.92 % cvc5 exiting %------------------------------------------------------------------------------