%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV076^5 : 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 : n007.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 152.13s 152.71s % Output : Proof 152.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV076^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n007.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 18:10:26 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.49 %----Proving TH0 % 152.13/152.71 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 152.13/152.71 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 152.13/152.71 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 152.13/152.71 --- Run --ho-elim --full-saturate-quant at 18s... % 152.13/152.71 % SZS status Theorem % 152.13/152.71 % SZS output start Proof % 152.13/152.71 ( % 152.13/152.71 (declare-sort tptp.a 0) % 152.13/152.71 (define @t1 () (@var "Xb" tptp.a)) % 152.13/152.71 (define @t2 () (@var "Xz" tptp.a)) % 152.13/152.71 (define @t3 () (@var "RRR" (-> tptp.a tptp.a Bool))) % 152.13/152.71 (define @t4 () (_ @t3 @t2)) % 152.13/152.71 (define @t5 () (_ @t4 @t1)) % 152.13/152.71 (define @t6 () (@var "Xs" (-> tptp.a Bool))) % 152.13/152.71 (define @t7 () (_ @t6 @t2)) % 152.13/152.71 (define @t8 () (@list @t2)) % 152.13/152.71 (define @t9 () (forall @t8 (=> @t7 @t5))) % 152.13/152.71 (define @t10 () (@list @t1)) % 152.13/152.71 (define @t11 () (exists @t10 @t9)) % 152.13/152.71 (define @t12 () (@list @t6)) % 152.13/152.71 (define @t13 () (forall @t12 @t11)) % 152.13/152.71 (define @t14 () (@var "Xj" tptp.a)) % 152.13/152.71 (define @t15 () (@var "U" (-> (-> tptp.a Bool) tptp.a))) % 152.13/152.71 (define @t16 () (_ @t15 @t6)) % 152.13/152.71 (define @t17 () (_ (_ @t3 @t16) @t14)) % 152.13/152.71 (define @t18 () (@var "Xk" tptp.a)) % 152.13/152.71 (define @t19 () (_ (_ @t3 @t18) @t14)) % 152.13/152.71 (define @t20 () (_ @t6 @t18)) % 152.13/152.71 (define @t21 () (@list @t18)) % 152.13/152.71 (define @t22 () (forall @t21 (=> @t20 @t19))) % 152.13/152.71 (define @t23 () (=> @t22 @t17)) % 152.13/152.71 (define @t24 () (@list @t14)) % 152.13/152.71 (define @t25 () (forall @t24 @t23)) % 152.13/152.71 (define @t26 () (_ @t4 @t16)) % 152.13/152.71 (define @t27 () (forall @t8 (=> @t7 @t26))) % 152.13/152.71 (define @t28 () (and @t27 @t25)) % 152.13/152.71 (define @t29 () (forall @t12 @t28)) % 152.13/152.71 (define @t30 () (@var "Xx" tptp.a)) % 152.13/152.71 (define @t31 () (_ @t3 @t30)) % 152.13/152.71 (define @t32 () (_ @t31 @t2)) % 152.13/152.71 (define @t33 () (@var "Xy" tptp.a)) % 152.13/152.71 (define @t34 () (_ (_ @t3 @t33) @t2)) % 152.13/152.71 (define @t35 () (_ @t31 @t33)) % 152.13/152.71 (define @t36 () (and @t35 @t34)) % 152.13/152.71 (define @t37 () (@list @t30 @t33 @t2)) % 152.13/152.71 (define @t38 () (forall @t37 (=> @t36 @t32))) % 152.13/152.71 (define @t39 () (and @t38 @t29)) % 152.13/152.71 (define @t40 () (=> @t39 @t13)) % 152.13/152.71 (define @t41 () (@list @t3 @t15)) % 152.13/152.71 (define @t42 () (forall @t41 @t40)) % 152.13/152.71 (define @t43 () (not @t42)) % 152.13/152.71 (define @t44 () (@var "BOUND_VARIABLE_7568" (@ho-elim-sort (-> tptp.a tptp.a Bool)))) % 152.13/152.71 (define @t45 () (@const 0 (-> (@ho-elim-sort (-> tptp.a tptp.a Bool)) tptp.a (@ho-elim-sort (-> tptp.a Bool))))) % 152.13/152.71 (define @t46 () (_ @t45 @t44 @t2)) % 152.13/152.71 (define @t47 () (@const 1 (-> (@ho-elim-sort (-> tptp.a Bool)) tptp.a Bool))) % 152.13/152.71 (define @t48 () (@var "BOUND_VARIABLE_7577" (@ho-elim-sort (-> tptp.a Bool)))) % 152.13/152.71 (define @t49 () (@var "BOUND_VARIABLE_7588" (@ho-elim-sort (-> tptp.a Bool)))) % 152.13/152.71 (define @t50 () (@var "BOUND_VARIABLE_7591" (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.a Bool)) tptp.a)))) % 152.13/152.71 (define @t51 () (@const 2 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.a Bool)) tptp.a)) (@ho-elim-sort (-> tptp.a Bool)) tptp.a))) % 152.13/152.71 (define @t52 () (not (_ @t47 @t49 @t18))) % 152.13/152.71 (define @t53 () (@list @t49 @t14)) % 152.13/152.71 (define @t54 () (@var "BOUND_VARIABLE_7611" (@ho-elim-sort (-> tptp.a Bool)))) % 152.13/152.71 (define @t55 () (not (_ @t47 @t54 @t2))) % 152.13/152.71 (define @t56 () (@list @t54 @t2)) % 152.13/152.71 (define @t57 () (_ @t45 @t44 @t30)) % 152.13/152.71 (define @t58 () (forall (@list @t44 @t50 @t48) (or (not (forall @t37 (or (not (_ @t47 @t57 @t33)) (not (_ @t47 (_ @t45 @t44 @t33) @t2)) (_ @t47 @t57 @t2)))) (not (forall @t56 (or @t55 (_ @t47 @t46 (_ @t51 @t50 @t54))))) (not (forall @t53 (or (not (forall @t21 (or @t52 (_ @t47 (_ @t45 @t44 @t18) @t14)))) (_ @t47 (_ @t45 @t44 (_ @t51 @t50 @t49)) @t14)))) (not (forall @t10 (not (forall @t8 (or (not (_ @t47 @t48 @t2)) (_ @t47 @t46 @t1))))))))) % 152.13/152.71 (define @t59 () (_ @t3 @t2 @t1)) % 152.13/152.71 (define @t60 () (@var "BOUND_VARIABLE_7554" (-> tptp.a Bool))) % 152.13/152.71 (define @t61 () (not (forall @t10 (not (forall @t8 (or (not (_ @t60 @t2)) @t59)))))) % 152.13/152.71 (define @t62 () (@var "BOUND_VARIABLE_7514" (-> tptp.a Bool))) % 152.13/152.71 (define @t63 () (_ @t3 @t18 @t14)) % 152.13/152.71 (define @t64 () (or (not (forall @t21 (or (not (_ @t62 @t18)) @t63))) (_ @t3 (_ @t15 @t62) @t14))) % 152.13/152.71 (define @t65 () (forall (@list @t62 @t14) @t64)) % 152.13/152.71 (define @t66 () (not @t65)) % 152.13/152.71 (define @t67 () (@var "BOUND_VARIABLE_7504" (-> tptp.a Bool))) % 152.13/152.71 (define @t68 () (or (not (_ @t67 @t2)) (_ @t3 @t2 (_ @t15 @t67)))) % 152.13/152.71 (define @t69 () (forall (@list @t67 @t2) @t68)) % 152.13/152.71 (define @t70 () (not @t69)) % 152.13/152.71 (define @t71 () (_ @t3 @t30 @t2)) % 152.13/152.71 (define @t72 () (_ @t3 @t33 @t2)) % 152.13/152.71 (define @t73 () (_ @t3 @t30 @t33)) % 152.13/152.71 (define @t74 () (forall @t37 (or (not @t73) (not @t72) @t71))) % 152.13/152.71 (define @t75 () (not @t74)) % 152.13/152.71 (define @t76 () (or @t75 @t70 @t66 @t61)) % 152.13/152.71 (define @t77 () (forall (@list @t3 @t15 @t60) @t76)) % 152.13/152.71 (define @t78 () (@list @t60)) % 152.13/152.71 (define @t79 () (forall @t78 @t76)) % 152.13/152.71 (define @t80 () (forall @t78 @t61)) % 152.13/152.71 (define @t81 () (@list @t6)) % 152.13/152.71 (define @t82 () (or @t75 @t70 @t66 @t80)) % 152.13/152.71 (define @t83 () (_ @t6 @t2)) % 152.13/152.71 (define @t84 () (not @t83)) % 152.13/152.71 (define @t85 () (forall @t8 (or @t84 @t59))) % 152.13/152.71 (define @t86 () (not (forall @t10 (not @t85)))) % 152.13/152.71 (define @t87 () (forall @t12 @t86)) % 152.13/152.71 (define @t88 () (or @t75 @t70 @t66 @t87)) % 152.13/152.71 (define @t89 () (or @t75 @t70 @t66)) % 152.13/152.71 (define @t90 () (and @t69 @t65)) % 152.13/152.71 (define @t91 () (and @t74 @t69 @t65)) % 152.13/152.71 (define @t92 () (not @t7)) % 152.13/152.71 (define @t93 () (or @t92 @t5)) % 152.13/152.71 (define @t94 () (forall (@list @t62) (forall @t24 @t64))) % 152.13/152.71 (define @t95 () (forall (@list @t67) (forall @t8 @t68))) % 152.13/152.71 (define @t96 () (_ @t15 @t6)) % 152.13/152.71 (define @t97 () (_ @t3 @t96 @t14)) % 152.13/152.71 (define @t98 () (_ @t6 @t18)) % 152.13/152.71 (define @t99 () (forall @t21 (or (not @t98) @t63))) % 152.13/152.71 (define @t100 () (not @t99)) % 152.13/152.71 (define @t101 () (forall @t24 (or @t100 @t97))) % 152.13/152.71 (define @t102 () (forall @t12 @t101)) % 152.13/152.71 (define @t103 () (_ @t3 @t2 @t96)) % 152.13/152.71 (define @t104 () (forall @t8 (or @t84 @t103))) % 152.13/152.71 (define @t105 () (forall @t12 @t104)) % 152.13/152.71 (define @t106 () (and @t105 @t102)) % 152.13/152.71 (define @t107 () (or @t100 @t17)) % 152.13/152.71 (define @t108 () (not @t20)) % 152.13/152.71 (define @t109 () (or @t108 @t19)) % 152.13/152.71 (define @t110 () (or @t92 @t26)) % 152.13/152.71 (define @t111 () (not @t34)) % 152.13/152.71 (define @t112 () (not @t35)) % 152.13/152.71 (define @t113 () (or @t112 @t111 @t32)) % 152.13/152.71 (define @t114 () (@quantifiers_skolemize @t58 1)) % 152.13/152.71 (define @t115 () (@quantifiers_skolemize @t58 0)) % 152.13/152.71 (define @t116 () (_ @t45 @t115 @t2)) % 152.13/152.71 (define @t117 () (forall @t56 (or @t55 (_ @t47 @t116 (_ @t51 @t114 @t54))))) % 152.13/152.71 (define @t118 () (@quantifiers_skolemize @t58 2)) % 152.13/152.71 (define @t119 () (not (_ @t47 @t118 @t2))) % 152.13/152.71 (define @t120 () (forall @t10 (not (forall @t8 (or @t119 (_ @t47 @t116 @t1)))))) % 152.13/152.71 (define @t121 () (not @t120)) % 152.13/152.71 (define @t122 () (not @t117)) % 152.13/152.71 (define @t123 () (_ @t45 @t115 @t30)) % 152.13/152.71 (define @t124 () (or (not (forall @t37 (or (not (_ @t47 @t123 @t33)) (not (_ @t47 (_ @t45 @t115 @t33) @t2)) (_ @t47 @t123 @t2)))) @t122 (not (forall @t53 (or (not (forall @t21 (or @t52 (_ @t47 (_ @t45 @t115 @t18) @t14)))) (_ @t47 (_ @t45 @t115 (_ @t51 @t114 @t49)) @t14)))) @t121)) % 152.13/152.71 (define @t125 () (@list true)) % 152.13/152.71 (define @t126 () (@list @t124)) % 152.13/152.71 (define @t127 () (_ @t51 @t114 @t118)) % 152.13/152.71 (define @t128 () (@quantifiers_skolemize (forall @t8 (or @t119 (_ @t47 @t116 @t127))) 0)) % 152.13/152.71 (define @t129 () (or (not (_ @t47 @t118 @t128)) (_ @t47 (_ @t45 @t115 @t128) @t127))) % 152.13/152.71 (assume @p1 @t43) % 152.13/152.71 (assume @p2 true) % 152.13/152.71 ; WARNING: add trust step for TRUST % 152.13/152.71 ; trust TRUST PREPROCESS_HO_ELIM % 152.13/152.71 (step @p3 :rule trust :premises () :args ((= (not @t77) (not @t58)))) % 152.13/152.71 (step @p4 :rule quant-merge-prenex :args ((= (forall @t41 @t79) @t77))) % 152.13/152.71 (step @p5 :rule alpha_equiv :args (@t80 (@list @t60) @t81)) % 152.13/152.71 (step @p6 :rule refl :args (@t66)) % 152.13/152.71 (step @p7 :rule refl :args (@t70)) % 152.13/152.71 (step @p8 :rule refl :args (@t75)) % 152.13/152.71 (step @p9 :rule nary_cong :premises (@p8 @p7 @p6 @p5) :args (@t82)) % 152.13/152.71 (step @p10 :rule quant-miniscope-or :args ((= @t79 @t82))) % 152.13/152.71 (step @p11 :rule trans :premises (@p10 @p9)) % 152.13/152.71 (step @p12 :rule symm :premises (@p11)) % 152.13/152.71 (step @p13 :rule cong :premises (@p12) :args ((forall @t41 @t88))) % 152.13/152.71 (step @p14 :rule trans :premises (@p13 @p4)) % 152.13/152.71 (step @p15 :rule aci_norm :args ((= (or @t89 @t87) @t88))) % 152.13/152.71 (step @p16 :rule refl :args (@t87)) % 152.13/152.71 (step @p17 :rule aci_norm :args ((= (or @t75 (or @t70 @t66)) @t89))) % 152.13/152.71 (step @p18 :rule bool-and-de-morgan :args (@t69 @t65 true)) % 152.13/152.71 (step @p19 :rule nary_cong :premises (@p8 @p18) :args ((or @t75 (not @t90)))) % 152.13/152.71 (step @p20 :rule bool-and-de-morgan :args (@t74 @t69 (and @t65))) % 152.13/152.71 (step @p21 :rule trans :premises (@p20 @p19)) % 152.13/152.71 (step @p22 :rule trans :premises (@p21 @p17)) % 152.13/152.71 (step @p23 :rule nary_cong :premises (@p22 @p16) :args ((or (not @t91) @t87))) % 152.13/152.71 (step @p24 :rule trans :premises (@p23 @p15)) % 152.13/152.71 (step @p25 :rule bool-impl-elim :args (@t91 @t87)) % 152.13/152.71 (step @p26 :rule trans :premises (@p25 @p24)) % 152.13/152.71 (step @p27 :rule cong :premises (@p26) :args ((forall @t41 (=> @t91 @t87)))) % 152.13/152.71 (step @p28 :rule trans :premises (@p27 @p14)) % 152.13/152.71 (step @p29 :rule exists-elim :args ((= (exists @t10 @t85) @t86))) % 152.13/152.71 (step @p30 :rule refl :args (@t59)) % 152.13/152.71 (step @p31 :rule refl :args (@t5)) % 152.13/152.71 (step @p32 :rule cong :premises (@p31 @p30) :args ((= @t5 @t59))) % 152.13/152.71 (step @p33 :rule symm :premises (@p32)) % 152.13/152.71 (step @p34 :rule eq_resolve :premises (@p31 @p33)) % 152.13/152.71 (step @p35 :rule refl :args (@t83)) % 152.13/152.71 (step @p36 :rule refl :args (@t7)) % 152.13/152.71 (step @p37 :rule cong :premises (@p36 @p35) :args ((= @t7 @t83))) % 152.13/152.71 (step @p38 :rule symm :premises (@p37)) % 152.13/152.71 (step @p39 :rule eq_resolve :premises (@p36 @p38)) % 152.13/152.71 (step @p40 :rule cong :premises (@p39) :args (@t92)) % 152.13/152.71 (step @p41 :rule nary_cong :premises (@p40 @p34) :args (@t93)) % 152.13/152.71 (step @p42 :rule cong :premises (@p41) :args ((forall @t8 @t93))) % 152.13/152.71 (step @p43 :rule bool-impl-elim :args (@t7 @t5)) % 152.13/152.71 (step @p44 :rule cong :premises (@p43) :args (@t9)) % 152.13/152.71 (step @p45 :rule trans :premises (@p44 @p42)) % 152.13/152.71 (step @p46 :rule cong :premises (@p45) :args (@t11)) % 152.13/152.71 (step @p47 :rule trans :premises (@p46 @p29)) % 152.13/152.71 (step @p48 :rule cong :premises (@p47) :args (@t13)) % 152.13/152.71 (step @p49 :rule aci_norm :args ((= (and @t74 @t90) @t91))) % 152.13/152.71 (step @p50 :rule quant-merge-prenex :args ((= @t94 @t65))) % 152.13/152.71 (step @p51 :rule quant-merge-prenex :args ((= @t95 @t69))) % 152.13/152.71 (step @p52 :rule nary_cong :premises (@p51 @p50) :args ((and @t95 @t94))) % 152.13/152.71 (step @p53 :rule alpha_equiv :args (@t102 @t81 (@list @t62))) % 152.13/152.71 (step @p54 :rule alpha_equiv :args (@t105 @t81 (@list @t67))) % 152.13/152.71 (step @p55 :rule nary_cong :premises (@p54 @p53) :args (@t106)) % 152.13/152.71 (step @p56 :rule quant-miniscope-and :args ((= (forall @t12 (and @t104 @t101)) @t106))) % 152.13/152.71 (step @p57 :rule trans :premises (@p56 @p55)) % 152.13/152.71 (step @p58 :rule trans :premises (@p57 @p52)) % 152.13/152.71 (step @p59 :rule refl :args ((_ @t3 @t16 @t14))) % 152.13/152.71 (step @p60 :rule refl :args (@t14)) % 152.13/152.71 (step @p61 :rule refl :args (@t96)) % 152.13/152.71 (step @p62 :rule cong :premises (@p61 @p60) :args (@t97)) % 152.13/152.71 (step @p63 :rule trans :premises (@p62 @p59)) % 152.13/152.71 (step @p64 :rule refl :args (@t3)) % 152.13/152.71 (step @p65 :rule ho_cong :premises (@p64 @p61)) % 152.13/152.71 (step @p66 :rule ho_cong :premises (@p65 @p60)) % 152.13/152.71 (step @p67 :rule cong :premises (@p66 @p63) :args ((= (_ (_ @t3 @t96) @t14) @t97))) % 152.13/152.71 (step @p68 :rule symm :premises (@p67)) % 152.13/152.71 (step @p69 :rule refl :args (@t17)) % 152.13/152.71 (step @p70 :rule eq_resolve :premises (@p69 @p68)) % 152.13/152.71 (step @p71 :rule refl :args (@t16)) % 152.13/152.71 (step @p72 :rule cong :premises (@p71 @p61) :args ((= @t16 @t96))) % 152.13/152.71 (step @p73 :rule symm :premises (@p72)) % 152.13/152.71 (step @p74 :rule eq_resolve :premises (@p71 @p73)) % 152.13/152.71 (step @p75 :rule ho_cong :premises (@p64 @p74)) % 152.13/152.71 (step @p76 :rule ho_cong :premises (@p75 @p60)) % 152.13/152.71 (step @p77 :rule trans :premises (@p76 @p70)) % 152.13/152.71 (step @p78 :rule refl :args (@t100)) % 152.13/152.71 (step @p79 :rule nary_cong :premises (@p78 @p77) :args (@t107)) % 152.13/152.71 (step @p80 :rule cong :premises (@p79) :args ((forall @t24 @t107))) % 152.13/152.71 (step @p81 :rule bool-impl-elim :args (@t99 @t17)) % 152.13/152.71 (step @p82 :rule cong :premises (@p81) :args ((forall @t24 (=> @t99 @t17)))) % 152.13/152.71 (step @p83 :rule trans :premises (@p82 @p80)) % 152.13/152.71 (step @p84 :rule refl :args (@t17)) % 152.13/152.71 (step @p85 :rule refl :args (@t63)) % 152.13/152.71 (step @p86 :rule refl :args (@t19)) % 152.13/152.71 (step @p87 :rule cong :premises (@p86 @p85) :args ((= @t19 @t63))) % 152.13/152.71 (step @p88 :rule symm :premises (@p87)) % 152.13/152.71 (step @p89 :rule eq_resolve :premises (@p86 @p88)) % 152.13/152.71 (step @p90 :rule refl :args (@t98)) % 152.13/152.71 (step @p91 :rule refl :args (@t20)) % 152.13/152.71 (step @p92 :rule cong :premises (@p91 @p90) :args ((= @t20 @t98))) % 152.13/152.71 (step @p93 :rule symm :premises (@p92)) % 152.13/152.71 (step @p94 :rule eq_resolve :premises (@p91 @p93)) % 152.13/152.71 (step @p95 :rule cong :premises (@p94) :args (@t108)) % 152.13/152.71 (step @p96 :rule nary_cong :premises (@p95 @p89) :args (@t109)) % 152.13/152.71 (step @p97 :rule cong :premises (@p96) :args ((forall @t21 @t109))) % 152.13/152.71 (step @p98 :rule bool-impl-elim :args (@t20 @t19)) % 152.13/152.71 (step @p99 :rule cong :premises (@p98) :args (@t22)) % 152.13/152.71 (step @p100 :rule trans :premises (@p99 @p97)) % 152.13/152.71 (step @p101 :rule cong :premises (@p100 @p84) :args (@t23)) % 152.13/152.71 (step @p102 :rule cong :premises (@p101) :args (@t25)) % 152.13/152.71 (step @p103 :rule trans :premises (@p102 @p83)) % 152.13/152.71 (step @p104 :rule refl :args ((_ @t3 @t2 @t16))) % 152.13/152.71 (step @p105 :rule refl :args (@t2)) % 152.13/152.71 (step @p106 :rule cong :premises (@p105 @p61) :args (@t103)) % 152.13/152.71 (step @p107 :rule trans :premises (@p106 @p104)) % 152.13/152.71 (step @p108 :rule refl :args (@t4)) % 152.13/152.71 (step @p109 :rule ho_cong :premises (@p108 @p61)) % 152.13/152.71 (step @p110 :rule cong :premises (@p109 @p107) :args ((= (_ @t4 @t96) @t103))) % 152.13/152.71 (step @p111 :rule symm :premises (@p110)) % 152.13/152.71 (step @p112 :rule refl :args (@t26)) % 152.13/152.71 (step @p113 :rule eq_resolve :premises (@p112 @p111)) % 152.13/152.71 (step @p114 :rule ho_cong :premises (@p108 @p74)) % 152.13/152.71 (step @p115 :rule trans :premises (@p114 @p113)) % 152.13/152.71 (step @p116 :rule nary_cong :premises (@p40 @p115) :args (@t110)) % 152.13/152.71 (step @p117 :rule cong :premises (@p116) :args ((forall @t8 @t110))) % 152.13/152.71 (step @p118 :rule bool-impl-elim :args (@t7 @t26)) % 152.13/152.71 (step @p119 :rule cong :premises (@p118) :args (@t27)) % 152.13/152.71 (step @p120 :rule trans :premises (@p119 @p117)) % 152.13/152.71 (step @p121 :rule nary_cong :premises (@p120 @p103) :args (@t28)) % 152.13/152.71 (step @p122 :rule cong :premises (@p121) :args (@t29)) % 152.13/152.71 (step @p123 :rule trans :premises (@p122 @p58)) % 152.13/152.71 (step @p124 :rule refl :args (@t71)) % 152.13/152.71 (step @p125 :rule refl :args (@t32)) % 152.13/152.71 (step @p126 :rule cong :premises (@p125 @p124) :args ((= @t32 @t71))) % 152.13/152.71 (step @p127 :rule symm :premises (@p126)) % 152.13/152.71 (step @p128 :rule eq_resolve :premises (@p125 @p127)) % 152.13/152.71 (step @p129 :rule refl :args (@t72)) % 152.13/152.71 (step @p130 :rule refl :args (@t34)) % 152.13/152.71 (step @p131 :rule cong :premises (@p130 @p129) :args ((= @t34 @t72))) % 152.13/152.71 (step @p132 :rule symm :premises (@p131)) % 152.13/152.71 (step @p133 :rule eq_resolve :premises (@p130 @p132)) % 152.13/152.71 (step @p134 :rule cong :premises (@p133) :args (@t111)) % 152.13/152.71 (step @p135 :rule refl :args (@t73)) % 152.13/152.71 (step @p136 :rule refl :args (@t35)) % 152.13/152.71 (step @p137 :rule cong :premises (@p136 @p135) :args ((= @t35 @t73))) % 152.13/152.71 (step @p138 :rule symm :premises (@p137)) % 152.13/152.71 (step @p139 :rule eq_resolve :premises (@p136 @p138)) % 152.13/152.71 (step @p140 :rule cong :premises (@p139) :args (@t112)) % 152.13/152.71 (step @p141 :rule nary_cong :premises (@p140 @p134 @p128) :args (@t113)) % 152.13/152.71 (step @p142 :rule cong :premises (@p141) :args ((forall @t37 @t113))) % 152.13/152.71 (step @p143 :rule aci_norm :args ((= (or (or @t112 @t111) @t32) @t113))) % 152.13/152.71 (step @p144 :rule bool-and-de-morgan :args (@t35 @t34 true)) % 152.13/152.71 (step @p145 :rule nary_cong :premises (@p144 @p125) :args ((or (not @t36) @t32))) % 152.13/152.71 (step @p146 :rule trans :premises (@p145 @p143)) % 152.13/152.71 (step @p147 :rule bool-impl-elim :args (@t36 @t32)) % 152.13/152.71 (step @p148 :rule trans :premises (@p147 @p146)) % 152.13/152.71 (step @p149 :rule cong :premises (@p148) :args (@t38)) % 152.13/152.71 (step @p150 :rule trans :premises (@p149 @p142)) % 152.13/152.71 (step @p151 :rule nary_cong :premises (@p150 @p123) :args (@t39)) % 152.13/152.71 (step @p152 :rule trans :premises (@p151 @p49)) % 152.13/152.71 (step @p153 :rule cong :premises (@p152 @p48) :args (@t40)) % 152.13/152.71 (step @p154 :rule cong :premises (@p153) :args (@t42)) % 152.13/152.71 (step @p155 :rule trans :premises (@p154 @p28)) % 152.13/152.71 (step @p156 :rule cong :premises (@p155) :args (@t43)) % 152.13/152.71 (step @p157 :rule trans :premises (@p156 @p3)) % 152.13/152.71 (step @p158 :rule eq_resolve :premises (@p1 @p157)) % 152.13/152.71 (step @p159 :rule skolemize :premises (@p158)) % 152.13/152.71 (step @p160 :rule bool-double-not-elim :args (@t117)) % 152.13/152.71 (step @p161 :rule refl :args (@t124)) % 152.13/152.71 (step @p162 :rule nary_cong :premises (@p161 @p160) :args ((or @t124 (not @t122)))) % 152.13/152.71 (step @p163 :rule cnf_or_neg :args (@t124 1)) % 152.13/152.71 (step @p164 :rule eq_resolve :premises (@p163 @p162)) % 152.13/152.71 (step @p165 :rule reordering :premises (@p164) :args ((or @t117 @t124))) % 152.13/152.71 (step @p166 :rule chain_m_resolution :premises (@p165 @p159) :args (@t117 @t125 @t126)) % 152.13/152.71 (step @p167 :rule bool-double-not-elim :args (@t120)) % 152.13/152.71 (step @p168 :rule nary_cong :premises (@p161 @p167) :args ((or @t124 (not @t121)))) % 152.13/152.71 (step @p169 :rule cnf_or_neg :args (@t124 3)) % 152.13/152.71 (step @p170 :rule eq_resolve :premises (@p169 @p168)) % 152.13/152.71 (step @p171 :rule reordering :premises (@p170) :args ((or @t120 @t124))) % 152.13/152.71 (step @p172 :rule chain_m_resolution :premises (@p171 @p159) :args (@t120 @t125 @t126)) % 152.13/152.71 (step @p173 :rule instantiate :premises (@p172) :args ((@list @t127))) % 152.13/152.71 (step @p174 :rule skolemize :premises (@p173)) % 152.13/152.71 (assume-push @p181 @t117) % 152.13/152.71 (step @p176 :rule instantiate :premises (@p166) :args ((@list @t118 @t128))) % 152.13/152.71 (step-pop @p182 :rule scope :premises (@p176)) % 152.13/152.71 (step @p177 :rule process_scope :premises (@p182) :args (@t129)) % 152.13/152.71 (step @p179 :rule implies_elim :premises (@p177)) % 152.13/152.71 (step @p180 false :rule chain_m_resolution :premises (@p179 @p174 @p166) :args (false (@list true false) (@list @t129 @t117))) % 152.13/152.71 ) % 152.13/152.71 % SZS output end Proof % 152.13/152.71 % cvc5 exiting %------------------------------------------------------------------------------