%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM696^1 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n009.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 08:40:24 AM UTC 2026 % Result : Theorem 202.78s 203.09s % Output : Proof 202.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM696^1 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n009.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 11:57:44 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.48 %----Proving TH0 % 202.78/203.09 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 202.78/203.09 --- 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... % 202.78/203.09 --- 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... % 202.78/203.09 --- Run --ho-elim --full-saturate-quant at 18s... % 202.78/203.09 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 202.78/203.09 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 12s... % 202.78/203.09 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 9s... % 202.78/203.09 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 6s... % 202.78/203.09 % SZS status Theorem % 202.78/203.09 % SZS output start Proof % 202.78/203.09 ( % 202.78/203.09 (declare-sort tptp.nat 0) % 202.78/203.09 (declare-const tptp.n_1 tptp.nat) % 202.78/203.09 (declare-const tptp.y tptp.nat) % 202.78/203.09 (declare-const tptp.pl (-> tptp.nat tptp.nat tptp.nat)) % 202.78/203.09 (declare-const tptp.x tptp.nat) % 202.78/203.09 (define @t1 () (@var "Xx_0" tptp.nat)) % 202.78/203.09 (define @t2 () (_ tptp.pl tptp.x)) % 202.78/203.09 (define @t3 () (_ @t2 @t1)) % 202.78/203.09 (define @t4 () (= tptp.y @t3)) % 202.78/203.09 (define @t5 () (not @t4)) % 202.78/203.09 (define @t6 () (@list @t1)) % 202.78/203.09 (define @t7 () (forall @t6 @t5)) % 202.78/203.09 (define @t8 () (not @t7)) % 202.78/203.09 (define @t9 () (@var "Xa" Bool)) % 202.78/203.09 (define @t10 () (@var "Xx" tptp.nat)) % 202.78/203.09 (define @t11 () (_ (_ tptp.pl tptp.n_1) @t1)) % 202.78/203.09 (define @t12 () (= @t10 @t11)) % 202.78/203.09 (define @t13 () (not @t12)) % 202.78/203.09 (define @t14 () (forall @t6 @t13)) % 202.78/203.09 (define @t15 () (=> (not (not @t14)) (= @t10 tptp.n_1))) % 202.78/203.09 (define @t16 () (@list @t10)) % 202.78/203.09 (define @t17 () (forall @t16 @t15)) % 202.78/203.09 (define @t18 () (@var "Xz" tptp.nat)) % 202.78/203.09 (define @t19 () (@var "Xy" tptp.nat)) % 202.78/203.09 (define @t20 () (_ tptp.pl @t19)) % 202.78/203.09 (define @t21 () (_ @t20 @t18)) % 202.78/203.09 (define @t22 () (_ (_ tptp.pl @t21) @t1)) % 202.78/203.09 (define @t23 () (_ tptp.pl @t10)) % 202.78/203.09 (define @t24 () (_ @t23 @t18)) % 202.78/203.09 (define @t25 () (= @t24 @t22)) % 202.78/203.09 (define @t26 () (not @t25)) % 202.78/203.09 (define @t27 () (forall @t6 @t26)) % 202.78/203.09 (define @t28 () (not @t27)) % 202.78/203.09 (define @t29 () (_ @t20 @t1)) % 202.78/203.09 (define @t30 () (= @t10 @t29)) % 202.78/203.09 (define @t31 () (not @t30)) % 202.78/203.09 (define @t32 () (forall @t6 @t31)) % 202.78/203.09 (define @t33 () (not @t32)) % 202.78/203.09 (define @t34 () (=> @t33 @t28)) % 202.78/203.09 (define @t35 () (@list @t10 @t19 @t18)) % 202.78/203.09 (define @t36 () (forall @t35 @t34)) % 202.78/203.09 (define @t37 () (_ @t20 @t10)) % 202.78/203.09 (define @t38 () (_ @t23 @t19)) % 202.78/203.09 (define @t39 () (= @t38 @t37)) % 202.78/203.09 (define @t40 () (@list @t10 @t19)) % 202.78/203.09 (define @t41 () (forall @t40 @t39)) % 202.78/203.09 (define @t42 () (_ @t2 tptp.n_1)) % 202.78/203.09 (define @t43 () (= tptp.y @t42)) % 202.78/203.09 (define @t44 () (_ (_ tptp.pl @t42) @t1)) % 202.78/203.09 (define @t45 () (= tptp.y @t44)) % 202.78/203.09 (define @t46 () (not @t45)) % 202.78/203.09 (define @t47 () (forall @t6 @t46)) % 202.78/203.09 (define @t48 () (=> (not (not @t47)) @t43)) % 202.78/203.09 (define @t49 () (not @t48)) % 202.78/203.09 (define @t50 () (tptp.pl tptp.x tptp.n_1)) % 202.78/203.09 (define @t51 () (tptp.pl @t50 @t1)) % 202.78/203.09 (define @t52 () (forall @t6 (not (= tptp.y @t51)))) % 202.78/203.09 (define @t53 () (=> @t52 @t43)) % 202.78/203.09 (define @t54 () (tptp.pl tptp.x @t1)) % 202.78/203.09 (define @t55 () (forall @t6 (not (= tptp.y @t54)))) % 202.78/203.09 (define @t56 () (@quantifiers_skolemize @t55 0)) % 202.78/203.09 (define @t57 () (tptp.pl tptp.x @t56)) % 202.78/203.09 (define @t58 () (= tptp.y @t57)) % 202.78/203.09 (define @t59 () (not @t55)) % 202.78/203.09 (define @t60 () (not @t58)) % 202.78/203.09 (define @t61 () (not @t60)) % 202.78/203.09 (define @t62 () (@list true)) % 202.78/203.09 (define @t63 () (tptp.pl tptp.n_1 @t1)) % 202.78/203.09 (define @t64 () (forall @t6 (not (= @t10 @t63)))) % 202.78/203.09 (define @t65 () (= tptp.n_1 @t10)) % 202.78/203.09 (define @t66 () (= tptp.n_1 @t56)) % 202.78/203.09 (define @t67 () (not (= @t56 @t63))) % 202.78/203.09 (define @t68 () (forall @t6 @t67)) % 202.78/203.09 (define @t69 () (not @t68)) % 202.78/203.09 (define @t70 () (or @t69 @t66)) % 202.78/203.09 (define @t71 () (forall @t16 (or (not @t64) @t65))) % 202.78/203.09 (define @t72 () (forall @t6 (not (= @t63 @t56)))) % 202.78/203.09 (define @t73 () (not @t72)) % 202.78/203.09 (define @t74 () (or @t73 @t66)) % 202.78/203.09 (define @t75 () (@list false)) % 202.78/203.09 (define @t76 () (tptp.pl @t19 @t10)) % 202.78/203.09 (define @t77 () (tptp.pl @t10 @t19)) % 202.78/203.09 (define @t78 () (@quantifiers_skolemize @t72 0)) % 202.78/203.09 (define @t79 () (tptp.pl tptp.n_1 @t78)) % 202.78/203.09 (define @t80 () (tptp.pl @t79 tptp.x)) % 202.78/203.09 (define @t81 () (tptp.pl tptp.n_1 tptp.x)) % 202.78/203.09 (define @t82 () (forall @t6 (not (= (tptp.pl @t81 @t1) @t80)))) % 202.78/203.09 (define @t83 () (@quantifiers_skolemize @t82 0)) % 202.78/203.09 (define @t84 () (@var "BOUND_VARIABLE_7515" tptp.nat)) % 202.78/203.09 (define @t85 () (tptp.pl @t19 @t84)) % 202.78/203.09 (define @t86 () (tptp.pl @t85 @t18)) % 202.78/203.09 (define @t87 () (tptp.pl @t19 @t18)) % 202.78/203.09 (define @t88 () (tptp.pl @t87 @t1)) % 202.78/203.09 (define @t89 () (not (forall @t6 (not (= @t88 @t86))))) % 202.78/203.09 (define @t90 () (not (= @t86 @t88))) % 202.78/203.09 (define @t91 () (forall @t6 @t90)) % 202.78/203.09 (define @t92 () (not @t91)) % 202.78/203.09 (define @t93 () (not (= @t85 @t85))) % 202.78/203.09 (define @t94 () (or @t93 @t92)) % 202.78/203.09 (define @t95 () (@list @t19 @t18 @t84)) % 202.78/203.09 (define @t96 () (tptp.pl @t10 @t18)) % 202.78/203.09 (define @t97 () (not (forall @t6 (not (= @t96 @t88))))) % 202.78/203.09 (define @t98 () (not (= @t10 @t85))) % 202.78/203.09 (define @t99 () (or @t98 @t98 @t97)) % 202.78/203.09 (define @t100 () (or @t98 @t97)) % 202.78/203.09 (define @t101 () (forall @t16 @t100)) % 202.78/203.09 (define @t102 () (forall @t95 @t101)) % 202.78/203.09 (define @t103 () (forall (@list @t19 @t18 @t84 @t10) @t100)) % 202.78/203.09 (define @t104 () (forall (@list @t10 @t19 @t18 @t84) @t100)) % 202.78/203.09 (define @t105 () (@list @t84)) % 202.78/203.09 (define @t106 () (forall @t105 @t100)) % 202.78/203.09 (define @t107 () (forall @t105 @t98)) % 202.78/203.09 (define @t108 () (or @t107 @t97)) % 202.78/203.09 (define @t109 () (tptp.pl @t19 @t1)) % 202.78/203.09 (define @t110 () (forall @t6 (not (= @t10 @t109)))) % 202.78/203.09 (define @t111 () (not @t110)) % 202.78/203.09 (define @t112 () (tptp.pl @t81 @t83)) % 202.78/203.09 (define @t113 () (= @t80 @t112)) % 202.78/203.09 (define @t114 () (not @t82)) % 202.78/203.09 (define @t115 () (= @t112 @t80)) % 202.78/203.09 (define @t116 () (not (not @t115))) % 202.78/203.09 (define @t117 () (tptp.pl @t56 tptp.x)) % 202.78/203.09 (define @t118 () (forall @t40 (= @t77 @t76))) % 202.78/203.09 (define @t119 () (= @t117 @t57)) % 202.78/203.09 (define @t120 () (= @t57 @t117)) % 202.78/203.09 (define @t121 () (= @t56 @t79)) % 202.78/203.09 (define @t122 () (tptp.pl @t78 tptp.n_1)) % 202.78/203.09 (define @t123 () (= @t79 @t122)) % 202.78/203.09 (define @t124 () (= @t50 @t81)) % 202.78/203.09 (define @t125 () (= tptp.y (tptp.pl @t50 @t83))) % 202.78/203.09 (define @t126 () (and @t58 @t120 @t121 @t123 @t113 @t124)) % 202.78/203.09 (define @t127 () (not @t121)) % 202.78/203.09 (define @t128 () (= @t79 @t56)) % 202.78/203.09 (define @t129 () (not (not @t128))) % 202.78/203.09 (define @t130 () (= tptp.y @t50)) % 202.78/203.09 (define @t131 () (and @t58 @t66)) % 202.78/203.09 (assume @p1 @t8) % 202.78/203.09 (assume @p2 (forall (@list @t9) (=> (not (not @t9)) @t9))) % 202.78/203.09 (assume @p3 @t17) % 202.78/203.09 (assume @p4 @t36) % 202.78/203.09 (assume @p5 @t41) % 202.78/203.09 (assume @p6 @t49) % 202.78/203.09 (assume @p7 true) % 202.78/203.09 (step @p8 :rule refl :args (@t50)) % 202.78/203.09 (step @p9 :rule refl :args (@t42)) % 202.78/203.09 (step @p10 :rule cong :premises (@p9 @p8) :args ((= @t42 @t50))) % 202.78/203.09 (step @p11 :rule symm :premises (@p10)) % 202.78/203.09 (step @p12 :rule eq_resolve :premises (@p9 @p11)) % 202.78/203.09 (step @p13 :rule refl :args (tptp.y)) % 202.78/203.09 (step @p14 :rule cong :premises (@p13 @p12) :args (@t43)) % 202.78/203.09 (step @p15 :rule refl :args (@t52)) % 202.78/203.09 (step @p16 :rule cong :premises (@p15 @p14) :args (@t53)) % 202.78/203.09 (step @p17 :rule cong :premises (@p16) :args ((not @t53))) % 202.78/203.09 (step @p18 :rule refl :args (@t43)) % 202.78/203.09 (step @p19 :rule refl :args ((tptp.pl @t42 @t1))) % 202.78/203.09 (step @p20 :rule refl :args (@t1)) % 202.78/203.09 (step @p21 :rule cong :premises (@p8 @p20) :args (@t51)) % 202.78/203.09 (step @p22 :rule trans :premises (@p21 @p19)) % 202.78/203.09 (step @p23 :rule refl :args (tptp.pl)) % 202.78/203.09 (step @p24 :rule ho_cong :premises (@p23 @p8)) % 202.78/203.09 (step @p25 :rule ho_cong :premises (@p24 @p20)) % 202.78/203.09 (step @p26 :rule cong :premises (@p25 @p22) :args ((= (_ (_ tptp.pl @t50) @t1) @t51))) % 202.78/203.09 (step @p27 :rule symm :premises (@p26)) % 202.78/203.09 (step @p28 :rule refl :args (@t44)) % 202.78/203.09 (step @p29 :rule eq_resolve :premises (@p28 @p27)) % 202.78/203.09 (step @p30 :rule eq_resolve :premises (@p9 @p11)) % 202.78/203.09 (step @p31 :rule ho_cong :premises (@p23 @p30)) % 202.78/203.09 (step @p32 :rule ho_cong :premises (@p31 @p20)) % 202.78/203.09 (step @p33 :rule trans :premises (@p32 @p29)) % 202.78/203.09 (step @p34 :rule refl :args (tptp.y)) % 202.78/203.09 (step @p35 :rule cong :premises (@p34 @p33) :args (@t45)) % 202.78/203.09 (step @p36 :rule cong :premises (@p35) :args (@t46)) % 202.78/203.09 (step @p37 :rule cong :premises (@p36) :args (@t47)) % 202.78/203.09 (step @p38 :rule bool-double-not-elim :args (@t47)) % 202.78/203.09 (step @p39 :rule trans :premises (@p38 @p37)) % 202.78/203.09 (step @p40 :rule cong :premises (@p39 @p18) :args (@t48)) % 202.78/203.09 (step @p41 :rule cong :premises (@p40) :args (@t49)) % 202.78/203.09 (step @p42 :rule trans :premises (@p41 @p17)) % 202.78/203.09 (step @p43 :rule eq_resolve :premises (@p6 @p42)) % 202.78/203.09 (step @p44 :rule not_implies_elim2 :premises (@p43)) % 202.78/203.09 (step @p45 :rule refl :args (@t54)) % 202.78/203.09 (step @p46 :rule refl :args (@t3)) % 202.78/203.09 (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t3 @t54))) % 202.78/203.09 (step @p48 :rule symm :premises (@p47)) % 202.78/203.09 (step @p49 :rule eq_resolve :premises (@p46 @p48)) % 202.78/203.09 (step @p50 :rule cong :premises (@p34 @p49) :args (@t4)) % 202.78/203.09 (step @p51 :rule cong :premises (@p50) :args (@t5)) % 202.78/203.09 (step @p52 :rule cong :premises (@p51) :args (@t7)) % 202.78/203.09 (step @p53 :rule cong :premises (@p52) :args (@t8)) % 202.78/203.09 (step @p54 :rule eq_resolve :premises (@p1 @p53)) % 202.78/203.09 (step @p55 :rule refl :args (@t58)) % 202.78/203.09 (step @p56 :rule bool-double-not-elim :args (@t55)) % 202.78/203.09 (step @p57 :rule nary_cong :premises (@p56 @p55) :args ((or (not @t59) @t58))) % 202.78/203.09 (step @p58 :rule bool-double-not-elim :args (@t58)) % 202.78/203.09 (step @p59 :rule refl :args (@t59)) % 202.78/203.09 (step @p60 :rule cong :premises (@p59 @p58) :args ((=> @t59 @t61))) % 202.78/203.09 (assume-push @p304 @t59) % 202.78/203.09 (step @p62 :rule skolemize :premises (@p54)) % 202.78/203.09 (step-pop @p305 :rule scope :premises (@p62)) % 202.78/203.09 (step @p63 :rule process_scope :premises (@p305) :args (@t61)) % 202.78/203.09 (step @p65 :rule eq_resolve :premises (@p63 @p60)) % 202.78/203.09 (step @p66 :rule implies_elim :premises (@p65)) % 202.78/203.09 (step @p67 :rule eq_resolve :premises (@p66 @p57)) % 202.78/203.09 (step @p68 :rule chain_m_resolution :premises (@p67 @p54) :args (@t58 @t62 (@list @t55))) % 202.78/203.09 (step @p69 :rule bool-impl-elim :args (@t64 @t65)) % 202.78/203.09 (step @p70 :rule cong :premises (@p69) :args ((forall @t16 (=> @t64 @t65)))) % 202.78/203.09 (step @p71 :rule eq-symm :args (@t10 tptp.n_1)) % 202.78/203.09 (step @p72 :rule refl :args (@t63)) % 202.78/203.09 (step @p73 :rule refl :args (@t11)) % 202.78/203.09 (step @p74 :rule cong :premises (@p73 @p72) :args ((= @t11 @t63))) % 202.78/203.09 (step @p75 :rule symm :premises (@p74)) % 202.78/203.09 (step @p76 :rule eq_resolve :premises (@p73 @p75)) % 202.78/203.09 (step @p77 :rule refl :args (@t10)) % 202.78/203.09 (step @p78 :rule cong :premises (@p77 @p76) :args (@t12)) % 202.78/203.09 (step @p79 :rule cong :premises (@p78) :args (@t13)) % 202.78/203.09 (step @p80 :rule cong :premises (@p79) :args (@t14)) % 202.78/203.09 (step @p81 :rule bool-double-not-elim :args (@t14)) % 202.78/203.09 (step @p82 :rule trans :premises (@p81 @p80)) % 202.78/203.09 (step @p83 :rule cong :premises (@p82 @p71) :args (@t15)) % 202.78/203.09 (step @p84 :rule cong :premises (@p83) :args (@t17)) % 202.78/203.09 (step @p85 :rule trans :premises (@p84 @p70)) % 202.78/203.09 (step @p86 :rule eq_resolve :premises (@p3 @p85)) % 202.78/203.09 (step @p87 :rule refl :args (@t66)) % 202.78/203.09 (step @p88 :rule eq-symm :args (@t56 @t63)) % 202.78/203.09 (step @p89 :rule cong :premises (@p88) :args (@t67)) % 202.78/203.09 (step @p90 :rule cong :premises (@p89) :args (@t68)) % 202.78/203.09 (step @p91 :rule cong :premises (@p90) :args (@t69)) % 202.78/203.09 (step @p92 :rule nary_cong :premises (@p91 @p87) :args (@t70)) % 202.78/203.09 (step @p93 :rule refl :args (@t71)) % 202.78/203.09 (step @p94 :rule cong :premises (@p93 @p92) :args ((=> @t71 @t70))) % 202.78/203.09 (assume-push @p306 @t71) % 202.78/203.09 (step @p96 :rule instantiate :premises (@p86) :args ((@list @t56))) % 202.78/203.09 (step-pop @p307 :rule scope :premises (@p96)) % 202.78/203.09 (step @p97 :rule process_scope :premises (@p307) :args (@t70)) % 202.78/203.09 (step @p99 :rule eq_resolve :premises (@p97 @p94)) % 202.78/203.09 (step @p100 :rule implies_elim :premises (@p99)) % 202.78/203.09 (step @p101 :rule chain_m_resolution :premises (@p100 @p86) :args (@t74 @t75 (@list @t71))) % 202.78/203.09 (step @p102 :rule refl :args (@t76)) % 202.78/203.09 (step @p103 :rule refl :args (@t37)) % 202.78/203.09 (step @p104 :rule cong :premises (@p103 @p102) :args ((= @t37 @t76))) % 202.78/203.09 (step @p105 :rule symm :premises (@p104)) % 202.78/203.09 (step @p106 :rule eq_resolve :premises (@p103 @p105)) % 202.78/203.09 (step @p107 :rule refl :args (@t77)) % 202.78/203.09 (step @p108 :rule refl :args (@t38)) % 202.78/203.09 (step @p109 :rule cong :premises (@p108 @p107) :args ((= @t38 @t77))) % 202.78/203.09 (step @p110 :rule symm :premises (@p109)) % 202.78/203.09 (step @p111 :rule eq_resolve :premises (@p108 @p110)) % 202.78/203.09 (step @p112 :rule cong :premises (@p111 @p106) :args (@t39)) % 202.78/203.09 (step @p113 :rule cong :premises (@p112) :args (@t41)) % 202.78/203.09 (step @p114 :rule eq_resolve :premises (@p5 @p113)) % 202.78/203.09 (step @p115 :rule instantiate :premises (@p114) :args ((@list tptp.x tptp.n_1))) % 202.78/203.09 (step @p116 :rule not_implies_elim1 :premises (@p43)) % 202.78/203.09 (step @p117 :rule instantiate :premises (@p116) :args ((@list @t83))) % 202.78/203.09 (step @p118 :rule aci_norm :args ((= (or false @t89) @t89))) % 202.78/203.09 (step @p119 :rule eq-symm :args (@t86 @t88)) % 202.78/203.09 (step @p120 :rule cong :premises (@p119) :args (@t90)) % 202.78/203.09 (step @p121 :rule cong :premises (@p120) :args (@t91)) % 202.78/203.09 (step @p122 :rule cong :premises (@p121) :args (@t92)) % 202.78/203.09 (step @p123 :rule evaluate :args ((not true))) % 202.78/203.09 (step @p124 :rule eq-refl :args (@t85)) % 202.78/203.09 (step @p125 :rule cong :premises (@p124) :args (@t93)) % 202.78/203.09 (step @p126 :rule trans :premises (@p125 @p123)) % 202.78/203.09 (step @p127 :rule nary_cong :premises (@p126 @p122) :args (@t94)) % 202.78/203.09 (step @p128 :rule trans :premises (@p127 @p118)) % 202.78/203.09 (step @p129 :rule cong :premises (@p128) :args ((forall @t95 @t94))) % 202.78/203.09 (step @p130 :rule quant-var-elim-eq :args ((= (forall @t16 @t99) @t94))) % 202.78/203.09 (step @p131 :rule aci_norm :args ((= @t100 @t99))) % 202.78/203.09 (step @p132 :rule cong :premises (@p131) :args (@t101)) % 202.78/203.09 (step @p133 :rule trans :premises (@p132 @p130)) % 202.78/203.09 (step @p134 :rule cong :premises (@p133) :args (@t102)) % 202.78/203.09 (step @p135 :rule quant-merge-prenex :args ((= @t102 @t103))) % 202.78/203.09 (step @p136 :rule symm :premises (@p135)) % 202.78/203.09 (step @p137 :rule quant_var_reordering :args ((= @t104 @t103))) % 202.78/203.09 (step @p138 :rule trans :premises (@p137 @p136 @p134)) % 202.78/203.09 (step @p139 :rule trans :premises (@p138 @p129)) % 202.78/203.09 (step @p140 :rule quant-merge-prenex :args ((= (forall @t35 @t106) @t104))) % 202.78/203.09 (step @p141 :rule refl :args (@t97)) % 202.78/203.09 (step @p142 :rule alpha_equiv :args (@t107 (@list @t84) (@list @t1))) % 202.78/203.09 (step @p143 :rule nary_cong :premises (@p142 @p141) :args (@t108)) % 202.78/203.09 (step @p144 :rule quant-miniscope-or :args ((= @t106 @t108))) % 202.78/203.09 (step @p145 :rule trans :premises (@p144 @p143)) % 202.78/203.09 (step @p146 :rule symm :premises (@p145)) % 202.78/203.09 (step @p147 :rule cong :premises (@p146) :args ((forall @t35 (or @t110 @t97)))) % 202.78/203.09 (step @p148 :rule trans :premises (@p147 @p140)) % 202.78/203.09 (step @p149 :rule trans :premises (@p148 @p139)) % 202.78/203.09 (step @p150 :rule bool-double-not-elim :args (@t110)) % 202.78/203.09 (step @p151 :rule nary_cong :premises (@p150 @p141) :args ((or (not @t111) @t97))) % 202.78/203.09 (step @p152 :rule bool-impl-elim :args (@t111 @t97)) % 202.78/203.09 (step @p153 :rule trans :premises (@p152 @p151)) % 202.78/203.09 (step @p154 :rule cong :premises (@p153) :args ((forall @t35 (=> @t111 @t97)))) % 202.78/203.09 (step @p155 :rule trans :premises (@p154 @p149)) % 202.78/203.09 (step @p156 :rule refl :args ((tptp.pl @t21 @t1))) % 202.78/203.09 (step @p157 :rule refl :args (@t87)) % 202.78/203.09 (step @p158 :rule cong :premises (@p157 @p20) :args (@t88)) % 202.78/203.09 (step @p159 :rule trans :premises (@p158 @p156)) % 202.78/203.09 (step @p160 :rule ho_cong :premises (@p23 @p157)) % 202.78/203.09 (step @p161 :rule ho_cong :premises (@p160 @p20)) % 202.78/203.09 (step @p162 :rule cong :premises (@p161 @p159) :args ((= (_ (_ tptp.pl @t87) @t1) @t88))) % 202.78/203.09 (step @p163 :rule symm :premises (@p162)) % 202.78/203.09 (step @p164 :rule refl :args (@t22)) % 202.78/203.09 (step @p165 :rule eq_resolve :premises (@p164 @p163)) % 202.78/203.09 (step @p166 :rule refl :args (@t21)) % 202.78/203.09 (step @p167 :rule cong :premises (@p166 @p157) :args ((= @t21 @t87))) % 202.78/203.09 (step @p168 :rule symm :premises (@p167)) % 202.78/203.09 (step @p169 :rule eq_resolve :premises (@p166 @p168)) % 202.78/203.09 (step @p170 :rule ho_cong :premises (@p23 @p169)) % 202.78/203.09 (step @p171 :rule ho_cong :premises (@p170 @p20)) % 202.78/203.09 (step @p172 :rule trans :premises (@p171 @p165)) % 202.78/203.09 (step @p173 :rule refl :args (@t96)) % 202.78/203.09 (step @p174 :rule refl :args (@t24)) % 202.78/203.09 (step @p175 :rule cong :premises (@p174 @p173) :args ((= @t24 @t96))) % 202.78/203.09 (step @p176 :rule symm :premises (@p175)) % 202.78/203.09 (step @p177 :rule eq_resolve :premises (@p174 @p176)) % 202.78/203.09 (step @p178 :rule cong :premises (@p177 @p172) :args (@t25)) % 202.78/203.09 (step @p179 :rule cong :premises (@p178) :args (@t26)) % 202.78/203.09 (step @p180 :rule cong :premises (@p179) :args (@t27)) % 202.78/203.09 (step @p181 :rule cong :premises (@p180) :args (@t28)) % 202.78/203.09 (step @p182 :rule refl :args (@t109)) % 202.78/203.09 (step @p183 :rule refl :args (@t29)) % 202.78/203.09 (step @p184 :rule cong :premises (@p183 @p182) :args ((= @t29 @t109))) % 202.78/203.09 (step @p185 :rule symm :premises (@p184)) % 202.78/203.09 (step @p186 :rule eq_resolve :premises (@p183 @p185)) % 202.78/203.09 (step @p187 :rule cong :premises (@p77 @p186) :args (@t30)) % 202.78/203.09 (step @p188 :rule cong :premises (@p187) :args (@t31)) % 202.78/203.09 (step @p189 :rule cong :premises (@p188) :args (@t32)) % 202.78/203.09 (step @p190 :rule cong :premises (@p189) :args (@t33)) % 202.78/203.09 (step @p191 :rule cong :premises (@p190 @p181) :args (@t34)) % 202.78/203.09 (step @p192 :rule cong :premises (@p191) :args (@t36)) % 202.78/203.09 (step @p193 :rule trans :premises (@p192 @p155)) % 202.78/203.09 (step @p194 :rule eq_resolve :premises (@p4 @p193)) % 202.78/203.09 (step @p195 :rule instantiate :premises (@p194) :args ((@list tptp.n_1 tptp.x @t78))) % 202.78/203.09 (step @p196 :rule refl :args (@t113)) % 202.78/203.09 (step @p197 :rule bool-double-not-elim :args (@t82)) % 202.78/203.09 (step @p198 :rule nary_cong :premises (@p197 @p196) :args ((or (not @t114) @t113))) % 202.78/203.09 (step @p199 :rule eq-symm :args (@t112 @t80)) % 202.78/203.09 (step @p200 :rule bool-double-not-elim :args (@t115)) % 202.78/203.09 (step @p201 :rule trans :premises (@p200 @p199)) % 202.78/203.09 (step @p202 :rule refl :args (@t114)) % 202.78/203.09 (step @p203 :rule cong :premises (@p202 @p201) :args ((=> @t114 @t116))) % 202.78/203.09 (assume-push @p308 @t114) % 202.78/203.09 (step @p205 :rule skolemize :premises (@p195)) % 202.78/203.09 (step-pop @p309 :rule scope :premises (@p205)) % 202.78/203.09 (step @p206 :rule process_scope :premises (@p309) :args (@t116)) % 202.78/203.09 (step @p208 :rule eq_resolve :premises (@p206 @p203)) % 202.78/203.09 (step @p209 :rule implies_elim :premises (@p208)) % 202.78/203.09 (step @p210 :rule eq_resolve :premises (@p209 @p198)) % 202.78/203.09 (step @p211 :rule chain_m_resolution :premises (@p210 @p195) :args (@t113 @t62 (@list @t82))) % 202.78/203.09 (step @p212 :rule instantiate :premises (@p114) :args ((@list tptp.n_1 @t78))) % 202.78/203.09 (step @p213 :rule eq-symm :args (@t117 @t57)) % 202.78/203.09 (step @p214 :rule refl :args (@t118)) % 202.78/203.09 (step @p215 :rule cong :premises (@p214 @p213) :args ((=> @t118 @t119))) % 202.78/203.09 (assume-push @p310 @t118) % 202.78/203.09 (step @p217 :rule instantiate :premises (@p114) :args ((@list @t56 tptp.x))) % 202.78/203.09 (step-pop @p311 :rule scope :premises (@p217)) % 202.78/203.09 (step @p218 :rule process_scope :premises (@p311) :args (@t119)) % 202.78/203.09 (step @p220 :rule eq_resolve :premises (@p218 @p215)) % 202.78/203.09 (step @p221 :rule implies_elim :premises (@p220)) % 202.78/203.09 (step @p222 :rule chain_m_resolution :premises (@p221 @p114) :args (@t120 @t75 (@list @t118))) % 202.78/203.09 (assume-push @p312 @t58) % 202.78/203.09 (assume-push @p313 @t120) % 202.78/203.09 (assume-push @p314 @t121) % 202.78/203.09 (assume-push @p315 @t123) % 202.78/203.09 (assume-push @p316 @t113) % 202.78/203.09 (assume-push @p317 @t124) % 202.78/203.09 (assume-push @p318 @t124) % 202.78/203.09 (assume-push @p319 @t113) % 202.78/203.09 (assume-push @p320 @t123) % 202.78/203.09 (assume-push @p321 @t121) % 202.78/203.09 (assume-push @p322 @t120) % 202.78/203.09 (assume-push @p323 @t58) % 202.78/203.09 (step @p235 :rule refl :args (@t83)) % 202.78/203.09 (step @p236 :rule symm :premises (@p115)) % 202.78/203.09 (step @p237 :rule cong :premises (@p236 @p235) :args (@t112)) % 202.78/203.09 (step @p238 :rule refl :args (tptp.x)) % 202.78/203.09 (step @p239 :rule symm :premises (@p212)) % 202.78/203.09 (step @p240 :rule cong :premises (@p239 @p238) :args ((tptp.pl @t122 tptp.x))) % 202.78/203.09 (step @p241 :rule trans :premises (@p314 @p212)) % 202.78/203.09 (step @p242 :rule cong :premises (@p241 @p238) :args (@t117)) % 202.78/203.09 (step @p243 :rule trans :premises (@p68 @p222 @p242 @p240 @p211 @p237)) % 202.78/203.09 (step-pop @p324 :rule scope :premises (@p243)) % 202.78/203.09 (step-pop @p325 :rule scope :premises (@p324)) % 202.78/203.09 (step-pop @p326 :rule scope :premises (@p325)) % 202.78/203.09 (step-pop @p327 :rule scope :premises (@p326)) % 202.78/203.09 (step-pop @p328 :rule scope :premises (@p327)) % 202.78/203.09 (step-pop @p329 :rule scope :premises (@p328)) % 202.78/203.09 (step @p244 :rule process_scope :premises (@p329) :args (@t125)) % 202.78/203.09 (step @p251 :rule and_intro :premises (@p115 @p211 @p212 @p314 @p222 @p68)) % 202.78/203.09 (step @p252 :rule modus_ponens :premises (@p251 @p244)) % 202.78/203.09 (step-pop @p330 :rule scope :premises (@p252)) % 202.78/203.09 (step-pop @p331 :rule scope :premises (@p330)) % 202.78/203.09 (step-pop @p332 :rule scope :premises (@p331)) % 202.78/203.09 (step-pop @p333 :rule scope :premises (@p332)) % 202.78/203.09 (step-pop @p334 :rule scope :premises (@p333)) % 202.78/203.09 (step-pop @p335 :rule scope :premises (@p334)) % 202.78/203.09 (step @p253 :rule process_scope :premises (@p335) :args (@t125)) % 202.78/203.09 (step @p260 :rule implies_elim :premises (@p253)) % 202.78/203.09 (step @p261 :rule cnf_and_neg :args (@t126)) % 202.78/203.09 (step @p262 :rule resolution :premises (@p261 @p260) :args (true @t126)) % 202.78/203.09 (step @p263 :rule reordering :premises (@p262) :args ((or @t60 (not @t120) @t127 (not @t123) (not @t113) @t125 (not @t124)))) % 202.78/203.09 (step @p264 :rule chain_m_resolution :premises (@p263 @p68 @p222 @p212 @p211 @p117 @p115) :args (@t127 (@list false false false false true false) (@list @t58 @t120 @t123 @t113 @t125 @t124))) % 202.78/203.09 (step @p265 :rule refl :args (@t121)) % 202.78/203.09 (step @p266 :rule bool-double-not-elim :args (@t72)) % 202.78/203.09 (step @p267 :rule nary_cong :premises (@p266 @p265) :args ((or (not @t73) @t121))) % 202.78/203.09 (step @p268 :rule eq-symm :args (@t79 @t56)) % 202.78/203.09 (step @p269 :rule bool-double-not-elim :args (@t128)) % 202.78/203.09 (step @p270 :rule trans :premises (@p269 @p268)) % 202.78/203.09 (step @p271 :rule refl :args (@t73)) % 202.78/203.09 (step @p272 :rule cong :premises (@p271 @p270) :args ((=> @t73 @t129))) % 202.78/203.09 (assume-push @p336 @t73) % 202.78/203.09 (step @p274 :rule skolemize :premises (@p336)) % 202.78/203.09 (step-pop @p337 :rule scope :premises (@p274)) % 202.78/203.09 (step @p275 :rule process_scope :premises (@p337) :args (@t129)) % 202.78/203.09 (step @p277 :rule eq_resolve :premises (@p275 @p272)) % 202.78/203.09 (step @p278 :rule implies_elim :premises (@p277)) % 202.78/203.09 (step @p279 :rule eq_resolve :premises (@p278 @p267)) % 202.78/203.09 (step @p280 :rule chain_m_resolution :premises (@p279 @p264) :args (@t72 @t62 (@list @t121))) % 202.78/203.09 (step @p281 :rule cnf_or_pos :args (@t74)) % 202.78/203.09 (step @p282 :rule reordering :premises (@p281) :args ((or @t66 @t73 (not @t74)))) % 202.78/203.09 (step @p283 :rule chain_m_resolution :premises (@p282 @p280 @p101) :args (@t66 (@list false false) (@list @t72 @t74))) % 202.78/203.09 (assume-push @p338 @t58) % 202.78/203.09 (assume-push @p339 @t66) % 202.78/203.09 (assume-push @p340 @t66) % 202.78/203.09 (assume-push @p341 @t58) % 202.78/203.09 (step @p288 :rule symm :premises (@p339)) % 202.78/203.09 (step @p238 :rule refl :args (tptp.x)) % 202.78/203.09 (step @p289 :rule cong :premises (@p238 @p288) :args (@t57)) % 202.78/203.09 (step @p290 :rule trans :premises (@p68 @p289)) % 202.78/203.09 (step-pop @p342 :rule scope :premises (@p290)) % 202.78/203.09 (step-pop @p343 :rule scope :premises (@p342)) % 202.78/203.09 (step @p291 :rule process_scope :premises (@p343) :args (@t130)) % 202.78/203.09 (step @p294 :rule and_intro :premises (@p339 @p68)) % 202.78/203.09 (step @p295 :rule modus_ponens :premises (@p294 @p291)) % 202.78/203.09 (step-pop @p344 :rule scope :premises (@p295)) % 202.78/203.09 (step-pop @p345 :rule scope :premises (@p344)) % 202.78/203.09 (step @p296 :rule process_scope :premises (@p345) :args (@t130)) % 202.78/203.09 (step @p299 :rule implies_elim :premises (@p296)) % 202.78/203.09 (step @p300 :rule cnf_and_neg :args (@t131)) % 202.78/203.09 (step @p301 :rule resolution :premises (@p300 @p299) :args (true @t131)) % 202.78/203.09 (step @p302 :rule reordering :premises (@p301) :args ((or @t130 @t60 (not @t66)))) % 202.78/203.09 (step @p303 false :rule chain_m_resolution :premises (@p302 @p283 @p68 @p44) :args (false (@list false false true) (@list @t66 @t58 @t130))) % 202.78/203.09 ) % 202.78/203.09 % SZS output end Proof % 202.78/203.09 % cvc5 exiting %------------------------------------------------------------------------------