%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO268^5 : 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 : n003.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 09:12:20 AM UTC 2026 % Result : Theorem 7.41s 7.60s % Output : Proof 7.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO268^5 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n003.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Wed Jun 3 00:01:29 EDT 2026 % 0.18/0.35 % CPUTime : % 0.28/0.49 %----Proving TH0 % 7.41/7.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 7.41/7.60 % SZS status Theorem % 7.41/7.60 % SZS output start Proof % 7.41/7.60 ( % 7.41/7.60 (declare-sort tptp.b 0) % 7.41/7.60 (declare-sort tptp.a 0) % 7.41/7.60 (declare-const tptp.r (-> tptp.a tptp.b Bool)) % 7.41/7.60 (define @t1 () (@var "Xx" tptp.a)) % 7.41/7.60 (define @t2 () (@var "Xf" (-> tptp.a tptp.b))) % 7.41/7.60 (define @t3 () (_ @t2 @t1)) % 7.41/7.60 (define @t4 () (_ tptp.r @t1)) % 7.41/7.60 (define @t5 () (_ @t4 @t3)) % 7.41/7.60 (define @t6 () (@list @t1)) % 7.41/7.60 (define @t7 () (forall @t6 @t5)) % 7.41/7.60 (define @t8 () (@list @t2)) % 7.41/7.60 (define @t9 () (exists @t8 @t7)) % 7.41/7.60 (define @t10 () (@var "Xy" tptp.b)) % 7.41/7.60 (define @t11 () (_ @t4 @t10)) % 7.41/7.60 (define @t12 () (@list @t10)) % 7.41/7.60 (define @t13 () (exists @t12 @t11)) % 7.41/7.60 (define @t14 () (forall @t6 @t13)) % 7.41/7.60 (define @t15 () (= @t14 @t9)) % 7.41/7.60 (define @t16 () (@var "Xp" (-> tptp.b Bool))) % 7.41/7.60 (define @t17 () (@var "Xj" (-> (-> tptp.b Bool) tptp.b))) % 7.41/7.60 (define @t18 () (_ @t17 @t16)) % 7.41/7.60 (define @t19 () (_ @t16 @t18)) % 7.41/7.60 (define @t20 () (@var "Xx" tptp.b)) % 7.41/7.60 (define @t21 () (_ @t16 @t20)) % 7.41/7.60 (define @t22 () (@list @t20)) % 7.41/7.60 (define @t23 () (exists @t22 @t21)) % 7.41/7.60 (define @t24 () (=> @t23 @t19)) % 7.41/7.60 (define @t25 () (@list @t16)) % 7.41/7.60 (define @t26 () (forall @t25 @t24)) % 7.41/7.60 (define @t27 () (@list @t17)) % 7.41/7.60 (define @t28 () (exists @t27 @t26)) % 7.41/7.60 (define @t29 () (=> @t28 @t15)) % 7.41/7.60 (define @t30 () (not @t29)) % 7.41/7.60 (define @t31 () (_ @t2 @t1)) % 7.41/7.60 (define @t32 () (tptp.r @t1 @t31)) % 7.41/7.60 (define @t33 () (forall @t6 @t32)) % 7.41/7.60 (define @t34 () (forall @t8 (not @t33))) % 7.41/7.60 (define @t35 () (tptp.r @t1 @t10)) % 7.41/7.60 (define @t36 () (forall @t6 (not (forall @t12 (not @t35))))) % 7.41/7.60 (define @t37 () (not @t36)) % 7.41/7.60 (define @t38 () (not @t34)) % 7.41/7.60 (define @t39 () (not @t38)) % 7.41/7.60 (define @t40 () (not @t11)) % 7.41/7.60 (define @t41 () (forall @t12 @t40)) % 7.41/7.60 (define @t42 () (not @t41)) % 7.41/7.60 (define @t43 () (_ @t17 @t16)) % 7.41/7.60 (define @t44 () (_ @t16 @t43)) % 7.41/7.60 (define @t45 () (@var "BOUND_VARIABLE_7459" tptp.b)) % 7.41/7.60 (define @t46 () (not (_ @t16 @t45))) % 7.41/7.60 (define @t47 () (or @t46 @t44)) % 7.41/7.60 (define @t48 () (@list @t16 @t45)) % 7.41/7.60 (define @t49 () (forall @t48 @t47)) % 7.41/7.60 (define @t50 () (forall @t27 (not @t49))) % 7.41/7.60 (define @t51 () (not @t50)) % 7.41/7.60 (define @t52 () (@list @t45)) % 7.41/7.60 (define @t53 () (forall @t52 @t47)) % 7.41/7.60 (define @t54 () (forall @t52 @t46)) % 7.41/7.60 (define @t55 () (or @t54 @t44)) % 7.41/7.60 (define @t56 () (_ @t16 @t20)) % 7.41/7.60 (define @t57 () (forall @t22 (not @t56))) % 7.41/7.60 (define @t58 () (or @t57 @t19)) % 7.41/7.60 (define @t59 () (not @t57)) % 7.41/7.60 (define @t60 () (not @t21)) % 7.41/7.60 (define @t61 () (forall @t22 @t60)) % 7.41/7.60 (define @t62 () (not @t61)) % 7.41/7.60 (define @t63 () (@quantifiers_skolemize @t50 0)) % 7.41/7.60 (define @t64 () (_ @t63 @t4)) % 7.41/7.60 (define @t65 () (forall @t6 (tptp.r @t1 @t64))) % 7.41/7.60 (define @t66 () (@quantifiers_skolemize @t65 0)) % 7.41/7.60 (define @t67 () (forall @t12 (not (tptp.r @t66 @t10)))) % 7.41/7.60 (define @t68 () (not @t67)) % 7.41/7.60 (define @t69 () (@var "BOUND_VARIABLE_65419" tptp.a)) % 7.41/7.60 (define @t70 () (lambda (@list @t69) (_ @t63 (_ tptp.r @t69)))) % 7.41/7.60 (define @t71 () (_ @t70 @t1)) % 7.41/7.60 (define @t72 () (tptp.r @t1 @t71)) % 7.41/7.60 (define @t73 () (forall @t6 @t72)) % 7.41/7.60 (define @t74 () (not @t73)) % 7.41/7.60 (define @t75 () (@quantifiers_skolemize @t67 0)) % 7.41/7.60 (define @t76 () (tptp.r @t66 @t75)) % 7.41/7.60 (define @t77 () (not @t76)) % 7.41/7.60 (define @t78 () (not @t77)) % 7.41/7.60 (define @t79 () (_ tptp.r @t66)) % 7.41/7.60 (define @t80 () (_ @t63 @t79)) % 7.41/7.60 (define @t81 () (tptp.r @t66 @t80)) % 7.41/7.60 (define @t82 () (not @t81)) % 7.41/7.60 (define @t83 () (not @t65)) % 7.41/7.60 (define @t84 () (forall @t48 (or @t46 (_ @t16 (_ @t63 @t16))))) % 7.41/7.60 (define @t85 () (not (not @t84))) % 7.41/7.60 (define @t86 () (@list true)) % 7.41/7.60 (define @t87 () (_ @t63 @t79)) % 7.41/7.60 (define @t88 () (_ @t79 @t80)) % 7.41/7.60 (define @t89 () (_ @t79 @t75)) % 7.41/7.60 (define @t90 () (not @t89)) % 7.41/7.60 (define @t91 () (or @t90 @t88)) % 7.41/7.60 (define @t92 () (_ @t79 @t80)) % 7.41/7.60 (define @t93 () (_ @t79 @t75)) % 7.41/7.60 (define @t94 () (not @t93)) % 7.41/7.60 (define @t95 () (or @t94 @t92)) % 7.41/7.60 (define @t96 () (or @t77 @t81)) % 7.41/7.60 (define @t97 () (@list false)) % 7.41/7.60 (define @t98 () (@list @t84)) % 7.41/7.60 (define @t99 () (@list @t36)) % 7.41/7.60 (define @t100 () (@quantifiers_skolemize @t34 0)) % 7.41/7.60 (define @t101 () (forall @t6 (tptp.r @t1 (_ @t100 @t1)))) % 7.41/7.60 (define @t102 () (not @t101)) % 7.41/7.60 (define @t103 () (not @t102)) % 7.41/7.60 (define @t104 () (@quantifiers_skolemize @t36 0)) % 7.41/7.60 (define @t105 () (_ tptp.r @t104)) % 7.41/7.60 (define @t106 () (@var "BOUND_VARIABLE_29146" tptp.b)) % 7.41/7.60 (define @t107 () (lambda (@list @t106) (tptp.r @t104 @t106))) % 7.41/7.60 (define @t108 () (_ @t63 @t107)) % 7.41/7.60 (define @t109 () (tptp.r @t104 @t108)) % 7.41/7.60 (define @t110 () (_ @t100 @t104)) % 7.41/7.60 (define @t111 () (@purify @t110)) % 7.41/7.60 (define @t112 () (tptp.r @t104 @t111)) % 7.41/7.60 (define @t113 () (not @t112)) % 7.41/7.60 (define @t114 () (or @t113 @t109)) % 7.41/7.60 (define @t115 () (_ @t107 @t108)) % 7.41/7.60 (define @t116 () (_ @t107 @t111)) % 7.41/7.60 (define @t117 () (not @t116)) % 7.41/7.60 (define @t118 () (or @t117 @t115)) % 7.41/7.60 (define @t119 () (_ @t63 @t105)) % 7.41/7.60 (define @t120 () (tptp.r @t104 @t119)) % 7.41/7.60 (define @t121 () (or @t113 @t120)) % 7.41/7.60 (define @t122 () (forall @t12 (not (tptp.r @t104 @t10)))) % 7.41/7.60 (define @t123 () (not (not @t122))) % 7.41/7.60 (define @t124 () (@var "x" tptp.b)) % 7.41/7.60 (define @t125 () (forall (@list @t124) (not (tptp.r @t104 @t124)))) % 7.41/7.60 (define @t126 () (not @t120)) % 7.41/7.60 (define @t127 () (@list true false)) % 7.41/7.60 (define @t128 () (tptp.r @t104 @t110)) % 7.41/7.60 (define @t129 () (not @t128)) % 7.41/7.60 (define @t130 () (= @t110 @t111)) % 7.41/7.60 (define @t131 () (not @t130)) % 7.41/7.60 (define @t132 () (and @t130 @t113)) % 7.41/7.60 (assume @p1 @t30) % 7.41/7.60 (assume @p2 true) % 7.41/7.60 (step @p3 :rule bool-double-not-elim :args (@t34)) % 7.41/7.60 (step @p4 :rule refl :args (@t37)) % 7.41/7.60 (step @p5 :rule nary_cong :premises (@p4 @p3) :args ((or @t37 @t39))) % 7.41/7.60 (step @p6 :rule exists-elim :args ((= (exists @t8 @t33) @t38))) % 7.41/7.60 (step @p7 :rule refl :args ((tptp.r @t1 @t3))) % 7.41/7.60 (step @p8 :rule refl :args (@t31)) % 7.41/7.60 (step @p9 :rule refl :args (@t1)) % 7.41/7.60 (step @p10 :rule cong :premises (@p9 @p8) :args (@t32)) % 7.41/7.60 (step @p11 :rule trans :premises (@p10 @p7)) % 7.41/7.60 (step @p12 :rule refl :args (@t4)) % 7.41/7.60 (step @p13 :rule ho_cong :premises (@p12 @p8)) % 7.41/7.60 (step @p14 :rule cong :premises (@p13 @p11) :args ((= (_ @t4 @t31) @t32))) % 7.41/7.60 (step @p15 :rule symm :premises (@p14)) % 7.41/7.60 (step @p16 :rule refl :args (@t5)) % 7.41/7.60 (step @p17 :rule eq_resolve :premises (@p16 @p15)) % 7.41/7.60 (step @p18 :rule refl :args (@t3)) % 7.41/7.60 (step @p19 :rule cong :premises (@p18 @p8) :args ((= @t3 @t31))) % 7.41/7.60 (step @p20 :rule symm :premises (@p19)) % 7.41/7.60 (step @p21 :rule eq_resolve :premises (@p18 @p20)) % 7.41/7.60 (step @p22 :rule ho_cong :premises (@p12 @p21)) % 7.41/7.60 (step @p23 :rule trans :premises (@p22 @p17)) % 7.41/7.60 (step @p24 :rule cong :premises (@p23) :args (@t7)) % 7.41/7.60 (step @p25 :rule cong :premises (@p24) :args (@t9)) % 7.41/7.60 (step @p26 :rule trans :premises (@p25 @p6)) % 7.41/7.60 (step @p27 :rule refl :args (@t35)) % 7.41/7.60 (step @p28 :rule refl :args (@t11)) % 7.41/7.60 (step @p29 :rule cong :premises (@p28 @p27) :args ((= @t11 @t35))) % 7.41/7.60 (step @p30 :rule symm :premises (@p29)) % 7.41/7.60 (step @p31 :rule eq_resolve :premises (@p28 @p30)) % 7.41/7.60 (step @p32 :rule cong :premises (@p31) :args (@t40)) % 7.41/7.60 (step @p33 :rule cong :premises (@p32) :args (@t41)) % 7.41/7.60 (step @p34 :rule cong :premises (@p33) :args (@t42)) % 7.41/7.60 (step @p35 :rule exists-elim :args ((= @t13 @t42))) % 7.41/7.60 (step @p36 :rule trans :premises (@p35 @p34)) % 7.41/7.60 (step @p37 :rule cong :premises (@p36) :args (@t14)) % 7.41/7.60 (step @p38 :rule cong :premises (@p37 @p26) :args (@t15)) % 7.41/7.60 (step @p39 :rule exists-elim :args ((= (exists @t27 @t49) @t51))) % 7.41/7.60 (step @p40 :rule quant-merge-prenex :args ((= (forall @t25 @t53) @t49))) % 7.41/7.60 (step @p41 :rule refl :args (@t44)) % 7.41/7.60 (step @p42 :rule alpha_equiv :args (@t54 (@list @t45) (@list @t20))) % 7.41/7.60 (step @p43 :rule nary_cong :premises (@p42 @p41) :args (@t55)) % 7.41/7.60 (step @p44 :rule quant-miniscope-or :args ((= @t53 @t55))) % 7.41/7.60 (step @p45 :rule trans :premises (@p44 @p43)) % 7.41/7.60 (step @p46 :rule symm :premises (@p45)) % 7.41/7.60 (step @p47 :rule cong :premises (@p46) :args ((forall @t25 (or @t57 @t44)))) % 7.41/7.60 (step @p48 :rule trans :premises (@p47 @p40)) % 7.41/7.60 (step @p49 :rule refl :args ((_ @t16 @t18))) % 7.41/7.60 (step @p50 :rule refl :args (@t43)) % 7.41/7.60 (step @p51 :rule cong :premises (@p50) :args (@t44)) % 7.41/7.60 (step @p52 :rule trans :premises (@p51 @p49)) % 7.41/7.60 (step @p53 :rule refl :args (@t16)) % 7.41/7.60 (step @p54 :rule ho_cong :premises (@p53 @p50)) % 7.41/7.60 (step @p55 :rule cong :premises (@p54 @p52) :args ((= (_ @t16 @t43) @t44))) % 7.41/7.60 (step @p56 :rule symm :premises (@p55)) % 7.41/7.60 (step @p57 :rule refl :args (@t19)) % 7.41/7.60 (step @p58 :rule eq_resolve :premises (@p57 @p56)) % 7.41/7.60 (step @p59 :rule refl :args (@t18)) % 7.41/7.60 (step @p60 :rule cong :premises (@p59 @p50) :args ((= @t18 @t43))) % 7.41/7.60 (step @p61 :rule symm :premises (@p60)) % 7.41/7.60 (step @p62 :rule eq_resolve :premises (@p59 @p61)) % 7.41/7.60 (step @p63 :rule ho_cong :premises (@p53 @p62)) % 7.41/7.60 (step @p64 :rule trans :premises (@p63 @p58)) % 7.41/7.60 (step @p65 :rule refl :args (@t57)) % 7.41/7.60 (step @p66 :rule nary_cong :premises (@p65 @p64) :args (@t58)) % 7.41/7.60 (step @p67 :rule cong :premises (@p66) :args ((forall @t25 @t58))) % 7.41/7.60 (step @p68 :rule trans :premises (@p67 @p48)) % 7.41/7.60 (step @p69 :rule bool-double-not-elim :args (@t57)) % 7.41/7.60 (step @p70 :rule nary_cong :premises (@p69 @p57) :args ((or (not @t59) @t19))) % 7.41/7.60 (step @p71 :rule bool-impl-elim :args (@t59 @t19)) % 7.41/7.60 (step @p72 :rule trans :premises (@p71 @p70)) % 7.41/7.60 (step @p73 :rule cong :premises (@p72) :args ((forall @t25 (=> @t59 @t19)))) % 7.41/7.60 (step @p74 :rule trans :premises (@p73 @p68)) % 7.41/7.60 (step @p75 :rule refl :args (@t19)) % 7.41/7.60 (step @p76 :rule refl :args (@t56)) % 7.41/7.60 (step @p77 :rule refl :args (@t21)) % 7.41/7.60 (step @p78 :rule cong :premises (@p77 @p76) :args ((= @t21 @t56))) % 7.41/7.60 (step @p79 :rule symm :premises (@p78)) % 7.41/7.60 (step @p80 :rule eq_resolve :premises (@p77 @p79)) % 7.41/7.60 (step @p81 :rule cong :premises (@p80) :args (@t60)) % 7.41/7.60 (step @p82 :rule cong :premises (@p81) :args (@t61)) % 7.41/7.60 (step @p83 :rule cong :premises (@p82) :args (@t62)) % 7.41/7.60 (step @p84 :rule exists-elim :args ((= @t23 @t62))) % 7.41/7.60 (step @p85 :rule trans :premises (@p84 @p83)) % 7.41/7.60 (step @p86 :rule cong :premises (@p85 @p75) :args (@t24)) % 7.41/7.60 (step @p87 :rule cong :premises (@p86) :args (@t26)) % 7.41/7.60 (step @p88 :rule trans :premises (@p87 @p74)) % 7.41/7.60 (step @p89 :rule cong :premises (@p88) :args (@t28)) % 7.41/7.60 (step @p90 :rule trans :premises (@p89 @p39)) % 7.41/7.60 (step @p91 :rule cong :premises (@p90 @p38) :args (@t29)) % 7.41/7.60 (step @p92 :rule cong :premises (@p91) :args (@t30)) % 7.41/7.60 (step @p93 :rule eq_resolve :premises (@p1 @p92)) % 7.41/7.60 (step @p94 :rule not_implies_elim2 :premises (@p93)) % 7.41/7.60 (step @p95 :rule not_equiv_elim2 :premises (@p94)) % 7.41/7.60 (step @p96 :rule eq_resolve :premises (@p95 @p5)) % 7.41/7.60 (step @p97 :rule reordering :premises (@p96) :args ((or @t34 @t37))) % 7.41/7.60 (assume-push @p289 @t36) % 7.41/7.60 (step @p99 :rule instantiate :premises (@p289) :args ((@list @t66))) % 7.41/7.60 (step-pop @p290 :rule scope :premises (@p99)) % 7.41/7.60 (step @p100 :rule process_scope :premises (@p290) :args (@t68)) % 7.41/7.60 (step @p102 :rule implies_elim :premises (@p100)) % 7.41/7.60 (step @p103 :rule beta-reduce :args ((= @t71 @t64))) % 7.41/7.60 (step @p104 :rule refl :args (@t1)) % 7.41/7.60 (step @p105 :rule cong :premises (@p104 @p103) :args (@t72)) % 7.41/7.60 (step @p106 :rule cong :premises (@p105) :args (@t73)) % 7.41/7.60 (step @p107 :rule cong :premises (@p106) :args (@t74)) % 7.41/7.60 (step @p108 :rule refl :args (@t34)) % 7.41/7.60 (step @p109 :rule cong :premises (@p108 @p107) :args ((=> @t34 @t74))) % 7.41/7.60 (assume-push @p291 @t34) % 7.41/7.60 (step @p111 :rule instantiate :premises (@p291) :args ((@list @t70))) % 7.41/7.60 (step-pop @p292 :rule scope :premises (@p111)) % 7.41/7.60 (step @p112 :rule process_scope :premises (@p292) :args (@t74)) % 7.41/7.60 (step @p114 :rule eq_resolve :premises (@p112 @p109)) % 7.41/7.60 (step @p115 :rule implies_elim :premises (@p114)) % 7.41/7.60 (step @p116 :rule refl :args (@t76)) % 7.41/7.60 (step @p117 :rule bool-double-not-elim :args (@t67)) % 7.41/7.60 (step @p118 :rule nary_cong :premises (@p117 @p116) :args ((or (not @t68) @t76))) % 7.41/7.60 (step @p119 :rule bool-double-not-elim :args (@t76)) % 7.41/7.60 (step @p120 :rule refl :args (@t68)) % 7.41/7.60 (step @p121 :rule cong :premises (@p120 @p119) :args ((=> @t68 @t78))) % 7.41/7.60 (assume-push @p293 @t68) % 7.41/7.60 (step @p123 :rule skolemize :premises (@p293)) % 7.41/7.60 (step-pop @p294 :rule scope :premises (@p123)) % 7.41/7.60 (step @p124 :rule process_scope :premises (@p294) :args (@t78)) % 7.41/7.60 (step @p126 :rule eq_resolve :premises (@p124 @p121)) % 7.41/7.60 (step @p127 :rule implies_elim :premises (@p126)) % 7.41/7.60 (step @p128 :rule eq_resolve :premises (@p127 @p118)) % 7.41/7.60 (step @p129 :rule refl :args (@t82)) % 7.41/7.60 (step @p130 :rule bool-double-not-elim :args (@t65)) % 7.41/7.60 (step @p131 :rule nary_cong :premises (@p130 @p129) :args ((or (not @t83) @t82))) % 7.41/7.60 (assume-push @p295 @t83) % 7.41/7.60 (step @p133 :rule skolemize :premises (@p295)) % 7.41/7.60 (step-pop @p296 :rule scope :premises (@p133)) % 7.41/7.60 (step @p134 :rule process_scope :premises (@p296) :args (@t82)) % 7.41/7.60 (step @p136 :rule implies_elim :premises (@p134)) % 7.41/7.60 (step @p137 :rule eq_resolve :premises (@p136 @p131)) % 7.41/7.60 (step @p138 :rule not_implies_elim1 :premises (@p93)) % 7.41/7.60 (step @p139 :rule refl :args (@t84)) % 7.41/7.60 (step @p140 :rule bool-double-not-elim :args (@t50)) % 7.41/7.60 (step @p141 :rule nary_cong :premises (@p140 @p139) :args ((or (not @t51) @t84))) % 7.41/7.60 (step @p142 :rule bool-double-not-elim :args (@t84)) % 7.41/7.60 (step @p143 :rule refl :args (@t51)) % 7.41/7.60 (step @p144 :rule cong :premises (@p143 @p142) :args ((=> @t51 @t85))) % 7.41/7.60 (assume-push @p297 @t51) % 7.41/7.60 (step @p146 :rule skolemize :premises (@p138)) % 7.41/7.60 (step-pop @p298 :rule scope :premises (@p146)) % 7.41/7.60 (step @p147 :rule process_scope :premises (@p298) :args (@t85)) % 7.41/7.60 (step @p149 :rule eq_resolve :premises (@p147 @p144)) % 7.41/7.60 (step @p150 :rule implies_elim :premises (@p149)) % 7.41/7.60 (step @p151 :rule eq_resolve :premises (@p150 @p141)) % 7.41/7.60 (step @p152 :rule chain_m_resolution :premises (@p151 @p138) :args (@t84 @t86 (@list @t50))) % 7.41/7.60 (step @p153 :rule refl :args ((tptp.r @t66 @t87))) % 7.41/7.60 (step @p154 :rule refl :args (@t80)) % 7.41/7.60 (step @p155 :rule refl :args (@t66)) % 7.41/7.60 (step @p156 :rule cong :premises (@p155 @p154) :args (@t81)) % 7.41/7.60 (step @p157 :rule trans :premises (@p156 @p153)) % 7.41/7.60 (step @p158 :rule refl :args (@t79)) % 7.41/7.60 (step @p159 :rule ho_cong :premises (@p158 @p154)) % 7.41/7.60 (step @p160 :rule cong :premises (@p159 @p157) :args ((= @t88 @t81))) % 7.41/7.60 (step @p161 :rule symm :premises (@p160)) % 7.41/7.60 (step @p162 :rule refl :args ((_ @t79 @t87))) % 7.41/7.60 (step @p163 :rule eq_resolve :premises (@p162 @p161)) % 7.41/7.60 (step @p164 :rule refl :args (@t76)) % 7.41/7.60 (step @p165 :rule refl :args (@t89)) % 7.41/7.60 (step @p166 :rule cong :premises (@p165 @p164) :args ((= @t89 @t76))) % 7.41/7.60 (step @p167 :rule symm :premises (@p166)) % 7.41/7.60 (step @p168 :rule eq_resolve :premises (@p165 @p167)) % 7.41/7.60 (step @p169 :rule cong :premises (@p168) :args (@t90)) % 7.41/7.60 (step @p170 :rule nary_cong :premises (@p169 @p163) :args (@t91)) % 7.41/7.60 (step @p171 :rule cong :premises (@p139 @p170) :args ((=> @t84 @t91))) % 7.41/7.60 (step @p172 :rule refl :args ((_ @t79 @t87))) % 7.41/7.60 (step @p173 :rule cong :premises (@p154) :args (@t92)) % 7.41/7.60 (step @p174 :rule trans :premises (@p173 @p172)) % 7.41/7.60 (step @p175 :rule cong :premises (@p174 @p159) :args ((= @t92 @t88))) % 7.41/7.60 (step @p176 :rule symm :premises (@p175)) % 7.41/7.60 (step @p177 :rule eq_resolve :premises (@p162 @p176)) % 7.41/7.60 (step @p178 :rule refl :args (@t93)) % 7.41/7.60 (step @p179 :rule cong :premises (@p178) :args (@t94)) % 7.41/7.60 (step @p180 :rule nary_cong :premises (@p179 @p177) :args (@t95)) % 7.41/7.60 (step @p181 :rule cong :premises (@p139 @p180) :args ((=> @t84 @t95))) % 7.41/7.60 (assume-push @p299 @t84) % 7.41/7.60 (step @p183 :rule instantiate :premises (@p152) :args ((@list @t79 @t75))) % 7.41/7.60 (step-pop @p300 :rule scope :premises (@p183)) % 7.41/7.60 (step @p184 :rule process_scope :premises (@p300) :args (@t95)) % 7.41/7.60 (step @p186 :rule eq_resolve :premises (@p184 @p181)) % 7.41/7.60 (step @p187 :rule eq_resolve :premises (@p186 @p171)) % 7.41/7.60 (step @p188 :rule implies_elim :premises (@p187)) % 7.41/7.60 (step @p189 :rule chain_m_resolution :premises (@p188 @p152) :args (@t96 @t97 @t98)) % 7.41/7.60 (step @p190 :rule cnf_or_pos :args (@t96)) % 7.41/7.60 (step @p191 :rule reordering :premises (@p190) :args ((or @t81 @t77 (not @t96)))) % 7.41/7.60 (step @p192 :rule chain_m_resolution :premises (@p191 @p189 @p137 @p128 @p115 @p102 @p97) :args (@t37 (@list false true false true true false) (@list @t96 @t81 @t76 @t65 @t67 @t34))) % 7.41/7.60 (step @p193 :rule not_equiv_elim1 :premises (@p94)) % 7.41/7.60 (step @p194 :rule chain_m_resolution :premises (@p193 @p192) :args (@t38 @t86 @t99)) % 7.41/7.60 (step @p195 :rule refl :args (@t101)) % 7.41/7.60 (step @p196 :rule nary_cong :premises (@p3 @p195) :args ((or @t39 @t101))) % 7.41/7.60 (step @p197 :rule bool-double-not-elim :args (@t101)) % 7.41/7.60 (step @p198 :rule refl :args (@t38)) % 7.41/7.60 (step @p199 :rule cong :premises (@p198 @p197) :args ((=> @t38 @t103))) % 7.41/7.60 (assume-push @p301 @t38) % 7.41/7.60 (step @p201 :rule skolemize :premises (@p301)) % 7.41/7.60 (step-pop @p302 :rule scope :premises (@p201)) % 7.41/7.60 (step @p202 :rule process_scope :premises (@p302) :args (@t103)) % 7.41/7.60 (step @p204 :rule eq_resolve :premises (@p202 @p199)) % 7.41/7.60 (step @p205 :rule implies_elim :premises (@p204)) % 7.41/7.60 (step @p206 :rule eq_resolve :premises (@p205 @p196)) % 7.41/7.60 (step @p207 :rule chain_m_resolution :premises (@p206 @p194) :args (@t101 @t86 (@list @t34))) % 7.41/7.60 (step @p208 :rule lambda-elim :args ((= @t107 @t105))) % 7.41/7.60 (step @p209 :rule cong :premises (@p208) :args (@t108)) % 7.41/7.60 (step @p210 :rule refl :args (@t104)) % 7.41/7.60 (step @p211 :rule cong :premises (@p210 @p209) :args (@t109)) % 7.41/7.60 (step @p212 :rule refl :args (@t113)) % 7.41/7.60 (step @p213 :rule nary_cong :premises (@p212 @p211) :args (@t114)) % 7.41/7.60 (step @p214 :rule cong :premises (@p139 @p213) :args ((=> @t84 @t114))) % 7.41/7.60 (step @p215 :rule beta-reduce :args ((= @t115 @t109))) % 7.41/7.60 (step @p216 :rule beta-reduce :args ((= @t116 @t112))) % 7.41/7.60 (step @p217 :rule cong :premises (@p216) :args (@t117)) % 7.41/7.60 (step @p218 :rule nary_cong :premises (@p217 @p215) :args (@t118)) % 7.41/7.60 (step @p219 :rule cong :premises (@p139 @p218) :args ((=> @t84 @t118))) % 7.41/7.60 (assume-push @p303 @t84) % 7.41/7.60 (step @p221 :rule instantiate :premises (@p152) :args ((@list @t107 @t111))) % 7.41/7.60 (step-pop @p304 :rule scope :premises (@p221)) % 7.41/7.60 (step @p222 :rule process_scope :premises (@p304) :args (@t118)) % 7.41/7.60 (step @p224 :rule eq_resolve :premises (@p222 @p219)) % 7.41/7.60 (step @p225 :rule eq_resolve :premises (@p224 @p214)) % 7.41/7.60 (step @p226 :rule implies_elim :premises (@p225)) % 7.41/7.60 (step @p227 :rule chain_m_resolution :premises (@p226 @p152) :args (@t121 @t97 @t98)) % 7.41/7.60 (step @p228 :rule refl :args (@t122)) % 7.41/7.60 (step @p229 :rule bool-double-not-elim :args (@t36)) % 7.41/7.60 (step @p230 :rule nary_cong :premises (@p229 @p228) :args ((or (not @t37) @t122))) % 7.41/7.60 (step @p231 :rule bool-double-not-elim :args (@t122)) % 7.41/7.60 (step @p232 :rule cong :premises (@p4 @p231) :args ((=> @t37 @t123))) % 7.41/7.60 (assume-push @p305 @t37) % 7.41/7.60 (step @p234 :rule skolemize :premises (@p305)) % 7.41/7.60 (step-pop @p306 :rule scope :premises (@p234)) % 7.41/7.60 (step @p235 :rule process_scope :premises (@p306) :args (@t123)) % 7.41/7.60 (step @p237 :rule eq_resolve :premises (@p235 @p232)) % 7.41/7.60 (step @p238 :rule implies_elim :premises (@p237)) % 7.41/7.60 (step @p239 :rule eq_resolve :premises (@p238 @p230)) % 7.41/7.60 (step @p240 :rule chain_m_resolution :premises (@p239 @p192) :args (@t122 @t86 @t99)) % 7.41/7.60 (step @p241 :rule alpha_equiv :args (@t125 (@list @t124) (@list @t10))) % 7.41/7.60 (step @p242 :rule equiv_elim2 :premises (@p241)) % 7.41/7.60 (step @p243 :rule chain_m_resolution :premises (@p242 @p240) :args (@t125 @t97 (@list @t122))) % 7.41/7.60 (assume-push @p307 @t125) % 7.41/7.60 (step @p245 :rule instantiate :premises (@p307) :args ((@list @t119))) % 7.41/7.60 (step-pop @p308 :rule scope :premises (@p245)) % 7.41/7.60 (step @p246 :rule process_scope :premises (@p308) :args (@t126)) % 7.41/7.60 (step @p248 :rule implies_elim :premises (@p246)) % 7.41/7.60 (step @p249 :rule reordering :premises (@p248) :args ((or @t126 (not @t125)))) % 7.41/7.60 (step @p250 :rule chain_m_resolution :premises (@p249 @p243) :args (@t126 @t97 (@list @t125))) % 7.41/7.60 (step @p251 :rule cnf_or_pos :args (@t121)) % 7.41/7.60 (step @p252 :rule reordering :premises (@p251) :args ((or @t120 @t113 (not @t121)))) % 7.41/7.60 (step @p253 :rule chain_m_resolution :premises (@p252 @p250 @p227) :args (@t113 @t127 (@list @t120 @t121))) % 7.41/7.60 (step @p254 :rule skolem_intro :args (@t111)) % 7.41/7.60 (step @p255 :rule symm :premises (@p254)) % 7.41/7.60 (step @p256 :rule refl :args (@t129)) % 7.41/7.60 (step @p257 :rule bool-double-not-elim :args (@t112)) % 7.41/7.60 (step @p258 :rule refl :args (@t131)) % 7.41/7.60 (step @p259 :rule nary_cong :premises (@p258 @p257 @p256) :args ((or @t131 (not @t113) @t129))) % 7.41/7.60 (assume-push @p309 @t130) % 7.41/7.60 (assume-push @p310 @t113) % 7.41/7.60 (assume-push @p311 @t113) % 7.41/7.60 (assume-push @p312 @t130) % 7.41/7.60 (step @p264 :rule false_intro :premises (@p310)) % 7.41/7.60 (step @p265 :rule cong :premises (@p210 @p255) :args (@t128)) % 7.41/7.60 (step @p266 :rule trans :premises (@p265 @p264)) % 7.41/7.60 (step @p267 :rule false_elim :premises (@p266)) % 7.41/7.60 (step-pop @p313 :rule scope :premises (@p267)) % 7.41/7.60 (step-pop @p314 :rule scope :premises (@p313)) % 7.41/7.60 (step @p268 :rule process_scope :premises (@p314) :args (@t129)) % 7.41/7.60 (step @p271 :rule and_intro :premises (@p310 @p255)) % 7.41/7.60 (step @p272 :rule modus_ponens :premises (@p271 @p268)) % 7.41/7.60 (step-pop @p315 :rule scope :premises (@p272)) % 7.41/7.60 (step-pop @p316 :rule scope :premises (@p315)) % 7.41/7.60 (step @p273 :rule process_scope :premises (@p316) :args (@t129)) % 7.41/7.60 (step @p276 :rule implies_elim :premises (@p273)) % 7.41/7.60 (step @p277 :rule cnf_and_neg :args (@t132)) % 7.41/7.60 (step @p278 :rule resolution :premises (@p277 @p276) :args (true @t132)) % 7.41/7.60 (step @p279 :rule eq_resolve :premises (@p278 @p259)) % 7.41/7.60 (step @p280 :rule reordering :premises (@p279) :args ((or @t129 @t131 @t112))) % 7.41/7.60 (step @p281 :rule chain_m_resolution :premises (@p280 @p255 @p253) :args (@t129 (@list false true) (@list @t130 @t112))) % 7.41/7.60 (assume-push @p317 @t101) % 7.41/7.60 (step @p283 :rule instantiate :premises (@p317) :args ((@list @t104))) % 7.41/7.60 (step-pop @p318 :rule scope :premises (@p283)) % 7.41/7.60 (step @p284 :rule process_scope :premises (@p318) :args (@t128)) % 7.41/7.60 (step @p286 :rule implies_elim :premises (@p284)) % 7.41/7.60 (step @p287 :rule reordering :premises (@p286) :args ((or @t128 @t102))) % 7.41/7.60 (step @p288 false :rule chain_m_resolution :premises (@p287 @p281 @p207) :args (false @t127 (@list @t128 @t101))) % 7.41/7.61 ) % 7.41/7.61 % SZS output end Proof % 7.41/7.61 % cvc5 exiting %------------------------------------------------------------------------------