%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV214^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n002.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 08:55:37 AM UTC 2026 % Result : Theorem 0.35s 0.58s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV214^5 : TPTP v9.2.1. Released v4.0.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n002.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 18:19:48 EDT 2026 % 0.16/0.34 % CPUTime : % 0.26/0.50 %----Proving TH0 % 0.35/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.35/0.58 % SZS status Theorem % 0.35/0.58 % SZS output start Proof % 0.35/0.58 ( % 0.35/0.58 (declare-sort tptp.iS 0) % 0.35/0.58 (declare-const tptp.cP (-> tptp.iS tptp.iS tptp.iS)) % 0.35/0.58 (declare-const tptp.c0 tptp.iS) % 0.35/0.58 (define @t1 () (@var "Xy" tptp.iS)) % 0.35/0.58 (define @t2 () (@var "Xx" tptp.iS)) % 0.35/0.58 (define @t3 () (= @t2 @t1)) % 0.35/0.58 (define @t4 () (@list @t2 @t1)) % 0.35/0.58 (define @t5 () (_ (lambda @t4 @t3) tptp.c0)) % 0.35/0.58 (define @t6 () (_ tptp.cP @t2)) % 0.35/0.58 (define @t7 () (_ @t6 @t1)) % 0.35/0.58 (define @t8 () (= tptp.c0 @t7)) % 0.35/0.58 (define @t9 () (@list @t2)) % 0.35/0.58 (define @t10 () (exists @t9 @t8)) % 0.35/0.58 (define @t11 () (or (= @t1 tptp.c0) @t10)) % 0.35/0.58 (define @t12 () (@list @t1)) % 0.35/0.58 (define @t13 () (lambda @t12 @t11)) % 0.35/0.58 (define @t14 () (= @t13 @t5)) % 0.35/0.58 (define @t15 () (exists @t12 @t8)) % 0.35/0.58 (define @t16 () (or (= @t2 tptp.c0) @t15)) % 0.35/0.58 (define @t17 () (lambda @t9 @t16)) % 0.35/0.58 (define @t18 () (= @t17 @t5)) % 0.35/0.58 (define @t19 () (and @t18 @t14)) % 0.35/0.58 (define @t20 () (@var "X" (-> tptp.iS Bool))) % 0.35/0.58 (define @t21 () (_ @t20 @t2)) % 0.35/0.58 (define @t22 () (forall @t9 @t21)) % 0.35/0.58 (define @t23 () (_ @t20 @t7)) % 0.35/0.58 (define @t24 () (_ @t20 @t1)) % 0.35/0.58 (define @t25 () (and @t21 @t24)) % 0.35/0.58 (define @t26 () (forall @t4 (=> @t25 @t23))) % 0.35/0.58 (define @t27 () (_ @t20 tptp.c0)) % 0.35/0.58 (define @t28 () (and @t27 @t26)) % 0.35/0.58 (define @t29 () (=> @t28 @t22)) % 0.35/0.58 (define @t30 () (@list @t20)) % 0.35/0.58 (define @t31 () (forall @t30 @t29)) % 0.35/0.58 (define @t32 () (@var "Xv" tptp.iS)) % 0.35/0.58 (define @t33 () (@var "Xu" tptp.iS)) % 0.35/0.58 (define @t34 () (and @t3 (= @t33 @t32))) % 0.35/0.58 (define @t35 () (_ (_ tptp.cP @t1) @t32)) % 0.35/0.58 (define @t36 () (_ @t6 @t33)) % 0.35/0.58 (define @t37 () (= @t36 @t35)) % 0.35/0.58 (define @t38 () (@list @t2 @t1 @t33 @t32)) % 0.35/0.58 (define @t39 () (forall @t38 (=> @t37 @t34))) % 0.35/0.58 (define @t40 () (not (= @t7 tptp.c0))) % 0.35/0.58 (define @t41 () (forall @t4 @t40)) % 0.35/0.58 (define @t42 () (and @t41 @t39 @t31)) % 0.35/0.58 (define @t43 () (=> @t42 @t19)) % 0.35/0.58 (define @t44 () (not @t43)) % 0.35/0.58 (define @t45 () (= tptp.c0 @t1)) % 0.35/0.58 (define @t46 () (lambda @t12 @t45)) % 0.35/0.58 (define @t47 () (@purify @t46)) % 0.35/0.58 (define @t48 () (tptp.cP @t2 @t1)) % 0.35/0.58 (define @t49 () (not (= tptp.c0 @t48))) % 0.35/0.58 (define @t50 () (lambda @t12 (or @t45 (not (forall @t9 @t49))))) % 0.35/0.58 (define @t51 () (@purify @t50)) % 0.35/0.58 (define @t52 () (= @t46 @t50)) % 0.35/0.58 (define @t53 () (lambda @t9 (or (= tptp.c0 @t2) (not (forall @t12 @t49))))) % 0.35/0.58 (define @t54 () (@purify @t53)) % 0.35/0.58 (define @t55 () (= @t53 @t46)) % 0.35/0.58 (define @t56 () (and @t55 @t52)) % 0.35/0.58 (define @t57 () (@var "BOUND_VARIABLE_7508" tptp.iS)) % 0.35/0.58 (define @t58 () (_ @t20 @t57)) % 0.35/0.58 (define @t59 () (_ @t20 @t48)) % 0.35/0.58 (define @t60 () (_ @t20 @t1)) % 0.35/0.58 (define @t61 () (_ @t20 @t2)) % 0.35/0.58 (define @t62 () (forall @t4 (or (not @t61) (not @t60) @t59))) % 0.35/0.58 (define @t63 () (not @t62)) % 0.35/0.58 (define @t64 () (_ @t20 tptp.c0)) % 0.35/0.58 (define @t65 () (not @t64)) % 0.35/0.58 (define @t66 () (or @t65 @t63 @t58)) % 0.35/0.58 (define @t67 () (forall (@list @t20 @t57) @t66)) % 0.35/0.58 (define @t68 () (tptp.cP @t1 @t32)) % 0.35/0.58 (define @t69 () (tptp.cP @t2 @t33)) % 0.35/0.58 (define @t70 () (forall @t4 @t49)) % 0.35/0.58 (define @t71 () (and @t70 (forall @t38 (or (not (= @t69 @t68)) @t34)) @t67)) % 0.35/0.58 (define @t72 () (=> @t71 @t56)) % 0.35/0.58 (define @t73 () (not @t8)) % 0.35/0.58 (define @t74 () (forall @t9 @t73)) % 0.35/0.58 (define @t75 () (not @t74)) % 0.35/0.58 (define @t76 () (forall @t12 @t73)) % 0.35/0.58 (define @t77 () (not @t76)) % 0.35/0.58 (define @t78 () (@list @t57)) % 0.35/0.58 (define @t79 () (forall @t78 @t66)) % 0.35/0.58 (define @t80 () (forall @t78 @t58)) % 0.35/0.58 (define @t81 () (or @t65 @t63 @t80)) % 0.35/0.58 (define @t82 () (forall @t9 @t61)) % 0.35/0.58 (define @t83 () (not @t27)) % 0.35/0.58 (define @t84 () (or @t83 @t63 @t82)) % 0.35/0.58 (define @t85 () (and @t27 @t62)) % 0.35/0.58 (define @t86 () (not @t24)) % 0.35/0.58 (define @t87 () (not @t21)) % 0.35/0.58 (define @t88 () (or @t87 @t86 @t23)) % 0.35/0.58 (define @t89 () (not @t37)) % 0.35/0.58 (define @t90 () (or @t89 @t34)) % 0.35/0.58 (define @t91 () (@const 0 tptp.iS)) % 0.35/0.58 (define @t92 () (forall @t12 (not (= tptp.c0 (tptp.cP @t91 @t1))))) % 0.35/0.58 (define @t93 () (not @t92)) % 0.35/0.58 (define @t94 () (= tptp.c0 @t91)) % 0.35/0.58 (define @t95 () (or @t94 @t93)) % 0.35/0.58 (define @t96 () (= @t94 @t95)) % 0.35/0.58 (define @t97 () (@list false)) % 0.35/0.58 (define @t98 () (@quantifiers_skolemize @t92 0)) % 0.35/0.58 (define @t99 () (= tptp.c0 (tptp.cP @t91 @t98))) % 0.35/0.58 (define @t100 () (not (not @t99))) % 0.35/0.58 (define @t101 () (@list true)) % 0.35/0.58 (define @t102 () (= (_ @t53 @t91) @t95)) % 0.35/0.58 (define @t103 () (_ @t54 @t91)) % 0.35/0.58 (define @t104 () (_ @t46 @t91)) % 0.35/0.58 (define @t105 () (_ @t47 @t91)) % 0.35/0.58 (define @t106 () (= @t105 @t103)) % 0.35/0.58 (define @t107 () (not @t106)) % 0.35/0.58 (define @t108 () (= @t47 @t54)) % 0.35/0.58 (define @t109 () (or @t108 @t107)) % 0.35/0.58 (define @t110 () (= @t51 @t47)) % 0.35/0.58 (define @t111 () (@const 1 tptp.iS)) % 0.35/0.58 (define @t112 () (forall @t9 (not (= tptp.c0 (tptp.cP @t2 @t111))))) % 0.35/0.58 (define @t113 () (not @t112)) % 0.35/0.58 (define @t114 () (= tptp.c0 @t111)) % 0.35/0.58 (define @t115 () (or @t114 @t113)) % 0.35/0.58 (define @t116 () (= (_ @t46 @t111) @t114)) % 0.35/0.58 (define @t117 () (_ @t47 @t111)) % 0.35/0.58 (define @t118 () (= (_ @t50 @t111) @t115)) % 0.35/0.58 (define @t119 () (_ @t51 @t111)) % 0.35/0.58 (define @t120 () (= @t119 @t117)) % 0.35/0.58 (define @t121 () (not @t120)) % 0.35/0.58 (define @t122 () (or @t110 @t121)) % 0.35/0.58 (define @t123 () (= @t114 @t115)) % 0.35/0.58 (define @t124 () (@list true false)) % 0.35/0.58 (define @t125 () (@quantifiers_skolemize @t112 0)) % 0.35/0.58 (define @t126 () (= tptp.c0 (tptp.cP @t125 @t111))) % 0.35/0.58 (define @t127 () (not @t126)) % 0.35/0.58 (define @t128 () (not @t127)) % 0.35/0.58 (assume @p1 @t44) % 0.35/0.58 (assume @p2 true) % 0.35/0.58 (step @p3 :rule eq-symm :args (@t47 @t51)) % 0.35/0.58 (step @p4 :rule eq-refl :args (@t50)) % 0.35/0.58 (step @p5 :rule skolem_intro :args (@t51)) % 0.35/0.58 (step @p6 :rule refl :args (@t50)) % 0.35/0.58 (step @p7 :rule cong :premises (@p6 @p5) :args ((= @t50 @t51))) % 0.35/0.58 (step @p8 :rule trans :premises (@p7 @p4)) % 0.35/0.58 (step @p9 :rule true_elim :premises (@p8)) % 0.35/0.58 (step @p10 :rule eq-refl :args (@t46)) % 0.35/0.58 (step @p11 :rule skolem_intro :args (@t47)) % 0.35/0.58 (step @p12 :rule refl :args (@t46)) % 0.35/0.58 (step @p13 :rule cong :premises (@p12 @p11) :args ((= @t46 @t47))) % 0.35/0.58 (step @p14 :rule trans :premises (@p13 @p10)) % 0.35/0.58 (step @p15 :rule true_elim :premises (@p14)) % 0.35/0.58 (step @p16 :rule cong :premises (@p15 @p9) :args (@t52)) % 0.35/0.58 (step @p17 :rule trans :premises (@p16 @p3)) % 0.35/0.58 (step @p18 :rule eq-symm :args (@t54 @t47)) % 0.35/0.58 (step @p19 :rule eq-refl :args (@t53)) % 0.35/0.58 (step @p20 :rule skolem_intro :args (@t54)) % 0.35/0.58 (step @p21 :rule refl :args (@t53)) % 0.35/0.58 (step @p22 :rule cong :premises (@p21 @p20) :args ((= @t53 @t54))) % 0.35/0.58 (step @p23 :rule trans :premises (@p22 @p19)) % 0.35/0.58 (step @p24 :rule true_elim :premises (@p23)) % 0.35/0.58 (step @p25 :rule cong :premises (@p24 @p15) :args (@t55)) % 0.35/0.58 (step @p26 :rule trans :premises (@p25 @p18)) % 0.35/0.58 (step @p27 :rule nary_cong :premises (@p26 @p17) :args (@t56)) % 0.35/0.58 (step @p28 :rule refl :args (@t71)) % 0.35/0.58 (step @p29 :rule cong :premises (@p28 @p27) :args (@t72)) % 0.35/0.58 (step @p30 :rule cong :premises (@p29) :args ((not @t72))) % 0.35/0.58 (step @p31 :rule eq-symm :args (@t50 @t46)) % 0.35/0.58 (step @p32 :rule beta-reduce :args ((= @t5 @t46))) % 0.35/0.58 (step @p33 :rule refl :args (@t48)) % 0.35/0.58 (step @p34 :rule refl :args (@t7)) % 0.35/0.58 (step @p35 :rule cong :premises (@p34 @p33) :args ((= @t7 @t48))) % 0.35/0.58 (step @p36 :rule symm :premises (@p35)) % 0.35/0.58 (step @p37 :rule eq_resolve :premises (@p34 @p36)) % 0.35/0.58 (step @p38 :rule refl :args (tptp.c0)) % 0.35/0.58 (step @p39 :rule cong :premises (@p38 @p37) :args (@t8)) % 0.35/0.58 (step @p40 :rule cong :premises (@p39) :args (@t73)) % 0.35/0.58 (step @p41 :rule cong :premises (@p40) :args (@t74)) % 0.35/0.58 (step @p42 :rule cong :premises (@p41) :args (@t75)) % 0.35/0.58 (step @p43 :rule exists-elim :args ((= @t10 @t75))) % 0.35/0.58 (step @p44 :rule trans :premises (@p43 @p42)) % 0.35/0.58 (step @p45 :rule eq-symm :args (@t1 tptp.c0)) % 0.35/0.58 (step @p46 :rule nary_cong :premises (@p45 @p44) :args (@t11)) % 0.35/0.58 (step @p47 :rule cong :premises (@p46) :args (@t13)) % 0.35/0.58 (step @p48 :rule cong :premises (@p47 @p32) :args (@t14)) % 0.35/0.58 (step @p49 :rule trans :premises (@p48 @p31)) % 0.35/0.58 (step @p50 :rule cong :premises (@p40) :args (@t76)) % 0.35/0.58 (step @p51 :rule cong :premises (@p50) :args (@t77)) % 0.35/0.58 (step @p52 :rule exists-elim :args ((= @t15 @t77))) % 0.35/0.58 (step @p53 :rule trans :premises (@p52 @p51)) % 0.35/0.58 (step @p54 :rule eq-symm :args (@t2 tptp.c0)) % 0.35/0.58 (step @p55 :rule nary_cong :premises (@p54 @p53) :args (@t16)) % 0.35/0.58 (step @p56 :rule cong :premises (@p55) :args (@t17)) % 0.35/0.58 (step @p57 :rule cong :premises (@p56 @p32) :args (@t18)) % 0.35/0.58 (step @p58 :rule nary_cong :premises (@p57 @p49) :args (@t19)) % 0.35/0.58 (step @p59 :rule quant-merge-prenex :args ((= (forall @t30 @t79) @t67))) % 0.35/0.58 (step @p60 :rule alpha_equiv :args (@t80 (@list @t57) (@list @t2))) % 0.35/0.58 (step @p61 :rule refl :args (@t63)) % 0.35/0.58 (step @p62 :rule refl :args (@t65)) % 0.35/0.58 (step @p63 :rule nary_cong :premises (@p62 @p61 @p60) :args (@t81)) % 0.35/0.58 (step @p64 :rule quant-miniscope-or :args ((= @t79 @t81))) % 0.35/0.58 (step @p65 :rule trans :premises (@p64 @p63)) % 0.35/0.58 (step @p66 :rule symm :premises (@p65)) % 0.35/0.58 (step @p67 :rule cong :premises (@p66) :args ((forall @t30 (or @t65 @t63 @t82)))) % 0.35/0.58 (step @p68 :rule trans :premises (@p67 @p59)) % 0.35/0.58 (step @p69 :rule refl :args (@t82)) % 0.35/0.58 (step @p70 :rule refl :args (@t64)) % 0.35/0.58 (step @p71 :rule refl :args (@t27)) % 0.35/0.58 (step @p72 :rule cong :premises (@p71 @p70) :args ((= @t27 @t64))) % 0.35/0.58 (step @p73 :rule symm :premises (@p72)) % 0.35/0.58 (step @p74 :rule eq_resolve :premises (@p71 @p73)) % 0.35/0.58 (step @p75 :rule cong :premises (@p74) :args (@t83)) % 0.35/0.58 (step @p76 :rule nary_cong :premises (@p75 @p61 @p69) :args (@t84)) % 0.35/0.58 (step @p77 :rule cong :premises (@p76) :args ((forall @t30 @t84))) % 0.35/0.58 (step @p78 :rule trans :premises (@p77 @p68)) % 0.35/0.58 (step @p79 :rule aci_norm :args ((= (or (or @t83 @t63) @t82) @t84))) % 0.35/0.58 (step @p80 :rule bool-and-de-morgan :args (@t27 @t62 true)) % 0.35/0.58 (step @p81 :rule nary_cong :premises (@p80 @p69) :args ((or (not @t85) @t82))) % 0.35/0.58 (step @p82 :rule trans :premises (@p81 @p79)) % 0.35/0.58 (step @p83 :rule bool-impl-elim :args (@t85 @t82)) % 0.35/0.58 (step @p84 :rule trans :premises (@p83 @p82)) % 0.35/0.58 (step @p85 :rule cong :premises (@p84) :args ((forall @t30 (=> @t85 @t82)))) % 0.35/0.58 (step @p86 :rule trans :premises (@p85 @p78)) % 0.35/0.58 (step @p87 :rule refl :args (@t61)) % 0.35/0.58 (step @p88 :rule refl :args (@t21)) % 0.35/0.58 (step @p89 :rule cong :premises (@p88 @p87) :args ((= @t21 @t61))) % 0.35/0.58 (step @p90 :rule symm :premises (@p89)) % 0.35/0.58 (step @p91 :rule eq_resolve :premises (@p88 @p90)) % 0.35/0.58 (step @p92 :rule cong :premises (@p91) :args (@t22)) % 0.35/0.58 (step @p93 :rule refl :args ((_ @t20 @t7))) % 0.35/0.58 (step @p94 :rule cong :premises (@p33) :args (@t59)) % 0.35/0.58 (step @p95 :rule trans :premises (@p94 @p93)) % 0.35/0.58 (step @p96 :rule refl :args (@t20)) % 0.35/0.58 (step @p97 :rule ho_cong :premises (@p96 @p33)) % 0.35/0.58 (step @p98 :rule cong :premises (@p97 @p95) :args ((= (_ @t20 @t48) @t59))) % 0.35/0.58 (step @p99 :rule symm :premises (@p98)) % 0.35/0.58 (step @p100 :rule refl :args (@t23)) % 0.35/0.58 (step @p101 :rule eq_resolve :premises (@p100 @p99)) % 0.35/0.58 (step @p102 :rule ho_cong :premises (@p96 @p37)) % 0.35/0.58 (step @p103 :rule trans :premises (@p102 @p101)) % 0.35/0.58 (step @p104 :rule refl :args (@t60)) % 0.35/0.58 (step @p105 :rule refl :args (@t24)) % 0.35/0.58 (step @p106 :rule cong :premises (@p105 @p104) :args ((= @t24 @t60))) % 0.35/0.58 (step @p107 :rule symm :premises (@p106)) % 0.35/0.58 (step @p108 :rule eq_resolve :premises (@p105 @p107)) % 0.35/0.58 (step @p109 :rule cong :premises (@p108) :args (@t86)) % 0.35/0.58 (step @p110 :rule cong :premises (@p91) :args (@t87)) % 0.35/0.58 (step @p111 :rule nary_cong :premises (@p110 @p109 @p103) :args (@t88)) % 0.35/0.58 (step @p112 :rule cong :premises (@p111) :args ((forall @t4 @t88))) % 0.35/0.58 (step @p113 :rule aci_norm :args ((= (or (or @t87 @t86) @t23) @t88))) % 0.35/0.58 (step @p114 :rule bool-and-de-morgan :args (@t21 @t24 true)) % 0.35/0.58 (step @p115 :rule nary_cong :premises (@p114 @p100) :args ((or (not @t25) @t23))) % 0.35/0.58 (step @p116 :rule trans :premises (@p115 @p113)) % 0.35/0.58 (step @p117 :rule bool-impl-elim :args (@t25 @t23)) % 0.35/0.58 (step @p118 :rule trans :premises (@p117 @p116)) % 0.35/0.58 (step @p119 :rule cong :premises (@p118) :args (@t26)) % 0.35/0.58 (step @p120 :rule trans :premises (@p119 @p112)) % 0.35/0.58 (step @p121 :rule refl :args (@t27)) % 0.35/0.58 (step @p122 :rule nary_cong :premises (@p121 @p120) :args (@t28)) % 0.35/0.58 (step @p123 :rule cong :premises (@p122 @p92) :args (@t29)) % 0.35/0.58 (step @p124 :rule cong :premises (@p123) :args (@t31)) % 0.35/0.58 (step @p125 :rule trans :premises (@p124 @p86)) % 0.35/0.58 (step @p126 :rule refl :args (@t34)) % 0.35/0.58 (step @p127 :rule refl :args (@t68)) % 0.35/0.58 (step @p128 :rule refl :args (@t35)) % 0.35/0.58 (step @p129 :rule cong :premises (@p128 @p127) :args ((= @t35 @t68))) % 0.35/0.58 (step @p130 :rule symm :premises (@p129)) % 0.35/0.58 (step @p131 :rule eq_resolve :premises (@p128 @p130)) % 0.35/0.58 (step @p132 :rule refl :args (@t69)) % 0.35/0.58 (step @p133 :rule refl :args (@t36)) % 0.35/0.58 (step @p134 :rule cong :premises (@p133 @p132) :args ((= @t36 @t69))) % 0.35/0.58 (step @p135 :rule symm :premises (@p134)) % 0.35/0.58 (step @p136 :rule eq_resolve :premises (@p133 @p135)) % 0.35/0.58 (step @p137 :rule cong :premises (@p136 @p131) :args (@t37)) % 0.35/0.58 (step @p138 :rule cong :premises (@p137) :args (@t89)) % 0.35/0.58 (step @p139 :rule nary_cong :premises (@p138 @p126) :args (@t90)) % 0.35/0.58 (step @p140 :rule cong :premises (@p139) :args ((forall @t38 @t90))) % 0.35/0.58 (step @p141 :rule bool-impl-elim :args (@t37 @t34)) % 0.35/0.58 (step @p142 :rule cong :premises (@p141) :args (@t39)) % 0.35/0.58 (step @p143 :rule trans :premises (@p142 @p140)) % 0.35/0.58 (step @p144 :rule cong :premises (@p40) :args ((forall @t4 @t73))) % 0.35/0.58 (step @p145 :rule eq-symm :args (@t7 tptp.c0)) % 0.35/0.58 (step @p146 :rule cong :premises (@p145) :args (@t40)) % 0.35/0.58 (step @p147 :rule cong :premises (@p146) :args (@t41)) % 0.35/0.58 (step @p148 :rule trans :premises (@p147 @p144)) % 0.35/0.58 (step @p149 :rule nary_cong :premises (@p148 @p143 @p125) :args (@t42)) % 0.35/0.58 (step @p150 :rule cong :premises (@p149 @p58) :args (@t43)) % 0.35/0.58 (step @p151 :rule cong :premises (@p150) :args (@t44)) % 0.35/0.58 (step @p152 :rule trans :premises (@p151 @p30)) % 0.35/0.58 (step @p153 :rule eq_resolve :premises (@p1 @p152)) % 0.35/0.58 (step @p154 :rule not_implies_elim1 :premises (@p153)) % 0.35/0.58 (step @p155 :rule and_elim :premises (@p154) :args (0)) % 0.35/0.58 (step @p156 :rule cnf_or_neg :args (@t95 0)) % 0.35/0.58 (step @p157 :rule cnf_equiv_neg2 :args (@t96)) % 0.35/0.58 (step @p158 :rule chain_m_resolution :premises (@p157 @p156) :args ((or @t96 (not @t94)) @t97 (@list @t95))) % 0.35/0.58 (step @p159 :rule cnf_equiv_neg1 :args (@t96)) % 0.35/0.58 (step @p160 :rule reordering :premises (@p159) :args ((or @t94 @t95 @t96))) % 0.35/0.58 (step @p161 :rule instantiate :premises (@p155) :args ((@list @t91 @t98))) % 0.35/0.58 (step @p162 :rule refl :args (@t99)) % 0.35/0.58 (step @p163 :rule bool-double-not-elim :args (@t92)) % 0.35/0.58 (step @p164 :rule nary_cong :premises (@p163 @p162) :args ((or (not @t93) @t99))) % 0.35/0.58 (step @p165 :rule bool-double-not-elim :args (@t99)) % 0.35/0.58 (step @p166 :rule refl :args (@t93)) % 0.35/0.58 (step @p167 :rule cong :premises (@p166 @p165) :args ((=> @t93 @t100))) % 0.35/0.58 (assume-push @p267 @t93) % 0.35/0.58 (step @p169 :rule skolemize :premises (@p267)) % 0.35/0.58 (step-pop @p268 :rule scope :premises (@p169)) % 0.35/0.58 (step @p170 :rule process_scope :premises (@p268) :args (@t100)) % 0.35/0.58 (step @p172 :rule eq_resolve :premises (@p170 @p167)) % 0.35/0.58 (step @p173 :rule implies_elim :premises (@p172)) % 0.35/0.58 (step @p174 :rule eq_resolve :premises (@p173 @p164)) % 0.35/0.58 (step @p175 :rule chain_m_resolution :premises (@p174 @p161) :args (@t92 @t101 (@list @t99))) % 0.35/0.58 (step @p176 :rule cnf_or_pos :args (@t95)) % 0.35/0.58 (step @p177 :rule reordering :premises (@p176) :args ((or @t94 @t93 (not @t95)))) % 0.35/0.58 (step @p178 :rule chain_m_resolution :premises (@p177 @p175 @p160 @p158) :args (@t96 (@list false false true) (@list @t92 @t95 @t94))) % 0.35/0.58 (step @p179 :rule eq-refl :args (@t95)) % 0.35/0.58 (step @p180 :rule refl :args (@t95)) % 0.35/0.58 (step @p181 :rule beta-reduce :args (@t102)) % 0.35/0.58 (step @p182 :rule cong :premises (@p181 @p180) :args (@t102)) % 0.35/0.58 (step @p183 :rule trans :premises (@p182 @p179)) % 0.35/0.58 (step @p184 :rule refl :args (@t91)) % 0.35/0.58 (step @p185 :rule ho_cong :premises (@p20 @p184)) % 0.35/0.58 (step @p186 :rule cong :premises (@p185 @p180) :args ((= @t103 @t95))) % 0.35/0.58 (step @p187 :rule trans :premises (@p186 @p183)) % 0.35/0.58 (step @p188 :rule true_elim :premises (@p187)) % 0.35/0.58 (step @p189 :rule eq-refl :args (@t94)) % 0.35/0.58 (step @p190 :rule beta-reduce :args ((= @t104 @t94))) % 0.35/0.58 (step @p191 :rule refl :args (@t94)) % 0.35/0.58 (step @p192 :rule cong :premises (@p191 @p190) :args ((= @t94 @t104))) % 0.35/0.58 (step @p193 :rule trans :premises (@p192 @p189)) % 0.35/0.58 (step @p194 :rule eq-symm :args (@t104 @t94)) % 0.35/0.58 (step @p195 :rule trans :premises (@p194 @p193)) % 0.35/0.58 (step @p196 :rule ho_cong :premises (@p11 @p184)) % 0.35/0.58 (step @p197 :rule cong :premises (@p196 @p191) :args ((= @t105 @t94))) % 0.35/0.58 (step @p198 :rule trans :premises (@p197 @p195)) % 0.35/0.58 (step @p199 :rule true_elim :premises (@p198)) % 0.35/0.58 (step @p200 :rule cong :premises (@p199 @p188) :args (@t106)) % 0.35/0.58 (step @p201 :rule cong :premises (@p200) :args (@t107)) % 0.35/0.58 (step @p202 :rule refl :args (@t108)) % 0.35/0.58 (step @p203 :rule nary_cong :premises (@p202 @p201) :args (@t109)) % 0.35/0.58 ; WARNING: add trust step for TRUST % 0.35/0.58 ; trust TRUST THEORY_LEMMA % 0.35/0.58 (step @p204 :rule trust :premises () :args (@t109)) % 0.35/0.58 (step @p205 :rule eq_resolve :premises (@p204 @p203)) % 0.35/0.58 (step @p206 :rule chain_m_resolution :premises (@p205 @p178) :args (@t108 @t97 (@list @t96))) % 0.35/0.58 (step @p207 :rule not_implies_elim2 :premises (@p153)) % 0.35/0.58 (step @p208 :rule not_and :premises (@p207)) % 0.35/0.58 (step @p209 :rule chain_m_resolution :premises (@p208 @p206) :args ((not @t110) @t97 (@list @t108))) % 0.35/0.58 (step @p210 :rule eq-symm :args (@t115 @t114)) % 0.35/0.58 (step @p211 :rule eq-refl :args (@t114)) % 0.35/0.58 (step @p212 :rule refl :args (@t114)) % 0.35/0.58 (step @p213 :rule beta-reduce :args (@t116)) % 0.35/0.58 (step @p214 :rule cong :premises (@p213 @p212) :args (@t116)) % 0.35/0.58 (step @p215 :rule trans :premises (@p214 @p211)) % 0.35/0.58 (step @p216 :rule refl :args (@t111)) % 0.35/0.59 (step @p217 :rule ho_cong :premises (@p11 @p216)) % 0.35/0.59 (step @p218 :rule cong :premises (@p217 @p212) :args ((= @t117 @t114))) % 0.35/0.59 (step @p219 :rule trans :premises (@p218 @p215)) % 0.35/0.59 (step @p220 :rule true_elim :premises (@p219)) % 0.35/0.59 (step @p221 :rule eq-refl :args (@t115)) % 0.35/0.59 (step @p222 :rule refl :args (@t115)) % 0.35/0.59 (step @p223 :rule beta-reduce :args (@t118)) % 0.35/0.59 (step @p224 :rule cong :premises (@p223 @p222) :args (@t118)) % 0.35/0.59 (step @p225 :rule trans :premises (@p224 @p221)) % 0.35/0.59 (step @p226 :rule ho_cong :premises (@p5 @p216)) % 0.35/0.59 (step @p227 :rule cong :premises (@p226 @p222) :args ((= @t119 @t115))) % 0.35/0.59 (step @p228 :rule trans :premises (@p227 @p225)) % 0.35/0.59 (step @p229 :rule true_elim :premises (@p228)) % 0.35/0.59 (step @p230 :rule cong :premises (@p229 @p220) :args (@t120)) % 0.35/0.59 (step @p231 :rule trans :premises (@p230 @p210)) % 0.35/0.59 (step @p232 :rule cong :premises (@p231) :args (@t121)) % 0.35/0.59 (step @p233 :rule refl :args (@t110)) % 0.35/0.59 (step @p234 :rule nary_cong :premises (@p233 @p232) :args (@t122)) % 0.35/0.59 ; trust TRUST THEORY_LEMMA % 0.35/0.59 (step @p235 :rule trust :premises () :args (@t122)) % 0.35/0.59 (step @p236 :rule eq_resolve :premises (@p235 @p234)) % 0.35/0.59 (step @p237 :rule chain_m_resolution :premises (@p236 @p209) :args ((not @t123) @t101 (@list @t110))) % 0.35/0.59 (step @p238 :rule cnf_or_neg :args (@t115 0)) % 0.35/0.59 (step @p239 :rule cnf_equiv_neg2 :args (@t123)) % 0.35/0.59 (step @p240 :rule chain_m_resolution :premises (@p239 @p237 @p238) :args ((not @t114) @t124 (@list @t123 @t115))) % 0.35/0.59 (step @p241 :rule cnf_equiv_neg1 :args (@t123)) % 0.35/0.59 (step @p242 :rule reordering :premises (@p241) :args ((or @t114 @t115 @t123))) % 0.35/0.59 (step @p243 :rule chain_m_resolution :premises (@p242 @p240 @p237) :args (@t115 (@list true true) (@list @t114 @t123))) % 0.35/0.59 (step @p244 :rule cnf_or_pos :args (@t115)) % 0.35/0.59 (step @p245 :rule reordering :premises (@p244) :args ((or @t114 @t113 (not @t115)))) % 0.35/0.59 (step @p246 :rule chain_m_resolution :premises (@p245 @p240 @p243) :args (@t113 @t124 (@list @t114 @t115))) % 0.35/0.59 (step @p247 :rule refl :args (@t126)) % 0.35/0.59 (step @p248 :rule bool-double-not-elim :args (@t112)) % 0.35/0.59 (step @p249 :rule nary_cong :premises (@p248 @p247) :args ((or (not @t113) @t126))) % 0.35/0.59 (step @p250 :rule bool-double-not-elim :args (@t126)) % 0.35/0.59 (step @p251 :rule refl :args (@t113)) % 0.35/0.59 (step @p252 :rule cong :premises (@p251 @p250) :args ((=> @t113 @t128))) % 0.35/0.59 (assume-push @p269 @t113) % 0.35/0.59 (step @p254 :rule skolemize :premises (@p269)) % 0.35/0.59 (step-pop @p270 :rule scope :premises (@p254)) % 0.35/0.59 (step @p255 :rule process_scope :premises (@p270) :args (@t128)) % 0.35/0.59 (step @p257 :rule eq_resolve :premises (@p255 @p252)) % 0.35/0.59 (step @p258 :rule implies_elim :premises (@p257)) % 0.35/0.59 (step @p259 :rule eq_resolve :premises (@p258 @p249)) % 0.35/0.59 (step @p260 :rule chain_m_resolution :premises (@p259 @p246) :args (@t126 @t101 (@list @t112))) % 0.35/0.59 (assume-push @p271 @t70) % 0.35/0.59 (step @p262 :rule instantiate :premises (@p155) :args ((@list @t125 @t111))) % 0.35/0.59 (step-pop @p272 :rule scope :premises (@p262)) % 0.35/0.59 (step @p263 :rule process_scope :premises (@p272) :args (@t127)) % 0.35/0.59 (step @p265 :rule implies_elim :premises (@p263)) % 0.35/0.59 (step @p266 false :rule chain_m_resolution :premises (@p265 @p260 @p155) :args (false (@list false false) (@list @t126 @t70))) % 0.35/0.59 ) % 0.35/0.59 % SZS output end Proof % 0.35/0.59 % cvc5 exiting %------------------------------------------------------------------------------