%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO113^5 : 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 : n015.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 09:12:03 AM UTC 2026 % Result : Theorem 0.40s 0.59s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SYO113^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n015.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 23:59:19 EDT 2026 % 0.17/0.36 % CPUTime : % 0.31/0.51 %----Proving TH0 % 0.40/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.59 % SZS status Theorem % 0.40/0.59 % SZS output start Proof % 0.40/0.59 ( % 0.40/0.59 (declare-sort $$unsorted 0) % 0.40/0.59 (declare-const tptp.c0 $$unsorted) % 0.40/0.59 (declare-const tptp.cS (-> $$unsorted $$unsorted)) % 0.40/0.59 (declare-const tptp.cEVEN (-> $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.cODD (-> $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.cNUMBER (-> $$unsorted Bool)) % 0.40/0.59 (define @t1 () (@var "Xn" $$unsorted)) % 0.40/0.59 (define @t2 () (_ tptp.cNUMBER @t1)) % 0.40/0.59 (define @t3 () (@list @t1)) % 0.40/0.59 (define @t4 () (forall @t3 @t2)) % 0.40/0.59 (define @t5 () (_ tptp.cODD @t1)) % 0.40/0.59 (define @t6 () (_ tptp.cEVEN @t1)) % 0.40/0.59 (define @t7 () (or @t6 @t5)) % 0.40/0.59 (define @t8 () (= @t2 @t7)) % 0.40/0.59 (define @t9 () (forall @t3 @t8)) % 0.40/0.59 (define @t10 () (@var "Xx" $$unsorted)) % 0.40/0.59 (define @t11 () (_ tptp.cS @t10)) % 0.40/0.59 (define @t12 () (_ tptp.cNUMBER @t11)) % 0.40/0.59 (define @t13 () (_ tptp.cNUMBER @t10)) % 0.40/0.59 (define @t14 () (and @t13 @t12)) % 0.40/0.59 (define @t15 () (@list @t10)) % 0.40/0.59 (define @t16 () (forall @t15 @t14)) % 0.40/0.59 (define @t17 () (_ tptp.cS @t11)) % 0.40/0.59 (define @t18 () (_ tptp.cNUMBER @t17)) % 0.40/0.59 (define @t19 () (and @t12 @t18)) % 0.40/0.59 (define @t20 () (forall @t15 (=> @t14 @t19))) % 0.40/0.59 (define @t21 () (_ tptp.cS tptp.c0)) % 0.40/0.59 (define @t22 () (_ tptp.cNUMBER @t21)) % 0.40/0.59 (define @t23 () (_ tptp.cNUMBER tptp.c0)) % 0.40/0.59 (define @t24 () (and @t23 @t22 @t20)) % 0.40/0.59 (define @t25 () (=> @t24 @t16)) % 0.40/0.59 (define @t26 () (_ tptp.cS @t1)) % 0.40/0.59 (define @t27 () (_ tptp.cS @t26)) % 0.40/0.59 (define @t28 () (_ tptp.cODD @t27)) % 0.40/0.59 (define @t29 () (forall @t3 (=> @t5 @t28))) % 0.40/0.59 (define @t30 () (_ tptp.cODD @t21)) % 0.40/0.59 (define @t31 () (_ tptp.cEVEN @t27)) % 0.40/0.59 (define @t32 () (forall @t3 (=> @t6 @t31))) % 0.40/0.59 (define @t33 () (_ tptp.cEVEN tptp.c0)) % 0.40/0.59 (define @t34 () (and @t33 @t32 @t30 @t29 @t25 @t9)) % 0.40/0.59 (define @t35 () (=> @t34 @t4)) % 0.40/0.59 (define @t36 () (not @t35)) % 0.40/0.59 (define @t37 () (tptp.cNUMBER @t1)) % 0.40/0.59 (define @t38 () (forall @t3 @t37)) % 0.40/0.59 (define @t39 () (tptp.cODD @t1)) % 0.40/0.59 (define @t40 () (tptp.cEVEN @t1)) % 0.40/0.59 (define @t41 () (forall @t3 (= @t37 (or @t40 @t39)))) % 0.40/0.59 (define @t42 () (@var "BOUND_VARIABLE_7498" $$unsorted)) % 0.40/0.59 (define @t43 () (tptp.cS @t42)) % 0.40/0.59 (define @t44 () (tptp.cNUMBER @t43)) % 0.40/0.59 (define @t45 () (@list @t42)) % 0.40/0.59 (define @t46 () (@var "BOUND_VARIABLE_7493" $$unsorted)) % 0.40/0.59 (define @t47 () (tptp.cNUMBER @t46)) % 0.40/0.59 (define @t48 () (@list @t46)) % 0.40/0.59 (define @t49 () (forall @t48 @t47)) % 0.40/0.59 (define @t50 () (and @t49 (forall @t45 @t44))) % 0.40/0.59 (define @t51 () (tptp.cS @t10)) % 0.40/0.59 (define @t52 () (tptp.cS @t51)) % 0.40/0.59 (define @t53 () (tptp.cNUMBER @t52)) % 0.40/0.59 (define @t54 () (tptp.cNUMBER @t51)) % 0.40/0.59 (define @t55 () (tptp.cNUMBER @t10)) % 0.40/0.59 (define @t56 () (forall @t15 (or (not @t55) (not @t54) (and @t54 @t53)))) % 0.40/0.59 (define @t57 () (tptp.cS tptp.c0)) % 0.40/0.59 (define @t58 () (tptp.cNUMBER @t57)) % 0.40/0.59 (define @t59 () (tptp.cNUMBER tptp.c0)) % 0.40/0.59 (define @t60 () (and @t23 @t22 @t56)) % 0.40/0.59 (define @t61 () (=> @t60 @t50)) % 0.40/0.59 (define @t62 () (tptp.cS @t1)) % 0.40/0.59 (define @t63 () (tptp.cS @t62)) % 0.40/0.59 (define @t64 () (tptp.cODD @t63)) % 0.40/0.59 (define @t65 () (forall @t3 (or (not @t39) @t64))) % 0.40/0.59 (define @t66 () (tptp.cODD @t57)) % 0.40/0.59 (define @t67 () (tptp.cEVEN @t63)) % 0.40/0.59 (define @t68 () (forall @t3 (or (not @t40) @t67))) % 0.40/0.59 (define @t69 () (tptp.cEVEN tptp.c0)) % 0.40/0.59 (define @t70 () (and @t33 @t68 @t30 @t65 @t61 @t41)) % 0.40/0.59 (define @t71 () (=> @t70 @t38)) % 0.40/0.59 (define @t72 () (_ tptp.cS @t42)) % 0.40/0.59 (define @t73 () (_ tptp.cNUMBER @t72)) % 0.40/0.59 (define @t74 () (forall @t45 @t73)) % 0.40/0.59 (define @t75 () (_ tptp.cNUMBER @t46)) % 0.40/0.59 (define @t76 () (forall @t48 @t75)) % 0.40/0.59 (define @t77 () (forall @t15 @t12)) % 0.40/0.59 (define @t78 () (@list @t10)) % 0.40/0.59 (define @t79 () (forall @t15 @t13)) % 0.40/0.59 (define @t80 () (@list @t46)) % 0.40/0.59 (define @t81 () (and @t79 @t77)) % 0.40/0.59 (define @t82 () (not @t12)) % 0.40/0.59 (define @t83 () (not @t13)) % 0.40/0.59 (define @t84 () (or @t83 @t82 @t19)) % 0.40/0.59 (define @t85 () (not @t5)) % 0.40/0.59 (define @t86 () (or @t85 @t28)) % 0.40/0.59 (define @t87 () (not @t6)) % 0.40/0.59 (define @t88 () (or @t87 @t31)) % 0.40/0.59 (define @t89 () (@quantifiers_skolemize @t56 0)) % 0.40/0.59 (define @t90 () (@list @t89)) % 0.40/0.59 (define @t91 () (or (tptp.cEVEN @t57) @t66)) % 0.40/0.59 (define @t92 () (@list false)) % 0.40/0.59 (define @t93 () (= @t58 @t91)) % 0.40/0.59 (define @t94 () (@list false false)) % 0.40/0.59 (define @t95 () (or @t69 (tptp.cODD tptp.c0))) % 0.40/0.59 (define @t96 () (= @t59 @t95)) % 0.40/0.59 (define @t97 () (not @t49)) % 0.40/0.59 (define @t98 () (@list true)) % 0.40/0.59 (define @t99 () (not @t50)) % 0.40/0.59 (define @t100 () (and @t59 @t58 @t56)) % 0.40/0.59 (define @t101 () (not @t100)) % 0.40/0.59 (define @t102 () (tptp.cNUMBER @t89)) % 0.40/0.59 (define @t103 () (tptp.cS @t89)) % 0.40/0.59 (define @t104 () (tptp.cS @t103)) % 0.40/0.59 (define @t105 () (tptp.cNUMBER @t104)) % 0.40/0.59 (define @t106 () (tptp.cNUMBER @t103)) % 0.40/0.59 (define @t107 () (and @t106 @t105)) % 0.40/0.59 (define @t108 () (not @t106)) % 0.40/0.59 (define @t109 () (not @t102)) % 0.40/0.59 (define @t110 () (or @t109 @t108 @t107)) % 0.40/0.59 (define @t111 () (@list @t110)) % 0.40/0.59 (define @t112 () (tptp.cODD @t89)) % 0.40/0.59 (define @t113 () (tptp.cEVEN @t89)) % 0.40/0.59 (define @t114 () (or @t113 @t112)) % 0.40/0.59 (define @t115 () (= @t102 @t114)) % 0.40/0.59 (define @t116 () (not @t105)) % 0.40/0.59 (define @t117 () (tptp.cODD @t104)) % 0.40/0.59 (define @t118 () (tptp.cEVEN @t104)) % 0.40/0.59 (define @t119 () (or @t118 @t117)) % 0.40/0.59 (define @t120 () (= @t105 @t119)) % 0.40/0.59 (define @t121 () (not @t119)) % 0.40/0.59 (define @t122 () (@list true false)) % 0.40/0.59 (define @t123 () (@list @t119)) % 0.40/0.59 (define @t124 () (not @t113)) % 0.40/0.59 (define @t125 () (or @t124 @t118)) % 0.40/0.59 (define @t126 () (not @t112)) % 0.40/0.59 (define @t127 () (or @t126 @t117)) % 0.40/0.59 (assume @p1 @t36) % 0.40/0.59 (assume @p2 true) % 0.40/0.59 (step @p3 :rule refl :args (@t38)) % 0.40/0.59 (step @p4 :rule refl :args (@t41)) % 0.40/0.59 (step @p5 :rule refl :args (@t50)) % 0.40/0.59 (step @p6 :rule refl :args (@t56)) % 0.40/0.59 (step @p7 :rule refl :args ((tptp.cNUMBER @t21))) % 0.40/0.59 (step @p8 :rule refl :args (@t57)) % 0.40/0.59 (step @p9 :rule cong :premises (@p8) :args (@t58)) % 0.40/0.59 (step @p10 :rule trans :premises (@p9 @p7)) % 0.40/0.59 (step @p11 :rule refl :args (tptp.cNUMBER)) % 0.40/0.59 (step @p12 :rule ho_cong :premises (@p11 @p8)) % 0.40/0.59 (step @p13 :rule cong :premises (@p12 @p10) :args ((= (_ tptp.cNUMBER @t57) @t58))) % 0.40/0.59 (step @p14 :rule symm :premises (@p13)) % 0.40/0.59 (step @p15 :rule refl :args (@t22)) % 0.40/0.59 (step @p16 :rule eq_resolve :premises (@p15 @p14)) % 0.40/0.59 (step @p17 :rule refl :args (@t21)) % 0.40/0.59 (step @p18 :rule cong :premises (@p17 @p8) :args ((= @t21 @t57))) % 0.40/0.59 (step @p19 :rule symm :premises (@p18)) % 0.40/0.59 (step @p20 :rule eq_resolve :premises (@p17 @p19)) % 0.40/0.59 (step @p21 :rule refl :args (tptp.cNUMBER)) % 0.40/0.59 (step @p22 :rule ho_cong :premises (@p21 @p20)) % 0.40/0.59 (step @p23 :rule trans :premises (@p22 @p16)) % 0.40/0.59 (step @p24 :rule refl :args (@t59)) % 0.40/0.59 (step @p25 :rule refl :args (@t23)) % 0.40/0.59 (step @p26 :rule cong :premises (@p25 @p24) :args ((= @t23 @t59))) % 0.40/0.59 (step @p27 :rule symm :premises (@p26)) % 0.40/0.59 (step @p28 :rule eq_resolve :premises (@p25 @p27)) % 0.40/0.59 (step @p29 :rule nary_cong :premises (@p28 @p23 @p6) :args (@t60)) % 0.40/0.59 (step @p30 :rule cong :premises (@p29 @p5) :args (@t61)) % 0.40/0.59 (step @p31 :rule refl :args (@t65)) % 0.40/0.59 (step @p32 :rule refl :args ((tptp.cODD @t21))) % 0.40/0.59 (step @p33 :rule cong :premises (@p8) :args (@t66)) % 0.40/0.59 (step @p34 :rule trans :premises (@p33 @p32)) % 0.40/0.59 (step @p35 :rule refl :args (tptp.cODD)) % 0.40/0.59 (step @p36 :rule ho_cong :premises (@p35 @p8)) % 0.40/0.59 (step @p37 :rule cong :premises (@p36 @p34) :args ((= (_ tptp.cODD @t57) @t66))) % 0.40/0.59 (step @p38 :rule symm :premises (@p37)) % 0.40/0.59 (step @p39 :rule refl :args (@t30)) % 0.40/0.59 (step @p40 :rule eq_resolve :premises (@p39 @p38)) % 0.40/0.59 (step @p41 :rule refl :args (tptp.cODD)) % 0.40/0.59 (step @p42 :rule ho_cong :premises (@p41 @p20)) % 0.40/0.59 (step @p43 :rule trans :premises (@p42 @p40)) % 0.40/0.59 (step @p44 :rule refl :args (@t68)) % 0.40/0.59 (step @p45 :rule refl :args (@t69)) % 0.40/0.59 (step @p46 :rule refl :args (@t33)) % 0.40/0.59 (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t33 @t69))) % 0.40/0.59 (step @p48 :rule symm :premises (@p47)) % 0.40/0.59 (step @p49 :rule eq_resolve :premises (@p46 @p48)) % 0.40/0.59 (step @p50 :rule nary_cong :premises (@p49 @p44 @p43 @p31 @p30 @p4) :args (@t70)) % 0.40/0.59 (step @p51 :rule cong :premises (@p50 @p3) :args (@t71)) % 0.40/0.59 (step @p52 :rule cong :premises (@p51) :args ((not @t71))) % 0.40/0.59 (step @p53 :rule refl :args (@t37)) % 0.40/0.59 (step @p54 :rule refl :args (@t2)) % 0.40/0.59 (step @p55 :rule cong :premises (@p54 @p53) :args ((= @t2 @t37))) % 0.40/0.59 (step @p56 :rule symm :premises (@p55)) % 0.40/0.59 (step @p57 :rule eq_resolve :premises (@p54 @p56)) % 0.40/0.59 (step @p58 :rule cong :premises (@p57) :args (@t4)) % 0.40/0.59 (step @p59 :rule refl :args (@t39)) % 0.40/0.59 (step @p60 :rule refl :args (@t5)) % 0.40/0.59 (step @p61 :rule cong :premises (@p60 @p59) :args ((= @t5 @t39))) % 0.40/0.59 (step @p62 :rule symm :premises (@p61)) % 0.40/0.59 (step @p63 :rule eq_resolve :premises (@p60 @p62)) % 0.40/0.59 (step @p64 :rule refl :args (@t40)) % 0.40/0.59 (step @p65 :rule refl :args (@t6)) % 0.40/0.59 (step @p66 :rule cong :premises (@p65 @p64) :args ((= @t6 @t40))) % 0.40/0.59 (step @p67 :rule symm :premises (@p66)) % 0.40/0.59 (step @p68 :rule eq_resolve :premises (@p65 @p67)) % 0.40/0.59 (step @p69 :rule nary_cong :premises (@p68 @p63) :args (@t7)) % 0.40/0.59 (step @p70 :rule cong :premises (@p57 @p69) :args (@t8)) % 0.40/0.59 (step @p71 :rule cong :premises (@p70) :args (@t9)) % 0.40/0.59 (step @p72 :rule refl :args ((tptp.cNUMBER @t72))) % 0.40/0.59 (step @p73 :rule refl :args (@t43)) % 0.40/0.59 (step @p74 :rule cong :premises (@p73) :args (@t44)) % 0.40/0.59 (step @p75 :rule trans :premises (@p74 @p72)) % 0.40/0.59 (step @p76 :rule ho_cong :premises (@p11 @p73)) % 0.40/0.59 (step @p77 :rule cong :premises (@p76 @p75) :args ((= (_ tptp.cNUMBER @t43) @t44))) % 0.40/0.59 (step @p78 :rule symm :premises (@p77)) % 0.40/0.59 (step @p79 :rule refl :args (@t73)) % 0.40/0.59 (step @p80 :rule eq_resolve :premises (@p79 @p78)) % 0.40/0.59 (step @p81 :rule refl :args (@t72)) % 0.40/0.59 (step @p82 :rule cong :premises (@p81 @p73) :args ((= @t72 @t43))) % 0.40/0.59 (step @p83 :rule symm :premises (@p82)) % 0.40/0.59 (step @p84 :rule eq_resolve :premises (@p81 @p83)) % 0.40/0.59 (step @p85 :rule ho_cong :premises (@p11 @p84)) % 0.40/0.59 (step @p86 :rule trans :premises (@p85 @p80)) % 0.40/0.59 (step @p87 :rule cong :premises (@p86) :args (@t74)) % 0.40/0.59 (step @p88 :rule refl :args (@t47)) % 0.40/0.59 (step @p89 :rule refl :args (@t75)) % 0.40/0.59 (step @p90 :rule cong :premises (@p89 @p88) :args ((= @t75 @t47))) % 0.40/0.59 (step @p91 :rule symm :premises (@p90)) % 0.40/0.59 (step @p92 :rule eq_resolve :premises (@p89 @p91)) % 0.40/0.59 (step @p93 :rule cong :premises (@p92) :args (@t76)) % 0.40/0.59 (step @p94 :rule nary_cong :premises (@p93 @p87) :args ((and @t76 @t74))) % 0.40/0.59 (step @p95 :rule alpha_equiv :args (@t77 @t78 (@list @t42))) % 0.40/0.59 (step @p96 :rule alpha_equiv :args (@t79 @t78 @t80)) % 0.40/0.59 (step @p97 :rule nary_cong :premises (@p96 @p95) :args (@t81)) % 0.40/0.59 (step @p98 :rule quant-miniscope-and :args ((= @t16 @t81))) % 0.40/0.59 (step @p99 :rule trans :premises (@p98 @p97)) % 0.40/0.59 (step @p100 :rule trans :premises (@p99 @p94)) % 0.40/0.59 (step @p101 :rule refl :args ((tptp.cNUMBER @t17))) % 0.40/0.59 (step @p102 :rule refl :args ((tptp.cS @t11))) % 0.40/0.59 (step @p103 :rule refl :args (@t51)) % 0.40/0.59 (step @p104 :rule cong :premises (@p103) :args (@t52)) % 0.40/0.59 (step @p105 :rule trans :premises (@p104 @p102)) % 0.40/0.59 (step @p106 :rule cong :premises (@p105) :args (@t53)) % 0.40/0.59 (step @p107 :rule trans :premises (@p106 @p101)) % 0.40/0.59 (step @p108 :rule ho_cong :premises (@p11 @p105)) % 0.40/0.59 (step @p109 :rule cong :premises (@p108 @p107) :args ((= (_ tptp.cNUMBER @t52) @t53))) % 0.40/0.59 (step @p110 :rule symm :premises (@p109)) % 0.40/0.59 (step @p111 :rule refl :args (@t18)) % 0.40/0.59 (step @p112 :rule eq_resolve :premises (@p111 @p110)) % 0.40/0.59 (step @p113 :rule refl :args (tptp.cS)) % 0.40/0.59 (step @p114 :rule ho_cong :premises (@p113 @p103)) % 0.40/0.59 (step @p115 :rule cong :premises (@p114 @p105) :args ((= (_ tptp.cS @t51) @t52))) % 0.40/0.59 (step @p116 :rule symm :premises (@p115)) % 0.40/0.59 (step @p117 :rule refl :args (@t17)) % 0.40/0.59 (step @p118 :rule eq_resolve :premises (@p117 @p116)) % 0.40/0.59 (step @p119 :rule refl :args (@t11)) % 0.40/0.59 (step @p120 :rule cong :premises (@p119 @p103) :args ((= @t11 @t51))) % 0.40/0.59 (step @p121 :rule symm :premises (@p120)) % 0.40/0.59 (step @p122 :rule eq_resolve :premises (@p119 @p121)) % 0.40/0.59 (step @p123 :rule ho_cong :premises (@p113 @p122)) % 0.40/0.59 (step @p124 :rule trans :premises (@p123 @p118)) % 0.40/0.59 (step @p125 :rule ho_cong :premises (@p11 @p124)) % 0.40/0.59 (step @p126 :rule trans :premises (@p125 @p112)) % 0.40/0.59 (step @p127 :rule refl :args ((tptp.cNUMBER @t11))) % 0.40/0.59 (step @p128 :rule cong :premises (@p103) :args (@t54)) % 0.40/0.59 (step @p129 :rule trans :premises (@p128 @p127)) % 0.40/0.59 (step @p130 :rule ho_cong :premises (@p11 @p103)) % 0.40/0.59 (step @p131 :rule cong :premises (@p130 @p129) :args ((= (_ tptp.cNUMBER @t51) @t54))) % 0.40/0.59 (step @p132 :rule symm :premises (@p131)) % 0.40/0.59 (step @p133 :rule refl :args (@t12)) % 0.40/0.59 (step @p134 :rule eq_resolve :premises (@p133 @p132)) % 0.40/0.59 (step @p135 :rule ho_cong :premises (@p11 @p122)) % 0.40/0.59 (step @p136 :rule trans :premises (@p135 @p134)) % 0.40/0.59 (step @p137 :rule nary_cong :premises (@p136 @p126) :args (@t19)) % 0.40/0.59 (step @p138 :rule cong :premises (@p136) :args (@t82)) % 0.40/0.59 (step @p139 :rule refl :args (@t55)) % 0.40/0.59 (step @p140 :rule refl :args (@t13)) % 0.40/0.59 (step @p141 :rule cong :premises (@p140 @p139) :args ((= @t13 @t55))) % 0.40/0.59 (step @p142 :rule symm :premises (@p141)) % 0.40/0.59 (step @p143 :rule eq_resolve :premises (@p140 @p142)) % 0.40/0.59 (step @p144 :rule cong :premises (@p143) :args (@t83)) % 0.40/0.59 (step @p145 :rule nary_cong :premises (@p144 @p138 @p137) :args (@t84)) % 0.40/0.59 (step @p146 :rule cong :premises (@p145) :args ((forall @t15 @t84))) % 0.40/0.59 (step @p147 :rule aci_norm :args ((= (or (or @t83 @t82) @t19) @t84))) % 0.40/0.59 (step @p148 :rule refl :args (@t19)) % 0.40/0.59 (step @p149 :rule bool-and-de-morgan :args (@t13 @t12 true)) % 0.40/0.59 (step @p150 :rule nary_cong :premises (@p149 @p148) :args ((or (not @t14) @t19))) % 0.40/0.59 (step @p151 :rule trans :premises (@p150 @p147)) % 0.40/0.59 (step @p152 :rule bool-impl-elim :args (@t14 @t19)) % 0.40/0.59 (step @p153 :rule trans :premises (@p152 @p151)) % 0.40/0.59 (step @p154 :rule cong :premises (@p153) :args (@t20)) % 0.40/0.59 (step @p155 :rule trans :premises (@p154 @p146)) % 0.40/0.59 (step @p156 :rule refl :args (@t22)) % 0.40/0.59 (step @p157 :rule refl :args (@t23)) % 0.40/0.59 (step @p158 :rule nary_cong :premises (@p157 @p156 @p155) :args (@t24)) % 0.40/0.59 (step @p159 :rule cong :premises (@p158 @p100) :args (@t25)) % 0.40/0.59 (step @p160 :rule refl :args ((tptp.cODD @t27))) % 0.40/0.59 (step @p161 :rule refl :args ((tptp.cS @t26))) % 0.40/0.59 (step @p162 :rule refl :args (@t62)) % 0.40/0.59 (step @p163 :rule cong :premises (@p162) :args (@t63)) % 0.40/0.59 (step @p164 :rule trans :premises (@p163 @p161)) % 0.40/0.59 (step @p165 :rule cong :premises (@p164) :args (@t64)) % 0.40/0.59 (step @p166 :rule trans :premises (@p165 @p160)) % 0.40/0.59 (step @p167 :rule ho_cong :premises (@p35 @p164)) % 0.40/0.59 (step @p168 :rule cong :premises (@p167 @p166) :args ((= (_ tptp.cODD @t63) @t64))) % 0.40/0.59 (step @p169 :rule symm :premises (@p168)) % 0.40/0.59 (step @p170 :rule refl :args (@t28)) % 0.40/0.59 (step @p171 :rule eq_resolve :premises (@p170 @p169)) % 0.40/0.59 (step @p172 :rule ho_cong :premises (@p113 @p162)) % 0.40/0.59 (step @p173 :rule cong :premises (@p172 @p164) :args ((= (_ tptp.cS @t62) @t63))) % 0.40/0.59 (step @p174 :rule symm :premises (@p173)) % 0.40/0.59 (step @p175 :rule refl :args (@t27)) % 0.40/0.59 (step @p176 :rule eq_resolve :premises (@p175 @p174)) % 0.40/0.59 (step @p177 :rule refl :args (@t26)) % 0.40/0.59 (step @p178 :rule cong :premises (@p177 @p162) :args ((= @t26 @t62))) % 0.40/0.59 (step @p179 :rule symm :premises (@p178)) % 0.40/0.59 (step @p180 :rule eq_resolve :premises (@p177 @p179)) % 0.40/0.59 (step @p181 :rule ho_cong :premises (@p113 @p180)) % 0.40/0.59 (step @p182 :rule trans :premises (@p181 @p176)) % 0.40/0.59 (step @p183 :rule ho_cong :premises (@p35 @p182)) % 0.40/0.59 (step @p184 :rule trans :premises (@p183 @p171)) % 0.40/0.59 (step @p185 :rule cong :premises (@p63) :args (@t85)) % 0.40/0.59 (step @p186 :rule nary_cong :premises (@p185 @p184) :args (@t86)) % 0.40/0.59 (step @p187 :rule cong :premises (@p186) :args ((forall @t3 @t86))) % 0.40/0.59 (step @p188 :rule bool-impl-elim :args (@t5 @t28)) % 0.40/0.59 (step @p189 :rule cong :premises (@p188) :args (@t29)) % 0.40/0.59 (step @p190 :rule trans :premises (@p189 @p187)) % 0.40/0.59 (step @p191 :rule refl :args (@t30)) % 0.40/0.59 (step @p192 :rule refl :args ((tptp.cEVEN @t27))) % 0.40/0.59 (step @p193 :rule cong :premises (@p164) :args (@t67)) % 0.40/0.59 (step @p194 :rule trans :premises (@p193 @p192)) % 0.40/0.59 (step @p195 :rule refl :args (tptp.cEVEN)) % 0.40/0.59 (step @p196 :rule ho_cong :premises (@p195 @p164)) % 0.40/0.59 (step @p197 :rule cong :premises (@p196 @p194) :args ((= (_ tptp.cEVEN @t63) @t67))) % 0.40/0.59 (step @p198 :rule symm :premises (@p197)) % 0.40/0.59 (step @p199 :rule refl :args (@t31)) % 0.40/0.59 (step @p200 :rule eq_resolve :premises (@p199 @p198)) % 0.40/0.59 (step @p201 :rule ho_cong :premises (@p195 @p182)) % 0.40/0.59 (step @p202 :rule trans :premises (@p201 @p200)) % 0.40/0.59 (step @p203 :rule cong :premises (@p68) :args (@t87)) % 0.40/0.59 (step @p204 :rule nary_cong :premises (@p203 @p202) :args (@t88)) % 0.40/0.59 (step @p205 :rule cong :premises (@p204) :args ((forall @t3 @t88))) % 0.40/0.59 (step @p206 :rule bool-impl-elim :args (@t6 @t31)) % 0.40/0.59 (step @p207 :rule cong :premises (@p206) :args (@t32)) % 0.40/0.59 (step @p208 :rule trans :premises (@p207 @p205)) % 0.40/0.59 (step @p209 :rule refl :args (@t33)) % 0.40/0.59 (step @p210 :rule nary_cong :premises (@p209 @p208 @p191 @p190 @p159 @p71) :args (@t34)) % 0.40/0.59 (step @p211 :rule cong :premises (@p210 @p58) :args (@t35)) % 0.40/0.59 (step @p212 :rule cong :premises (@p211) :args (@t36)) % 0.40/0.59 (step @p213 :rule trans :premises (@p212 @p52)) % 0.40/0.59 (step @p214 :rule eq_resolve :premises (@p1 @p213)) % 0.40/0.59 (step @p215 :rule not_implies_elim1 :premises (@p214)) % 0.40/0.59 (step @p216 :rule and_elim :premises (@p215) :args (5)) % 0.40/0.59 (step @p217 :rule instantiate :premises (@p216) :args (@t90)) % 0.40/0.59 (step @p218 :rule instantiate :premises (@p216) :args ((@list @t57))) % 0.40/0.59 (step @p219 :rule and_elim :premises (@p215) :args (2)) % 0.40/0.59 (step @p220 :rule cnf_or_neg :args (@t91 1)) % 0.40/0.59 (step @p221 :rule reordering :premises (@p220) :args ((or (not @t66) @t91))) % 0.40/0.59 (step @p222 :rule chain_m_resolution :premises (@p221 @p219) :args (@t91 @t92 (@list @t66))) % 0.40/0.59 (step @p223 :rule cnf_equiv_pos2 :args (@t93)) % 0.40/0.59 (step @p224 :rule reordering :premises (@p223) :args ((or @t58 (not @t91) (not @t93)))) % 0.40/0.59 (step @p225 :rule chain_m_resolution :premises (@p224 @p222 @p218) :args (@t58 @t94 (@list @t91 @t93))) % 0.40/0.59 (step @p226 :rule instantiate :premises (@p216) :args ((@list tptp.c0))) % 0.40/0.59 (step @p227 :rule and_elim :premises (@p215) :args (0)) % 0.40/0.59 (step @p228 :rule cnf_or_neg :args (@t95 0)) % 0.40/0.59 (step @p229 :rule reordering :premises (@p228) :args ((or (not @t69) @t95))) % 0.40/0.59 (step @p230 :rule chain_m_resolution :premises (@p229 @p227) :args (@t95 @t92 (@list @t69))) % 0.40/0.59 (step @p231 :rule cnf_equiv_pos2 :args (@t96)) % 0.40/0.59 (step @p232 :rule reordering :premises (@p231) :args ((or @t59 (not @t95) (not @t96)))) % 0.40/0.59 (step @p233 :rule chain_m_resolution :premises (@p232 @p230 @p226) :args (@t59 @t94 (@list @t95 @t96))) % 0.40/0.59 (step @p234 :rule not_implies_elim2 :premises (@p214)) % 0.40/0.59 (step @p235 :rule alpha_equiv :args (@t49 @t80 (@list @t1))) % 0.40/0.59 (step @p236 :rule equiv_elim1 :premises (@p235)) % 0.40/0.59 (step @p237 :rule reordering :premises (@p236) :args ((or @t38 @t97))) % 0.40/0.59 (step @p238 :rule chain_m_resolution :premises (@p237 @p234) :args (@t97 @t98 (@list @t38))) % 0.40/0.59 (step @p239 :rule cnf_and_pos :args (@t50 0)) % 0.40/0.59 (step @p240 :rule reordering :premises (@p239) :args ((or @t49 @t99))) % 0.40/0.59 (step @p241 :rule chain_m_resolution :premises (@p240 @p238) :args (@t99 @t98 (@list @t49))) % 0.40/0.59 (step @p242 :rule and_elim :premises (@p215) :args (4)) % 0.40/0.59 (step @p243 :rule implies_elim :premises (@p242)) % 0.40/0.59 (step @p244 :rule reordering :premises (@p243) :args ((or @t50 @t101))) % 0.40/0.59 (step @p245 :rule chain_m_resolution :premises (@p244 @p241) :args (@t101 @t98 (@list @t50))) % 0.40/0.59 (step @p246 :rule cnf_and_neg :args (@t100)) % 0.40/0.59 (step @p247 :rule chain_m_resolution :premises (@p246 @p245 @p233 @p225) :args ((not @t56) (@list true false false) (@list @t100 @t59 @t58))) % 0.40/0.59 (step @p248 :rule skolemize :premises (@p247)) % 0.40/0.59 (step @p249 :rule bool-double-not-elim :args (@t102)) % 0.40/0.59 (step @p250 :rule refl :args (@t110)) % 0.40/0.59 (step @p251 :rule nary_cong :premises (@p250 @p249) :args ((or @t110 (not @t109)))) % 0.40/0.59 (step @p252 :rule cnf_or_neg :args (@t110 0)) % 0.40/0.59 (step @p253 :rule eq_resolve :premises (@p252 @p251)) % 0.40/0.59 (step @p254 :rule reordering :premises (@p253) :args ((or @t102 @t110))) % 0.40/0.59 (step @p255 :rule chain_m_resolution :premises (@p254 @p248) :args (@t102 @t98 @t111)) % 0.40/0.59 (step @p256 :rule cnf_equiv_pos1 :args (@t115)) % 0.40/0.59 (step @p257 :rule reordering :premises (@p256) :args ((or @t109 @t114 (not @t115)))) % 0.40/0.59 (step @p258 :rule chain_m_resolution :premises (@p257 @p255 @p217) :args (@t114 @t94 (@list @t102 @t115))) % 0.40/0.59 (step @p259 :rule and_elim :premises (@p215) :args (1)) % 0.40/0.59 (step @p260 :rule instantiate :premises (@p259) :args (@t90)) % 0.40/0.59 (step @p261 :rule instantiate :premises (@p216) :args ((@list @t104))) % 0.40/0.59 (step @p262 :rule cnf_or_neg :args (@t110 2)) % 0.40/0.59 (step @p263 :rule chain_m_resolution :premises (@p262 @p248) :args ((not @t107) @t98 @t111)) % 0.40/0.59 (step @p264 :rule bool-double-not-elim :args (@t106)) % 0.40/0.59 (step @p265 :rule nary_cong :premises (@p250 @p264) :args ((or @t110 (not @t108)))) % 0.40/0.59 (step @p266 :rule cnf_or_neg :args (@t110 1)) % 0.40/0.59 (step @p267 :rule eq_resolve :premises (@p266 @p265)) % 0.40/0.59 (step @p268 :rule reordering :premises (@p267) :args ((or @t106 @t110))) % 0.40/0.59 (step @p269 :rule chain_m_resolution :premises (@p268 @p248) :args (@t106 @t98 @t111)) % 0.40/0.59 (step @p270 :rule cnf_and_neg :args (@t107)) % 0.40/0.59 (step @p271 :rule reordering :premises (@p270) :args ((or @t108 @t107 @t116))) % 0.40/0.59 (step @p272 :rule chain_m_resolution :premises (@p271 @p269 @p263) :args (@t116 (@list false true) (@list @t106 @t107))) % 0.40/0.59 (step @p273 :rule cnf_equiv_pos2 :args (@t120)) % 0.40/0.59 (step @p274 :rule reordering :premises (@p273) :args ((or @t105 @t121 (not @t120)))) % 0.40/0.59 (step @p275 :rule chain_m_resolution :premises (@p274 @p272 @p261) :args (@t121 @t122 (@list @t105 @t120))) % 0.40/0.59 (step @p276 :rule cnf_or_neg :args (@t119 0)) % 0.40/0.59 (step @p277 :rule chain_m_resolution :premises (@p276 @p275) :args ((not @t118) @t98 @t123)) % 0.40/0.59 (step @p278 :rule cnf_or_pos :args (@t125)) % 0.40/0.59 (step @p279 :rule reordering :premises (@p278) :args ((or @t118 @t124 (not @t125)))) % 0.40/0.59 (step @p280 :rule chain_m_resolution :premises (@p279 @p277 @p260) :args (@t124 @t122 (@list @t118 @t125))) % 0.40/0.59 (step @p281 :rule and_elim :premises (@p215) :args (3)) % 0.40/0.59 (step @p282 :rule instantiate :premises (@p281) :args (@t90)) % 0.40/0.59 (step @p283 :rule cnf_or_neg :args (@t119 1)) % 0.40/0.59 (step @p284 :rule chain_m_resolution :premises (@p283 @p275) :args ((not @t117) @t98 @t123)) % 0.40/0.59 (step @p285 :rule cnf_or_pos :args (@t127)) % 0.40/0.59 (step @p286 :rule reordering :premises (@p285) :args ((or @t117 @t126 (not @t127)))) % 0.40/0.59 (step @p287 :rule chain_m_resolution :premises (@p286 @p284 @p282) :args (@t126 @t122 (@list @t117 @t127))) % 0.40/0.59 (step @p288 :rule cnf_or_pos :args (@t114)) % 0.40/0.59 (step @p289 :rule reordering :premises (@p288) :args ((or @t113 @t112 (not @t114)))) % 0.40/0.59 (step @p290 false :rule chain_m_resolution :premises (@p289 @p287 @p280 @p258) :args (false (@list true true false) (@list @t112 @t113 @t114))) % 0.40/0.59 ) % 0.40/0.59 % SZS output end Proof % 0.40/0.59 % cvc5 exiting %------------------------------------------------------------------------------