%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO272^5 : 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 : n025.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 0.39s 0.60s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SYO272^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n025.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Wed Jun 3 00:02:16 EDT 2026 % 0.18/0.35 % CPUTime : % 0.31/0.50 %----Proving TH0 % 0.39/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.60 % SZS status Theorem % 0.39/0.60 % SZS output start Proof % 0.39/0.60 ( % 0.39/0.60 (declare-sort $$unsorted 0) % 0.39/0.60 (declare-const tptp.c0 $$unsorted) % 0.39/0.60 (declare-const tptp.cS (-> $$unsorted $$unsorted)) % 0.39/0.60 (declare-const tptp.cDOUBLE (-> $$unsorted $$unsorted Bool)) % 0.39/0.60 (declare-const tptp.cHALF (-> $$unsorted $$unsorted Bool)) % 0.39/0.60 (define @t1 () (@var "Xu" $$unsorted)) % 0.39/0.60 (define @t2 () (@var "Xv" $$unsorted)) % 0.39/0.60 (define @t3 () (_ (_ tptp.cHALF @t2) @t1)) % 0.39/0.60 (define @t4 () (_ (_ tptp.cDOUBLE @t1) @t2)) % 0.39/0.60 (define @t5 () (@list @t1 @t2)) % 0.39/0.60 (define @t6 () (forall @t5 (=> @t4 @t3))) % 0.39/0.60 (define @t7 () (@var "Xy" $$unsorted)) % 0.39/0.60 (define @t8 () (_ tptp.cS @t7)) % 0.39/0.60 (define @t9 () (@var "Xx" $$unsorted)) % 0.39/0.60 (define @t10 () (_ tptp.cS @t9)) % 0.39/0.60 (define @t11 () (_ tptp.cS @t10)) % 0.39/0.60 (define @t12 () (_ (_ tptp.cHALF @t11) @t8)) % 0.39/0.60 (define @t13 () (_ (_ tptp.cHALF @t9) @t7)) % 0.39/0.60 (define @t14 () (@list @t9 @t7)) % 0.39/0.60 (define @t15 () (forall @t14 (=> @t13 @t12))) % 0.39/0.60 (define @t16 () (_ tptp.cS tptp.c0)) % 0.39/0.60 (define @t17 () (_ (_ tptp.cHALF @t16) tptp.c0)) % 0.39/0.60 (define @t18 () (_ (_ tptp.cHALF tptp.c0) tptp.c0)) % 0.39/0.60 (define @t19 () (@var "Q" (-> $$unsorted $$unsorted Bool))) % 0.39/0.60 (define @t20 () (_ (_ @t19 @t1) @t2)) % 0.39/0.60 (define @t21 () (_ tptp.cS @t8)) % 0.39/0.60 (define @t22 () (_ (_ @t19 @t10) @t21)) % 0.39/0.60 (define @t23 () (_ (_ @t19 @t9) @t7)) % 0.39/0.60 (define @t24 () (forall @t14 (=> @t23 @t22))) % 0.39/0.60 (define @t25 () (_ (_ @t19 tptp.c0) tptp.c0)) % 0.39/0.60 (define @t26 () (and @t25 @t24)) % 0.39/0.60 (define @t27 () (=> @t26 @t20)) % 0.39/0.60 (define @t28 () (@list @t19)) % 0.39/0.60 (define @t29 () (forall @t28 @t27)) % 0.39/0.60 (define @t30 () (= @t4 @t29)) % 0.39/0.60 (define @t31 () (forall @t5 @t30)) % 0.39/0.60 (define @t32 () (and @t31 @t18 @t17 @t15)) % 0.39/0.60 (define @t33 () (=> @t32 @t6)) % 0.39/0.60 (define @t34 () (not @t33)) % 0.39/0.60 (define @t35 () (tptp.cHALF @t2 @t1)) % 0.39/0.60 (define @t36 () (tptp.cDOUBLE @t1 @t2)) % 0.39/0.60 (define @t37 () (forall @t5 (or (not @t36) @t35))) % 0.39/0.60 (define @t38 () (tptp.cS @t7)) % 0.39/0.60 (define @t39 () (tptp.cS @t9)) % 0.39/0.60 (define @t40 () (tptp.cS @t39)) % 0.39/0.60 (define @t41 () (tptp.cHALF @t40 @t38)) % 0.39/0.60 (define @t42 () (tptp.cHALF @t9 @t7)) % 0.39/0.60 (define @t43 () (forall @t14 (or (not @t42) @t41))) % 0.39/0.60 (define @t44 () (tptp.cS tptp.c0)) % 0.39/0.60 (define @t45 () (tptp.cHALF @t44 tptp.c0)) % 0.39/0.60 (define @t46 () (tptp.cHALF tptp.c0 tptp.c0)) % 0.39/0.60 (define @t47 () (_ @t19 @t1 @t2)) % 0.39/0.60 (define @t48 () (tptp.cS @t38)) % 0.39/0.60 (define @t49 () (_ @t19 @t39 @t48)) % 0.39/0.60 (define @t50 () (_ @t19 @t9 @t7)) % 0.39/0.60 (define @t51 () (forall @t14 (or (not @t50) @t49))) % 0.39/0.60 (define @t52 () (not @t51)) % 0.39/0.60 (define @t53 () (_ @t19 tptp.c0 tptp.c0)) % 0.39/0.60 (define @t54 () (not @t53)) % 0.39/0.60 (define @t55 () (forall @t28 (or @t54 @t52 @t47))) % 0.39/0.60 (define @t56 () (forall @t5 (= @t55 @t36))) % 0.39/0.60 (define @t57 () (and @t56 @t18 @t17 @t43)) % 0.39/0.60 (define @t58 () (=> @t57 @t37)) % 0.39/0.60 (define @t59 () (not @t4)) % 0.39/0.60 (define @t60 () (or @t59 @t3)) % 0.39/0.60 (define @t61 () (not @t13)) % 0.39/0.60 (define @t62 () (or @t61 @t12)) % 0.39/0.60 (define @t63 () (= @t4 @t55)) % 0.39/0.60 (define @t64 () (not @t25)) % 0.39/0.60 (define @t65 () (or @t64 @t52 @t20)) % 0.39/0.60 (define @t66 () (and @t25 @t51)) % 0.39/0.60 (define @t67 () (not @t23)) % 0.39/0.60 (define @t68 () (or @t67 @t22)) % 0.39/0.60 (define @t69 () (@quantifiers_skolemize @t37 0)) % 0.39/0.60 (define @t70 () (@quantifiers_skolemize @t37 1)) % 0.39/0.60 (define @t71 () (tptp.cHALF @t70 @t69)) % 0.39/0.60 (define @t72 () (tptp.cDOUBLE @t69 @t70)) % 0.39/0.60 (define @t73 () (not @t72)) % 0.39/0.60 (define @t74 () (or @t73 @t71)) % 0.39/0.60 (define @t75 () (@list true)) % 0.39/0.60 (define @t76 () (@list @t74)) % 0.39/0.60 (define @t77 () (tptp.cHALF @t48 @t39)) % 0.39/0.60 (define @t78 () (tptp.cHALF @t7 @t9)) % 0.39/0.60 (define @t79 () (or (not @t78) @t77)) % 0.39/0.60 (define @t80 () (forall @t14 @t79)) % 0.39/0.60 (define @t81 () (@var "BOUND_VARIABLE_9230" $$unsorted)) % 0.39/0.60 (define @t82 () (@var "BOUND_VARIABLE_9229" $$unsorted)) % 0.39/0.60 (define @t83 () (@list @t82 @t81)) % 0.39/0.60 (define @t84 () (@list false)) % 0.39/0.60 (define @t85 () (forall @t28 (or @t54 @t52 (_ @t19 @t69 @t70)))) % 0.39/0.60 (define @t86 () (= @t85 @t72)) % 0.39/0.60 (define @t87 () (= @t72 @t85)) % 0.39/0.60 (define @t88 () (@var "BOUND_VARIABLE_7833" $$unsorted)) % 0.39/0.60 (define @t89 () (@var "BOUND_VARIABLE_7834" $$unsorted)) % 0.39/0.60 (define @t90 () (lambda (@list @t88 @t89) (tptp.cHALF @t89 @t88))) % 0.39/0.60 (define @t91 () (_ @t90 @t69 @t70)) % 0.39/0.60 (define @t92 () (_ @t90 @t39 @t48)) % 0.39/0.60 (define @t93 () (_ @t90 @t9 @t7)) % 0.39/0.60 (define @t94 () (not @t93)) % 0.39/0.60 (define @t95 () (or @t94 @t92)) % 0.39/0.60 (define @t96 () (forall @t14 @t95)) % 0.39/0.60 (define @t97 () (not @t96)) % 0.39/0.60 (define @t98 () (_ @t90 tptp.c0 tptp.c0)) % 0.39/0.60 (define @t99 () (not @t98)) % 0.39/0.60 (define @t100 () (or @t99 @t97 @t91)) % 0.39/0.60 (define @t101 () (not @t80)) % 0.39/0.60 (define @t102 () (not @t46)) % 0.39/0.60 (define @t103 () (or @t102 @t101 @t71)) % 0.39/0.60 (assume @p1 @t34) % 0.39/0.60 (assume @p2 true) % 0.39/0.60 (step @p3 :rule refl :args (@t37)) % 0.39/0.60 (step @p4 :rule refl :args (@t43)) % 0.39/0.60 (step @p5 :rule refl :args ((tptp.cHALF @t16 tptp.c0))) % 0.39/0.60 (step @p6 :rule refl :args (tptp.c0)) % 0.39/0.60 (step @p7 :rule refl :args (@t44)) % 0.39/0.60 (step @p8 :rule cong :premises (@p7 @p6) :args (@t45)) % 0.39/0.60 (step @p9 :rule trans :premises (@p8 @p5)) % 0.39/0.60 (step @p10 :rule refl :args (tptp.cHALF)) % 0.39/0.60 (step @p11 :rule ho_cong :premises (@p10 @p7)) % 0.39/0.60 (step @p12 :rule ho_cong :premises (@p11 @p6)) % 0.39/0.60 (step @p13 :rule cong :premises (@p12 @p9) :args ((= (_ (_ tptp.cHALF @t44) tptp.c0) @t45))) % 0.39/0.60 (step @p14 :rule symm :premises (@p13)) % 0.39/0.60 (step @p15 :rule refl :args (@t17)) % 0.39/0.60 (step @p16 :rule eq_resolve :premises (@p15 @p14)) % 0.39/0.60 (step @p17 :rule refl :args (tptp.c0)) % 0.39/0.60 (step @p18 :rule refl :args (@t16)) % 0.39/0.60 (step @p19 :rule cong :premises (@p18 @p7) :args ((= @t16 @t44))) % 0.39/0.60 (step @p20 :rule symm :premises (@p19)) % 0.39/0.60 (step @p21 :rule eq_resolve :premises (@p18 @p20)) % 0.39/0.60 (step @p22 :rule refl :args (tptp.cHALF)) % 0.39/0.60 (step @p23 :rule ho_cong :premises (@p22 @p21)) % 0.39/0.60 (step @p24 :rule ho_cong :premises (@p23 @p17)) % 0.39/0.60 (step @p25 :rule trans :premises (@p24 @p16)) % 0.39/0.60 (step @p26 :rule refl :args (@t46)) % 0.39/0.60 (step @p27 :rule refl :args (@t18)) % 0.39/0.60 (step @p28 :rule cong :premises (@p27 @p26) :args ((= @t18 @t46))) % 0.39/0.60 (step @p29 :rule symm :premises (@p28)) % 0.39/0.60 (step @p30 :rule eq_resolve :premises (@p27 @p29)) % 0.39/0.60 (step @p31 :rule refl :args (@t56)) % 0.39/0.60 (step @p32 :rule nary_cong :premises (@p31 @p30 @p25 @p4) :args (@t57)) % 0.39/0.60 (step @p33 :rule cong :premises (@p32 @p3) :args (@t58)) % 0.39/0.60 (step @p34 :rule cong :premises (@p33) :args ((not @t58))) % 0.39/0.60 (step @p35 :rule refl :args (@t35)) % 0.39/0.60 (step @p36 :rule refl :args (@t3)) % 0.39/0.60 (step @p37 :rule cong :premises (@p36 @p35) :args ((= @t3 @t35))) % 0.39/0.60 (step @p38 :rule symm :premises (@p37)) % 0.39/0.60 (step @p39 :rule eq_resolve :premises (@p36 @p38)) % 0.39/0.60 (step @p40 :rule refl :args (@t36)) % 0.39/0.60 (step @p41 :rule refl :args (@t4)) % 0.39/0.60 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t4 @t36))) % 0.39/0.60 (step @p43 :rule symm :premises (@p42)) % 0.39/0.60 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 0.39/0.60 (step @p45 :rule cong :premises (@p44) :args (@t59)) % 0.39/0.60 (step @p46 :rule nary_cong :premises (@p45 @p39) :args (@t60)) % 0.39/0.60 (step @p47 :rule cong :premises (@p46) :args ((forall @t5 @t60))) % 0.39/0.60 (step @p48 :rule bool-impl-elim :args (@t4 @t3)) % 0.39/0.60 (step @p49 :rule cong :premises (@p48) :args (@t6)) % 0.39/0.60 (step @p50 :rule trans :premises (@p49 @p47)) % 0.39/0.60 (step @p51 :rule refl :args ((tptp.cHALF @t11 @t8))) % 0.39/0.60 (step @p52 :rule refl :args (@t38)) % 0.39/0.60 (step @p53 :rule refl :args ((tptp.cS @t10))) % 0.39/0.60 (step @p54 :rule refl :args (@t39)) % 0.39/0.60 (step @p55 :rule cong :premises (@p54) :args (@t40)) % 0.39/0.60 (step @p56 :rule trans :premises (@p55 @p53)) % 0.39/0.60 (step @p57 :rule cong :premises (@p56 @p52) :args (@t41)) % 0.39/0.60 (step @p58 :rule trans :premises (@p57 @p51)) % 0.39/0.60 (step @p59 :rule ho_cong :premises (@p10 @p56)) % 0.39/0.60 (step @p60 :rule ho_cong :premises (@p59 @p52)) % 0.39/0.60 (step @p61 :rule cong :premises (@p60 @p58) :args ((= (_ (_ tptp.cHALF @t40) @t38) @t41))) % 0.39/0.60 (step @p62 :rule symm :premises (@p61)) % 0.39/0.60 (step @p63 :rule refl :args (@t12)) % 0.39/0.60 (step @p64 :rule eq_resolve :premises (@p63 @p62)) % 0.39/0.60 (step @p65 :rule refl :args (@t8)) % 0.39/0.60 (step @p66 :rule cong :premises (@p65 @p52) :args ((= @t8 @t38))) % 0.39/0.60 (step @p67 :rule symm :premises (@p66)) % 0.39/0.60 (step @p68 :rule eq_resolve :premises (@p65 @p67)) % 0.39/0.60 (step @p69 :rule refl :args (tptp.cS)) % 0.39/0.60 (step @p70 :rule ho_cong :premises (@p69 @p54)) % 0.39/0.60 (step @p71 :rule cong :premises (@p70 @p56) :args ((= (_ tptp.cS @t39) @t40))) % 0.39/0.60 (step @p72 :rule symm :premises (@p71)) % 0.39/0.60 (step @p73 :rule refl :args (@t11)) % 0.39/0.60 (step @p74 :rule eq_resolve :premises (@p73 @p72)) % 0.39/0.60 (step @p75 :rule refl :args (@t10)) % 0.39/0.60 (step @p76 :rule cong :premises (@p75 @p54) :args ((= @t10 @t39))) % 0.39/0.60 (step @p77 :rule symm :premises (@p76)) % 0.39/0.60 (step @p78 :rule eq_resolve :premises (@p75 @p77)) % 0.39/0.60 (step @p79 :rule ho_cong :premises (@p69 @p78)) % 0.39/0.60 (step @p80 :rule trans :premises (@p79 @p74)) % 0.39/0.60 (step @p81 :rule ho_cong :premises (@p10 @p80)) % 0.39/0.60 (step @p82 :rule ho_cong :premises (@p81 @p68)) % 0.39/0.60 (step @p83 :rule trans :premises (@p82 @p64)) % 0.39/0.60 (step @p84 :rule refl :args (@t42)) % 0.39/0.60 (step @p85 :rule refl :args (@t13)) % 0.39/0.60 (step @p86 :rule cong :premises (@p85 @p84) :args ((= @t13 @t42))) % 0.39/0.60 (step @p87 :rule symm :premises (@p86)) % 0.39/0.60 (step @p88 :rule eq_resolve :premises (@p85 @p87)) % 0.39/0.60 (step @p89 :rule cong :premises (@p88) :args (@t61)) % 0.39/0.60 (step @p90 :rule nary_cong :premises (@p89 @p83) :args (@t62)) % 0.39/0.60 (step @p91 :rule cong :premises (@p90) :args ((forall @t14 @t62))) % 0.39/0.60 (step @p92 :rule bool-impl-elim :args (@t13 @t12)) % 0.39/0.60 (step @p93 :rule cong :premises (@p92) :args (@t15)) % 0.39/0.60 (step @p94 :rule trans :premises (@p93 @p91)) % 0.39/0.60 (step @p95 :rule refl :args (@t17)) % 0.39/0.60 (step @p96 :rule refl :args (@t18)) % 0.39/0.60 (step @p97 :rule eq-symm :args (@t36 @t55)) % 0.39/0.60 (step @p98 :rule cong :premises (@p97) :args ((forall @t5 (= @t36 @t55)))) % 0.39/0.60 (step @p99 :rule refl :args (@t55)) % 0.39/0.60 (step @p100 :rule cong :premises (@p44 @p99) :args (@t63)) % 0.39/0.60 (step @p101 :rule cong :premises (@p100) :args ((forall @t5 @t63))) % 0.39/0.60 (step @p102 :rule trans :premises (@p101 @p98)) % 0.39/0.60 (step @p103 :rule refl :args (@t47)) % 0.39/0.60 (step @p104 :rule refl :args (@t20)) % 0.39/0.60 (step @p105 :rule cong :premises (@p104 @p103) :args ((= @t20 @t47))) % 0.39/0.60 (step @p106 :rule symm :premises (@p105)) % 0.39/0.60 (step @p107 :rule eq_resolve :premises (@p104 @p106)) % 0.39/0.60 (step @p108 :rule refl :args (@t52)) % 0.39/0.60 (step @p109 :rule refl :args (@t53)) % 0.39/0.60 (step @p110 :rule refl :args (@t25)) % 0.39/0.60 (step @p111 :rule cong :premises (@p110 @p109) :args ((= @t25 @t53))) % 0.39/0.60 (step @p112 :rule symm :premises (@p111)) % 0.39/0.60 (step @p113 :rule eq_resolve :premises (@p110 @p112)) % 0.39/0.60 (step @p114 :rule cong :premises (@p113) :args (@t64)) % 0.39/0.60 (step @p115 :rule nary_cong :premises (@p114 @p108 @p107) :args (@t65)) % 0.39/0.60 (step @p116 :rule cong :premises (@p115) :args ((forall @t28 @t65))) % 0.39/0.60 (step @p117 :rule aci_norm :args ((= (or (or @t64 @t52) @t20) @t65))) % 0.39/0.60 (step @p118 :rule bool-and-de-morgan :args (@t25 @t51 true)) % 0.39/0.60 (step @p119 :rule nary_cong :premises (@p118 @p104) :args ((or (not @t66) @t20))) % 0.39/0.60 (step @p120 :rule trans :premises (@p119 @p117)) % 0.39/0.60 (step @p121 :rule bool-impl-elim :args (@t66 @t20)) % 0.39/0.60 (step @p122 :rule trans :premises (@p121 @p120)) % 0.39/0.60 (step @p123 :rule cong :premises (@p122) :args ((forall @t28 (=> @t66 @t20)))) % 0.39/0.60 (step @p124 :rule trans :premises (@p123 @p116)) % 0.39/0.60 (step @p125 :rule refl :args (@t20)) % 0.39/0.60 (step @p126 :rule refl :args ((_ @t19 @t10 @t21))) % 0.39/0.60 (step @p127 :rule refl :args ((tptp.cS @t8))) % 0.39/0.60 (step @p128 :rule cong :premises (@p52) :args (@t48)) % 0.39/0.60 (step @p129 :rule trans :premises (@p128 @p127)) % 0.39/0.60 (step @p130 :rule cong :premises (@p54 @p129) :args (@t49)) % 0.39/0.60 (step @p131 :rule trans :premises (@p130 @p126)) % 0.39/0.60 (step @p132 :rule refl :args (@t19)) % 0.39/0.60 (step @p133 :rule ho_cong :premises (@p132 @p54)) % 0.39/0.60 (step @p134 :rule ho_cong :premises (@p133 @p129)) % 0.39/0.60 (step @p135 :rule cong :premises (@p134 @p131) :args ((= (_ (_ @t19 @t39) @t48) @t49))) % 0.39/0.60 (step @p136 :rule symm :premises (@p135)) % 0.39/0.60 (step @p137 :rule refl :args (@t22)) % 0.39/0.60 (step @p138 :rule eq_resolve :premises (@p137 @p136)) % 0.39/0.60 (step @p139 :rule ho_cong :premises (@p69 @p52)) % 0.39/0.60 (step @p140 :rule cong :premises (@p139 @p129) :args ((= (_ tptp.cS @t38) @t48))) % 0.39/0.60 (step @p141 :rule symm :premises (@p140)) % 0.39/0.60 (step @p142 :rule refl :args (@t21)) % 0.39/0.60 (step @p143 :rule eq_resolve :premises (@p142 @p141)) % 0.39/0.60 (step @p144 :rule ho_cong :premises (@p69 @p68)) % 0.39/0.60 (step @p145 :rule trans :premises (@p144 @p143)) % 0.39/0.60 (step @p146 :rule ho_cong :premises (@p132 @p78)) % 0.39/0.60 (step @p147 :rule ho_cong :premises (@p146 @p145)) % 0.39/0.60 (step @p148 :rule trans :premises (@p147 @p138)) % 0.39/0.60 (step @p149 :rule refl :args (@t50)) % 0.39/0.60 (step @p150 :rule refl :args (@t23)) % 0.39/0.60 (step @p151 :rule cong :premises (@p150 @p149) :args ((= @t23 @t50))) % 0.39/0.60 (step @p152 :rule symm :premises (@p151)) % 0.39/0.60 (step @p153 :rule eq_resolve :premises (@p150 @p152)) % 0.39/0.60 (step @p154 :rule cong :premises (@p153) :args (@t67)) % 0.39/0.60 (step @p155 :rule nary_cong :premises (@p154 @p148) :args (@t68)) % 0.39/0.60 (step @p156 :rule cong :premises (@p155) :args ((forall @t14 @t68))) % 0.39/0.60 (step @p157 :rule bool-impl-elim :args (@t23 @t22)) % 0.39/0.60 (step @p158 :rule cong :premises (@p157) :args (@t24)) % 0.39/0.60 (step @p159 :rule trans :premises (@p158 @p156)) % 0.39/0.60 (step @p160 :rule refl :args (@t25)) % 0.39/0.60 (step @p161 :rule nary_cong :premises (@p160 @p159) :args (@t26)) % 0.39/0.60 (step @p162 :rule cong :premises (@p161 @p125) :args (@t27)) % 0.39/0.60 (step @p163 :rule cong :premises (@p162) :args (@t29)) % 0.39/0.60 (step @p164 :rule trans :premises (@p163 @p124)) % 0.39/0.60 (step @p165 :rule refl :args (@t4)) % 0.39/0.60 (step @p166 :rule cong :premises (@p165 @p164) :args (@t30)) % 0.39/0.60 (step @p167 :rule cong :premises (@p166) :args (@t31)) % 0.39/0.60 (step @p168 :rule trans :premises (@p167 @p102)) % 0.39/0.60 (step @p169 :rule nary_cong :premises (@p168 @p96 @p95 @p94) :args (@t32)) % 0.39/0.60 (step @p170 :rule cong :premises (@p169 @p50) :args (@t33)) % 0.39/0.60 (step @p171 :rule cong :premises (@p170) :args (@t34)) % 0.39/0.60 (step @p172 :rule trans :premises (@p171 @p34)) % 0.39/0.60 (step @p173 :rule eq_resolve :premises (@p1 @p172)) % 0.39/0.60 (step @p174 :rule not_implies_elim1 :premises (@p173)) % 0.39/0.60 (step @p175 :rule and_elim :premises (@p174) :args (1)) % 0.39/0.60 (step @p176 :rule not_implies_elim2 :premises (@p173)) % 0.39/0.60 (step @p177 :rule skolemize :premises (@p176)) % 0.39/0.60 (step @p178 :rule cnf_or_neg :args (@t74 1)) % 0.39/0.60 (step @p179 :rule chain_m_resolution :premises (@p178 @p177) :args ((not @t71) @t75 @t76)) % 0.39/0.60 (step @p180 :rule and_elim :premises (@p174) :args (3)) % 0.39/0.60 (step @p181 :rule quant_var_reordering :args ((= (forall (@list @t7 @t9) @t79) @t80))) % 0.39/0.60 (step @p182 :rule alpha_equiv :args ((forall (@list @t82 @t81) (or (not (tptp.cHALF @t82 @t81)) (tptp.cHALF (tptp.cS (tptp.cS @t82)) (tptp.cS @t81)))) @t83 (@list @t7 @t9))) % 0.39/0.60 (step @p183 :rule alpha_equiv :args (@t43 (@list @t9 @t7) @t83)) % 0.39/0.60 (step @p184 :rule trans :premises (@p183 @p182 @p181)) % 0.39/0.60 (step @p185 :rule equiv_elim1 :premises (@p184)) % 0.39/0.60 (step @p186 :rule chain_m_resolution :premises (@p185 @p180) :args (@t80 @t84 (@list @t43))) % 0.39/0.60 (step @p187 :rule and_elim :premises (@p174) :args (0)) % 0.39/0.60 (step @p188 :rule eq-symm :args (@t85 @t72)) % 0.39/0.60 (step @p189 :rule cong :premises (@p31 @p188) :args ((=> @t56 @t86))) % 0.39/0.60 (assume-push @p229 @t56) % 0.39/0.60 (step @p191 :rule instantiate :premises (@p187) :args ((@list @t69 @t70))) % 0.39/0.60 (step-pop @p230 :rule scope :premises (@p191)) % 0.39/0.60 (step @p192 :rule process_scope :premises (@p230) :args (@t86)) % 0.39/0.60 (step @p194 :rule eq_resolve :premises (@p192 @p189)) % 0.39/0.60 (step @p195 :rule implies_elim :premises (@p194)) % 0.39/0.60 (step @p196 :rule chain_m_resolution :premises (@p195 @p187) :args (@t87 @t84 (@list @t56))) % 0.39/0.60 (step @p197 :rule bool-double-not-elim :args (@t72)) % 0.39/0.60 (step @p198 :rule refl :args (@t74)) % 0.39/0.60 (step @p199 :rule nary_cong :premises (@p198 @p197) :args ((or @t74 (not @t73)))) % 0.39/0.60 (step @p200 :rule cnf_or_neg :args (@t74 0)) % 0.39/0.60 (step @p201 :rule eq_resolve :premises (@p200 @p199)) % 0.39/0.60 (step @p202 :rule reordering :premises (@p201) :args ((or @t72 @t74))) % 0.39/0.60 (step @p203 :rule chain_m_resolution :premises (@p202 @p177) :args (@t72 @t75 @t76)) % 0.39/0.60 (step @p204 :rule cnf_equiv_pos1 :args (@t87)) % 0.39/0.60 (step @p205 :rule reordering :premises (@p204) :args ((or @t73 @t85 (not @t87)))) % 0.39/0.60 (step @p206 :rule chain_m_resolution :premises (@p205 @p203 @p196) :args (@t85 (@list false false) (@list @t72 @t87))) % 0.39/0.60 (step @p207 :rule beta-reduce :args ((= @t91 @t71))) % 0.39/0.60 (step @p208 :rule beta-reduce :args ((= @t92 @t77))) % 0.39/0.60 (step @p209 :rule beta-reduce :args ((= @t93 @t78))) % 0.39/0.60 (step @p210 :rule cong :premises (@p209) :args (@t94)) % 0.39/0.60 (step @p211 :rule nary_cong :premises (@p210 @p208) :args (@t95)) % 0.39/0.60 (step @p212 :rule cong :premises (@p211) :args (@t96)) % 0.39/0.60 (step @p213 :rule cong :premises (@p212) :args (@t97)) % 0.39/0.60 (step @p214 :rule beta-reduce :args ((= @t98 @t46))) % 0.39/0.60 (step @p215 :rule cong :premises (@p214) :args (@t99)) % 0.39/0.60 (step @p216 :rule nary_cong :premises (@p215 @p213 @p207) :args (@t100)) % 0.39/0.60 (step @p217 :rule refl :args (@t85)) % 0.39/0.60 (step @p218 :rule cong :premises (@p217 @p216) :args ((=> @t85 @t100))) % 0.39/0.60 (assume-push @p231 @t85) % 0.39/0.60 (step @p220 :rule instantiate :premises (@p206) :args ((@list @t90))) % 0.39/0.60 (step-pop @p232 :rule scope :premises (@p220)) % 0.39/0.60 (step @p221 :rule process_scope :premises (@p232) :args (@t100)) % 0.39/0.60 (step @p223 :rule eq_resolve :premises (@p221 @p218)) % 0.39/0.60 (step @p224 :rule implies_elim :premises (@p223)) % 0.39/0.60 (step @p225 :rule chain_m_resolution :premises (@p224 @p206) :args (@t103 @t84 (@list @t85))) % 0.39/0.60 (step @p226 :rule cnf_or_pos :args (@t103)) % 0.39/0.60 (step @p227 :rule reordering :premises (@p226) :args ((or @t102 @t71 @t101 (not @t103)))) % 0.39/0.60 (step @p228 false :rule chain_m_resolution :premises (@p227 @p225 @p186 @p179 @p175) :args (false (@list false false true false) (@list @t103 @t80 @t71 @t46))) % 0.39/0.60 ) % 0.39/0.60 % SZS output end Proof % 0.39/0.60 % cvc5 exiting %------------------------------------------------------------------------------