%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : MSC020^5 : 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 : n024.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 08:36:07 AM UTC 2026 % Result : Theorem 0.62s 0.89s % Output : Proof 0.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : MSC020^5 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n024.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 04:45:30 EDT 2026 % 0.07/0.25 % CPUTime : % 0.07/0.32 %----Proving TH0 % 0.62/0.89 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.62/0.89 % SZS status Theorem % 0.62/0.89 % SZS output start Proof % 0.62/0.89 ( % 0.62/0.89 (declare-sort $$unsorted 0) % 0.62/0.89 (declare-const tptp.c0 $$unsorted) % 0.62/0.89 (declare-const tptp.cS (-> $$unsorted $$unsorted)) % 0.62/0.89 (declare-const tptp.cDOUBLE (-> $$unsorted $$unsorted Bool)) % 0.62/0.89 (declare-const tptp.cHALF (-> $$unsorted $$unsorted Bool)) % 0.62/0.89 (define @t1 () (@var "Xu" $$unsorted)) % 0.62/0.89 (define @t2 () (@var "Xv" $$unsorted)) % 0.62/0.89 (define @t3 () (_ (_ tptp.cHALF @t2) @t1)) % 0.62/0.89 (define @t4 () (_ (_ tptp.cDOUBLE @t1) @t2)) % 0.62/0.89 (define @t5 () (@list @t1 @t2)) % 0.62/0.89 (define @t6 () (forall @t5 (=> @t4 @t3))) % 0.62/0.89 (define @t7 () (@var "Xy" $$unsorted)) % 0.62/0.89 (define @t8 () (_ tptp.cS @t7)) % 0.62/0.89 (define @t9 () (@var "Xx" $$unsorted)) % 0.62/0.89 (define @t10 () (_ tptp.cS @t9)) % 0.62/0.89 (define @t11 () (_ tptp.cS @t10)) % 0.62/0.89 (define @t12 () (_ (_ tptp.cHALF @t11) @t8)) % 0.62/0.89 (define @t13 () (_ (_ tptp.cHALF @t9) @t7)) % 0.62/0.89 (define @t14 () (@list @t9 @t7)) % 0.62/0.89 (define @t15 () (forall @t14 (=> @t13 @t12))) % 0.62/0.89 (define @t16 () (_ tptp.cS tptp.c0)) % 0.62/0.89 (define @t17 () (_ (_ tptp.cHALF @t16) tptp.c0)) % 0.62/0.89 (define @t18 () (_ (_ tptp.cHALF tptp.c0) tptp.c0)) % 0.62/0.89 (define @t19 () (@var "Q" (-> $$unsorted $$unsorted Bool))) % 0.62/0.89 (define @t20 () (_ (_ @t19 @t1) @t2)) % 0.62/0.89 (define @t21 () (_ tptp.cS @t8)) % 0.62/0.89 (define @t22 () (_ (_ @t19 @t10) @t21)) % 0.62/0.89 (define @t23 () (_ (_ @t19 @t9) @t7)) % 0.62/0.89 (define @t24 () (forall @t14 (=> @t23 @t22))) % 0.62/0.89 (define @t25 () (_ (_ @t19 tptp.c0) tptp.c0)) % 0.62/0.89 (define @t26 () (and @t4 @t25 @t24)) % 0.62/0.89 (define @t27 () (=> @t26 @t20)) % 0.62/0.89 (define @t28 () (@list @t19 @t1 @t2)) % 0.62/0.89 (define @t29 () (forall @t28 @t27)) % 0.62/0.89 (define @t30 () (and @t29 @t18 @t17 @t15)) % 0.62/0.89 (define @t31 () (=> @t30 @t6)) % 0.62/0.89 (define @t32 () (not @t31)) % 0.62/0.89 (define @t33 () (tptp.cHALF @t2 @t1)) % 0.62/0.89 (define @t34 () (tptp.cDOUBLE @t1 @t2)) % 0.62/0.89 (define @t35 () (not @t34)) % 0.62/0.89 (define @t36 () (forall @t5 (or @t35 @t33))) % 0.62/0.89 (define @t37 () (tptp.cS @t7)) % 0.62/0.89 (define @t38 () (tptp.cS @t9)) % 0.62/0.89 (define @t39 () (tptp.cS @t38)) % 0.62/0.89 (define @t40 () (tptp.cHALF @t39 @t37)) % 0.62/0.89 (define @t41 () (tptp.cHALF @t9 @t7)) % 0.62/0.89 (define @t42 () (forall @t14 (or (not @t41) @t40))) % 0.62/0.89 (define @t43 () (tptp.cS tptp.c0)) % 0.62/0.89 (define @t44 () (tptp.cHALF @t43 tptp.c0)) % 0.62/0.89 (define @t45 () (tptp.cHALF tptp.c0 tptp.c0)) % 0.62/0.89 (define @t46 () (_ @t19 @t1 @t2)) % 0.62/0.89 (define @t47 () (tptp.cS @t37)) % 0.62/0.89 (define @t48 () (_ @t19 @t38 @t47)) % 0.62/0.89 (define @t49 () (_ @t19 @t9 @t7)) % 0.62/0.89 (define @t50 () (forall @t14 (or (not @t49) @t48))) % 0.62/0.89 (define @t51 () (not @t50)) % 0.62/0.89 (define @t52 () (_ @t19 tptp.c0 tptp.c0)) % 0.62/0.89 (define @t53 () (forall @t28 (or @t35 (not @t52) @t51 @t46))) % 0.62/0.89 (define @t54 () (and @t53 @t18 @t17 @t42)) % 0.62/0.89 (define @t55 () (=> @t54 @t36)) % 0.62/0.89 (define @t56 () (not @t4)) % 0.62/0.89 (define @t57 () (or @t56 @t3)) % 0.62/0.89 (define @t58 () (not @t13)) % 0.62/0.89 (define @t59 () (or @t58 @t12)) % 0.62/0.89 (define @t60 () (not @t25)) % 0.62/0.89 (define @t61 () (or @t56 @t60 @t51 @t20)) % 0.62/0.89 (define @t62 () (or @t56 @t60 @t51)) % 0.62/0.89 (define @t63 () (and @t4 @t25 @t50)) % 0.62/0.89 (define @t64 () (not @t23)) % 0.62/0.89 (define @t65 () (or @t64 @t22)) % 0.62/0.89 (define @t66 () (@quantifiers_skolemize @t36 1)) % 0.62/0.89 (define @t67 () (@quantifiers_skolemize @t36 0)) % 0.62/0.89 (define @t68 () (tptp.cDOUBLE @t67 @t66)) % 0.62/0.89 (define @t69 () (tptp.cHALF @t66 @t67)) % 0.62/0.89 (define @t70 () (not @t68)) % 0.62/0.89 (define @t71 () (or @t70 @t69)) % 0.62/0.89 (define @t72 () (@list true)) % 0.62/0.89 (define @t73 () (@list @t71)) % 0.62/0.89 (define @t74 () (tptp.cHALF @t47 @t38)) % 0.62/0.89 (define @t75 () (tptp.cHALF @t7 @t9)) % 0.62/0.89 (define @t76 () (or (not @t75) @t74)) % 0.62/0.89 (define @t77 () (forall @t14 @t76)) % 0.62/0.89 (define @t78 () (@var "BOUND_VARIABLE_113939" $$unsorted)) % 0.62/0.89 (define @t79 () (@var "BOUND_VARIABLE_113938" $$unsorted)) % 0.62/0.89 (define @t80 () (@list @t79 @t78)) % 0.62/0.89 (define @t81 () (@list false)) % 0.62/0.89 (define @t82 () (@var "BOUND_VARIABLE_7785" $$unsorted)) % 0.62/0.89 (define @t83 () (@var "BOUND_VARIABLE_7786" $$unsorted)) % 0.62/0.89 (define @t84 () (lambda (@list @t82 @t83) (tptp.cHALF @t83 @t82))) % 0.62/0.89 (define @t85 () (_ @t84 @t67 @t66)) % 0.62/0.89 (define @t86 () (_ @t84 @t38 @t47)) % 0.62/0.89 (define @t87 () (_ @t84 @t9 @t7)) % 0.62/0.89 (define @t88 () (not @t87)) % 0.62/0.89 (define @t89 () (or @t88 @t86)) % 0.62/0.89 (define @t90 () (forall @t14 @t89)) % 0.62/0.89 (define @t91 () (not @t90)) % 0.62/0.89 (define @t92 () (_ @t84 tptp.c0 tptp.c0)) % 0.62/0.89 (define @t93 () (not @t92)) % 0.62/0.89 (define @t94 () (or @t70 @t93 @t91 @t85)) % 0.62/0.89 (define @t95 () (not @t77)) % 0.62/0.89 (define @t96 () (not @t45)) % 0.62/0.89 (define @t97 () (or @t70 @t96 @t95 @t69)) % 0.62/0.89 (assume @p1 @t32) % 0.62/0.89 (assume @p2 true) % 0.62/0.89 (step @p3 :rule refl :args (@t36)) % 0.62/0.89 (step @p4 :rule refl :args (@t42)) % 0.62/0.89 (step @p5 :rule refl :args ((tptp.cHALF @t16 tptp.c0))) % 0.62/0.89 (step @p6 :rule refl :args (tptp.c0)) % 0.62/0.89 (step @p7 :rule refl :args (@t43)) % 0.62/0.89 (step @p8 :rule cong :premises (@p7 @p6) :args (@t44)) % 0.62/0.89 (step @p9 :rule trans :premises (@p8 @p5)) % 0.62/0.89 (step @p10 :rule refl :args (tptp.cHALF)) % 0.62/0.89 (step @p11 :rule ho_cong :premises (@p10 @p7)) % 0.62/0.89 (step @p12 :rule ho_cong :premises (@p11 @p6)) % 0.62/0.89 (step @p13 :rule cong :premises (@p12 @p9) :args ((= (_ (_ tptp.cHALF @t43) tptp.c0) @t44))) % 0.62/0.89 (step @p14 :rule symm :premises (@p13)) % 0.62/0.89 (step @p15 :rule refl :args (@t17)) % 0.62/0.89 (step @p16 :rule eq_resolve :premises (@p15 @p14)) % 0.62/0.89 (step @p17 :rule refl :args (tptp.c0)) % 0.62/0.89 (step @p18 :rule refl :args (@t16)) % 0.62/0.89 (step @p19 :rule cong :premises (@p18 @p7) :args ((= @t16 @t43))) % 0.62/0.89 (step @p20 :rule symm :premises (@p19)) % 0.62/0.89 (step @p21 :rule eq_resolve :premises (@p18 @p20)) % 0.62/0.89 (step @p22 :rule refl :args (tptp.cHALF)) % 0.62/0.89 (step @p23 :rule ho_cong :premises (@p22 @p21)) % 0.62/0.89 (step @p24 :rule ho_cong :premises (@p23 @p17)) % 0.62/0.89 (step @p25 :rule trans :premises (@p24 @p16)) % 0.62/0.89 (step @p26 :rule refl :args (@t45)) % 0.62/0.89 (step @p27 :rule refl :args (@t18)) % 0.62/0.89 (step @p28 :rule cong :premises (@p27 @p26) :args ((= @t18 @t45))) % 0.62/0.89 (step @p29 :rule symm :premises (@p28)) % 0.62/0.89 (step @p30 :rule eq_resolve :premises (@p27 @p29)) % 0.62/0.89 (step @p31 :rule refl :args (@t53)) % 0.62/0.89 (step @p32 :rule nary_cong :premises (@p31 @p30 @p25 @p4) :args (@t54)) % 0.62/0.89 (step @p33 :rule cong :premises (@p32 @p3) :args (@t55)) % 0.62/0.89 (step @p34 :rule cong :premises (@p33) :args ((not @t55))) % 0.62/0.89 (step @p35 :rule refl :args (@t33)) % 0.62/0.89 (step @p36 :rule refl :args (@t3)) % 0.62/0.89 (step @p37 :rule cong :premises (@p36 @p35) :args ((= @t3 @t33))) % 0.62/0.89 (step @p38 :rule symm :premises (@p37)) % 0.62/0.89 (step @p39 :rule eq_resolve :premises (@p36 @p38)) % 0.62/0.89 (step @p40 :rule refl :args (@t34)) % 0.62/0.89 (step @p41 :rule refl :args (@t4)) % 0.62/0.89 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t4 @t34))) % 0.62/0.89 (step @p43 :rule symm :premises (@p42)) % 0.62/0.89 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 0.62/0.89 (step @p45 :rule cong :premises (@p44) :args (@t56)) % 0.62/0.89 (step @p46 :rule nary_cong :premises (@p45 @p39) :args (@t57)) % 0.62/0.89 (step @p47 :rule cong :premises (@p46) :args ((forall @t5 @t57))) % 0.62/0.89 (step @p48 :rule bool-impl-elim :args (@t4 @t3)) % 0.62/0.89 (step @p49 :rule cong :premises (@p48) :args (@t6)) % 0.62/0.89 (step @p50 :rule trans :premises (@p49 @p47)) % 0.62/0.89 (step @p51 :rule refl :args ((tptp.cHALF @t11 @t8))) % 0.62/0.89 (step @p52 :rule refl :args (@t37)) % 0.62/0.89 (step @p53 :rule refl :args ((tptp.cS @t10))) % 0.62/0.89 (step @p54 :rule refl :args (@t38)) % 0.62/0.89 (step @p55 :rule cong :premises (@p54) :args (@t39)) % 0.62/0.89 (step @p56 :rule trans :premises (@p55 @p53)) % 0.62/0.89 (step @p57 :rule cong :premises (@p56 @p52) :args (@t40)) % 0.62/0.89 (step @p58 :rule trans :premises (@p57 @p51)) % 0.62/0.89 (step @p59 :rule ho_cong :premises (@p10 @p56)) % 0.62/0.89 (step @p60 :rule ho_cong :premises (@p59 @p52)) % 0.62/0.89 (step @p61 :rule cong :premises (@p60 @p58) :args ((= (_ (_ tptp.cHALF @t39) @t37) @t40))) % 0.62/0.89 (step @p62 :rule symm :premises (@p61)) % 0.62/0.89 (step @p63 :rule refl :args (@t12)) % 0.62/0.89 (step @p64 :rule eq_resolve :premises (@p63 @p62)) % 0.62/0.89 (step @p65 :rule refl :args (@t8)) % 0.62/0.89 (step @p66 :rule cong :premises (@p65 @p52) :args ((= @t8 @t37))) % 0.62/0.89 (step @p67 :rule symm :premises (@p66)) % 0.62/0.89 (step @p68 :rule eq_resolve :premises (@p65 @p67)) % 0.62/0.89 (step @p69 :rule refl :args (tptp.cS)) % 0.62/0.89 (step @p70 :rule ho_cong :premises (@p69 @p54)) % 0.62/0.89 (step @p71 :rule cong :premises (@p70 @p56) :args ((= (_ tptp.cS @t38) @t39))) % 0.62/0.89 (step @p72 :rule symm :premises (@p71)) % 0.62/0.89 (step @p73 :rule refl :args (@t11)) % 0.62/0.89 (step @p74 :rule eq_resolve :premises (@p73 @p72)) % 0.62/0.89 (step @p75 :rule refl :args (@t10)) % 0.62/0.89 (step @p76 :rule cong :premises (@p75 @p54) :args ((= @t10 @t38))) % 0.62/0.89 (step @p77 :rule symm :premises (@p76)) % 0.62/0.89 (step @p78 :rule eq_resolve :premises (@p75 @p77)) % 0.62/0.89 (step @p79 :rule ho_cong :premises (@p69 @p78)) % 0.62/0.89 (step @p80 :rule trans :premises (@p79 @p74)) % 0.62/0.89 (step @p81 :rule ho_cong :premises (@p10 @p80)) % 0.62/0.89 (step @p82 :rule ho_cong :premises (@p81 @p68)) % 0.62/0.89 (step @p83 :rule trans :premises (@p82 @p64)) % 0.62/0.89 (step @p84 :rule refl :args (@t41)) % 0.62/0.89 (step @p85 :rule refl :args (@t13)) % 0.62/0.89 (step @p86 :rule cong :premises (@p85 @p84) :args ((= @t13 @t41))) % 0.62/0.89 (step @p87 :rule symm :premises (@p86)) % 0.62/0.89 (step @p88 :rule eq_resolve :premises (@p85 @p87)) % 0.62/0.89 (step @p89 :rule cong :premises (@p88) :args (@t58)) % 0.62/0.89 (step @p90 :rule nary_cong :premises (@p89 @p83) :args (@t59)) % 0.62/0.89 (step @p91 :rule cong :premises (@p90) :args ((forall @t14 @t59))) % 0.62/0.89 (step @p92 :rule bool-impl-elim :args (@t13 @t12)) % 0.62/0.89 (step @p93 :rule cong :premises (@p92) :args (@t15)) % 0.62/0.89 (step @p94 :rule trans :premises (@p93 @p91)) % 0.62/0.89 (step @p95 :rule refl :args (@t17)) % 0.62/0.89 (step @p96 :rule refl :args (@t18)) % 0.62/0.89 (step @p97 :rule refl :args (@t46)) % 0.62/0.89 (step @p98 :rule refl :args (@t20)) % 0.62/0.89 (step @p99 :rule cong :premises (@p98 @p97) :args ((= @t20 @t46))) % 0.62/0.89 (step @p100 :rule symm :premises (@p99)) % 0.62/0.89 (step @p101 :rule eq_resolve :premises (@p98 @p100)) % 0.62/0.89 (step @p102 :rule refl :args (@t51)) % 0.62/0.89 (step @p103 :rule refl :args (@t52)) % 0.62/0.89 (step @p104 :rule refl :args (@t25)) % 0.62/0.89 (step @p105 :rule cong :premises (@p104 @p103) :args ((= @t25 @t52))) % 0.62/0.89 (step @p106 :rule symm :premises (@p105)) % 0.62/0.89 (step @p107 :rule eq_resolve :premises (@p104 @p106)) % 0.62/0.89 (step @p108 :rule cong :premises (@p107) :args (@t60)) % 0.62/0.89 (step @p109 :rule nary_cong :premises (@p45 @p108 @p102 @p101) :args (@t61)) % 0.62/0.89 (step @p110 :rule cong :premises (@p109) :args ((forall @t28 @t61))) % 0.62/0.89 (step @p111 :rule aci_norm :args ((= (or @t62 @t20) @t61))) % 0.62/0.89 (step @p112 :rule aci_norm :args ((= (or @t56 (or @t60 @t51)) @t62))) % 0.62/0.89 (step @p113 :rule bool-and-de-morgan :args (@t25 @t50 true)) % 0.62/0.89 (step @p114 :rule refl :args (@t56)) % 0.62/0.89 (step @p115 :rule nary_cong :premises (@p114 @p113) :args ((or @t56 (not (and @t25 @t50))))) % 0.62/0.89 (step @p116 :rule bool-and-de-morgan :args (@t4 @t25 (and @t50))) % 0.62/0.89 (step @p117 :rule trans :premises (@p116 @p115)) % 0.62/0.89 (step @p118 :rule trans :premises (@p117 @p112)) % 0.62/0.89 (step @p119 :rule nary_cong :premises (@p118 @p98) :args ((or (not @t63) @t20))) % 0.62/0.89 (step @p120 :rule trans :premises (@p119 @p111)) % 0.62/0.89 (step @p121 :rule bool-impl-elim :args (@t63 @t20)) % 0.62/0.89 (step @p122 :rule trans :premises (@p121 @p120)) % 0.62/0.89 (step @p123 :rule cong :premises (@p122) :args ((forall @t28 (=> @t63 @t20)))) % 0.62/0.89 (step @p124 :rule trans :premises (@p123 @p110)) % 0.62/0.89 (step @p125 :rule refl :args (@t20)) % 0.62/0.89 (step @p126 :rule refl :args ((_ @t19 @t10 @t21))) % 0.62/0.89 (step @p127 :rule refl :args ((tptp.cS @t8))) % 0.62/0.89 (step @p128 :rule cong :premises (@p52) :args (@t47)) % 0.62/0.89 (step @p129 :rule trans :premises (@p128 @p127)) % 0.62/0.89 (step @p130 :rule cong :premises (@p54 @p129) :args (@t48)) % 0.62/0.89 (step @p131 :rule trans :premises (@p130 @p126)) % 0.62/0.89 (step @p132 :rule refl :args (@t19)) % 0.62/0.89 (step @p133 :rule ho_cong :premises (@p132 @p54)) % 0.62/0.89 (step @p134 :rule ho_cong :premises (@p133 @p129)) % 0.62/0.89 (step @p135 :rule cong :premises (@p134 @p131) :args ((= (_ (_ @t19 @t38) @t47) @t48))) % 0.62/0.89 (step @p136 :rule symm :premises (@p135)) % 0.62/0.89 (step @p137 :rule refl :args (@t22)) % 0.62/0.89 (step @p138 :rule eq_resolve :premises (@p137 @p136)) % 0.62/0.89 (step @p139 :rule ho_cong :premises (@p69 @p52)) % 0.62/0.89 (step @p140 :rule cong :premises (@p139 @p129) :args ((= (_ tptp.cS @t37) @t47))) % 0.62/0.89 (step @p141 :rule symm :premises (@p140)) % 0.62/0.89 (step @p142 :rule refl :args (@t21)) % 0.62/0.89 (step @p143 :rule eq_resolve :premises (@p142 @p141)) % 0.62/0.89 (step @p144 :rule ho_cong :premises (@p69 @p68)) % 0.62/0.89 (step @p145 :rule trans :premises (@p144 @p143)) % 0.62/0.89 (step @p146 :rule ho_cong :premises (@p132 @p78)) % 0.62/0.89 (step @p147 :rule ho_cong :premises (@p146 @p145)) % 0.62/0.89 (step @p148 :rule trans :premises (@p147 @p138)) % 0.62/0.89 (step @p149 :rule refl :args (@t49)) % 0.62/0.89 (step @p150 :rule refl :args (@t23)) % 0.62/0.89 (step @p151 :rule cong :premises (@p150 @p149) :args ((= @t23 @t49))) % 0.62/0.89 (step @p152 :rule symm :premises (@p151)) % 0.62/0.89 (step @p153 :rule eq_resolve :premises (@p150 @p152)) % 0.62/0.89 (step @p154 :rule cong :premises (@p153) :args (@t64)) % 0.62/0.89 (step @p155 :rule nary_cong :premises (@p154 @p148) :args (@t65)) % 0.62/0.89 (step @p156 :rule cong :premises (@p155) :args ((forall @t14 @t65))) % 0.62/0.89 (step @p157 :rule bool-impl-elim :args (@t23 @t22)) % 0.62/0.89 (step @p158 :rule cong :premises (@p157) :args (@t24)) % 0.62/0.89 (step @p159 :rule trans :premises (@p158 @p156)) % 0.62/0.89 (step @p160 :rule refl :args (@t25)) % 0.62/0.89 (step @p161 :rule refl :args (@t4)) % 0.62/0.89 (step @p162 :rule nary_cong :premises (@p161 @p160 @p159) :args (@t26)) % 0.62/0.89 (step @p163 :rule cong :premises (@p162 @p125) :args (@t27)) % 0.62/0.89 (step @p164 :rule cong :premises (@p163) :args (@t29)) % 0.62/0.89 (step @p165 :rule trans :premises (@p164 @p124)) % 0.62/0.89 (step @p166 :rule nary_cong :premises (@p165 @p96 @p95 @p94) :args (@t30)) % 0.62/0.89 (step @p167 :rule cong :premises (@p166 @p50) :args (@t31)) % 0.62/0.89 (step @p168 :rule cong :premises (@p167) :args (@t32)) % 0.62/0.89 (step @p169 :rule trans :premises (@p168 @p34)) % 0.62/0.89 (step @p170 :rule eq_resolve :premises (@p1 @p169)) % 0.62/0.89 (step @p171 :rule not_implies_elim1 :premises (@p170)) % 0.62/0.89 (step @p172 :rule and_elim :premises (@p171) :args (1)) % 0.62/0.89 (step @p173 :rule not_implies_elim2 :premises (@p170)) % 0.62/0.89 (step @p174 :rule skolemize :premises (@p173)) % 0.62/0.89 (step @p175 :rule bool-double-not-elim :args (@t68)) % 0.62/0.89 (step @p176 :rule refl :args (@t71)) % 0.62/0.89 (step @p177 :rule nary_cong :premises (@p176 @p175) :args ((or @t71 (not @t70)))) % 0.62/0.89 (step @p178 :rule cnf_or_neg :args (@t71 0)) % 0.62/0.89 (step @p179 :rule eq_resolve :premises (@p178 @p177)) % 0.62/0.89 (step @p180 :rule reordering :premises (@p179) :args ((or @t68 @t71))) % 0.62/0.89 (step @p181 :rule chain_m_resolution :premises (@p180 @p174) :args (@t68 @t72 @t73)) % 0.62/0.89 (step @p182 :rule cnf_or_neg :args (@t71 1)) % 0.62/0.89 (step @p183 :rule chain_m_resolution :premises (@p182 @p174) :args ((not @t69) @t72 @t73)) % 0.62/0.89 (step @p184 :rule and_elim :premises (@p171) :args (3)) % 0.62/0.89 (step @p185 :rule quant_var_reordering :args ((= (forall (@list @t7 @t9) @t76) @t77))) % 0.62/0.89 (step @p186 :rule alpha_equiv :args ((forall (@list @t79 @t78) (or (not (tptp.cHALF @t79 @t78)) (tptp.cHALF (tptp.cS (tptp.cS @t79)) (tptp.cS @t78)))) @t80 (@list @t7 @t9))) % 0.62/0.89 (step @p187 :rule alpha_equiv :args (@t42 (@list @t9 @t7) @t80)) % 0.62/0.89 (step @p188 :rule trans :premises (@p187 @p186 @p185)) % 0.62/0.89 (step @p189 :rule equiv_elim1 :premises (@p188)) % 0.62/0.89 (step @p190 :rule chain_m_resolution :premises (@p189 @p184) :args (@t77 @t81 (@list @t42))) % 0.62/0.89 (step @p191 :rule and_elim :premises (@p171) :args (0)) % 0.62/0.89 (step @p192 :rule beta-reduce :args ((= @t85 @t69))) % 0.62/0.89 (step @p193 :rule beta-reduce :args ((= @t86 @t74))) % 0.62/0.89 (step @p194 :rule beta-reduce :args ((= @t87 @t75))) % 0.62/0.89 (step @p195 :rule cong :premises (@p194) :args (@t88)) % 0.62/0.89 (step @p196 :rule nary_cong :premises (@p195 @p193) :args (@t89)) % 0.62/0.89 (step @p197 :rule cong :premises (@p196) :args (@t90)) % 0.62/0.89 (step @p198 :rule cong :premises (@p197) :args (@t91)) % 0.62/0.89 (step @p199 :rule beta-reduce :args ((= @t92 @t45))) % 0.62/0.89 (step @p200 :rule cong :premises (@p199) :args (@t93)) % 0.62/0.89 (step @p201 :rule refl :args (@t70)) % 0.62/0.89 (step @p202 :rule nary_cong :premises (@p201 @p200 @p198 @p192) :args (@t94)) % 0.62/0.89 (step @p203 :rule cong :premises (@p31 @p202) :args ((=> @t53 @t94))) % 0.62/0.89 (assume-push @p214 @t53) % 0.62/0.89 (step @p205 :rule instantiate :premises (@p191) :args ((@list @t84 @t67 @t66))) % 0.62/0.89 (step-pop @p215 :rule scope :premises (@p205)) % 0.62/0.89 (step @p206 :rule process_scope :premises (@p215) :args (@t94)) % 0.62/0.89 (step @p208 :rule eq_resolve :premises (@p206 @p203)) % 0.62/0.89 (step @p209 :rule implies_elim :premises (@p208)) % 0.62/0.89 (step @p210 :rule chain_m_resolution :premises (@p209 @p191) :args (@t97 @t81 (@list @t53))) % 0.62/0.89 (step @p211 :rule cnf_or_pos :args (@t97)) % 0.62/0.89 (step @p212 :rule reordering :premises (@p211) :args ((or @t96 @t70 @t69 @t95 (not @t97)))) % 0.62/0.89 (step @p213 false :rule chain_m_resolution :premises (@p212 @p210 @p190 @p183 @p181 @p172) :args (false (@list false false true false false) (@list @t97 @t77 @t69 @t68 @t45))) % 0.62/0.89 ) % 0.62/0.89 % SZS output end Proof % 0.62/0.89 % cvc5 exiting %------------------------------------------------------------------------------