%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : PUZ109^5 : TPTP v9.2.1. Bugfixed v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n027.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 08:44:13 AM UTC 2026 % Result : Theorem 0.37s 0.58s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : PUZ109^5 : TPTP v9.2.1. Bugfixed v5.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n027.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 13:18:36 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.49 %----Proving TH0 % 0.37/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.58 % SZS status Theorem % 0.37/0.58 % SZS output start Proof % 0.37/0.58 ( % 0.37/0.58 (declare-sort $$unsorted 0) % 0.37/0.58 (declare-const tptp.s (-> $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.c1 $$unsorted) % 0.37/0.58 (define tptp.cCKB6_BLACK () (let ((_let_1 (@var "Xv" $$unsorted))) (let ((_let_2 (@var "Xu" $$unsorted))) (let ((_let_3 (@var "Xw" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "Xk" $$unsorted))) (let ((_let_5 (@var "Xj" $$unsorted))) (let ((_let_6 (_ tptp.s _let_5))) (lambda (@list _let_2 _let_1) (forall (@list _let_3) (=> (and (_ (_ _let_3 tptp.c1) tptp.c1) (forall (@list _let_5 _let_4) (=> (_ (_ _let_3 _let_5) _let_4) (and (_ (_ _let_3 (_ tptp.s _let_6)) _let_4) (_ (_ _let_3 _let_6) (_ tptp.s _let_4)))))) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.37/0.58 (define @t1 () (@var "Xk" $$unsorted)) % 0.37/0.58 (define @t2 () (_ tptp.s @t1)) % 0.37/0.58 (define @t3 () (@var "Xj" $$unsorted)) % 0.37/0.58 (define @t4 () (_ tptp.s @t3)) % 0.37/0.58 (define @t5 () (=> (_ (_ tptp.cCKB6_BLACK @t3) @t1) (_ (_ tptp.cCKB6_BLACK @t4) @t2))) % 0.37/0.58 (define @t6 () (@list @t3 @t1)) % 0.37/0.58 (define @t7 () (forall @t6 @t5)) % 0.37/0.58 (define @t8 () (not @t7)) % 0.37/0.58 (define @t9 () (@var "Xv" $$unsorted)) % 0.37/0.58 (define @t10 () (@var "Xu" $$unsorted)) % 0.37/0.58 (define @t11 () (@var "Xw" (-> $$unsorted $$unsorted Bool))) % 0.37/0.58 (define @t12 () (_ (_ @t11 @t10) @t9)) % 0.37/0.58 (define @t13 () (_ (_ @t11 @t4) @t2)) % 0.37/0.58 (define @t14 () (_ tptp.s @t4)) % 0.37/0.58 (define @t15 () (_ (_ @t11 @t14) @t1)) % 0.37/0.58 (define @t16 () (and @t15 @t13)) % 0.37/0.58 (define @t17 () (_ (_ @t11 @t3) @t1)) % 0.37/0.58 (define @t18 () (forall @t6 (=> @t17 @t16))) % 0.37/0.58 (define @t19 () (_ (_ @t11 tptp.c1) tptp.c1)) % 0.37/0.58 (define @t20 () (and @t19 @t18)) % 0.37/0.58 (define @t21 () (=> @t20 @t12)) % 0.37/0.58 (define @t22 () (@list @t11)) % 0.37/0.58 (define @t23 () (forall @t22 @t21)) % 0.37/0.58 (define @t24 () (@list @t10 @t9)) % 0.37/0.58 (define @t25 () (lambda @t24 @t23)) % 0.37/0.58 (define @t26 () (tptp.s @t1)) % 0.37/0.58 (define @t27 () (tptp.s @t3)) % 0.37/0.58 (define @t28 () (@var "BOUND_VARIABLE_7593" (-> $$unsorted $$unsorted Bool))) % 0.37/0.58 (define @t29 () (_ @t28 @t27 @t26)) % 0.37/0.58 (define @t30 () (@var "BOUND_VARIABLE_7567" $$unsorted)) % 0.37/0.58 (define @t31 () (tptp.s @t30)) % 0.37/0.58 (define @t32 () (@var "BOUND_VARIABLE_7540" $$unsorted)) % 0.37/0.58 (define @t33 () (tptp.s @t32)) % 0.37/0.58 (define @t34 () (tptp.s @t33)) % 0.37/0.58 (define @t35 () (@list @t32 @t30)) % 0.37/0.58 (define @t36 () (not (forall @t35 (or (not (_ @t28 @t32 @t30)) (and (_ @t28 @t34 @t30) (_ @t28 @t33 @t31)))))) % 0.37/0.58 (define @t37 () (not (_ @t28 tptp.c1 tptp.c1))) % 0.37/0.58 (define @t38 () (_ @t11 @t3 @t1)) % 0.37/0.58 (define @t39 () (@var "BOUND_VARIABLE_7522" $$unsorted)) % 0.37/0.58 (define @t40 () (tptp.s @t39)) % 0.37/0.58 (define @t41 () (@var "BOUND_VARIABLE_7499" $$unsorted)) % 0.37/0.58 (define @t42 () (tptp.s @t41)) % 0.37/0.58 (define @t43 () (tptp.s @t42)) % 0.37/0.58 (define @t44 () (@list @t41 @t39)) % 0.37/0.58 (define @t45 () (not (forall @t44 (or (not (_ @t11 @t41 @t39)) (and (_ @t11 @t43 @t39) (_ @t11 @t42 @t40)))))) % 0.37/0.58 (define @t46 () (_ @t11 tptp.c1 tptp.c1)) % 0.37/0.58 (define @t47 () (not @t46)) % 0.37/0.58 (define @t48 () (forall @t22 (or @t47 @t45 @t38))) % 0.37/0.58 (define @t49 () (not @t48)) % 0.37/0.58 (define @t50 () (or @t49 @t37 @t36 @t29)) % 0.37/0.58 (define @t51 () (or @t37 @t36 @t29)) % 0.37/0.58 (define @t52 () (or @t49 @t51)) % 0.37/0.58 (define @t53 () (@list @t3 @t1 @t28)) % 0.37/0.58 (define @t54 () (forall @t53 @t52)) % 0.37/0.58 (define @t55 () (@list @t28)) % 0.37/0.58 (define @t56 () (forall @t55 @t52)) % 0.37/0.58 (define @t57 () (forall @t55 @t51)) % 0.37/0.58 (define @t58 () (or @t49 @t57)) % 0.37/0.58 (define @t59 () (_ @t11 @t27 @t26)) % 0.37/0.58 (define @t60 () (not (forall @t35 (or (not (_ @t11 @t32 @t30)) (and (_ @t11 @t34 @t30) (_ @t11 @t33 @t31)))))) % 0.37/0.58 (define @t61 () (forall @t22 (or @t47 @t60 @t59))) % 0.37/0.58 (define @t62 () (_ @t11 @t27 @t2)) % 0.37/0.58 (define @t63 () (or @t47 @t60 @t62)) % 0.37/0.58 (define @t64 () (forall @t22 @t63)) % 0.37/0.58 (define @t65 () (_ @t11 @t27 @t9)) % 0.37/0.58 (define @t66 () (@list @t9)) % 0.37/0.58 (define @t67 () (forall (@list @t32 @t1) (or (not (_ @t11 @t32 @t1)) (and (_ @t11 @t34 @t1) (_ @t11 @t33 @t26))))) % 0.37/0.58 (define @t68 () (@list @t1)) % 0.37/0.58 (define @t69 () (not @t67)) % 0.37/0.58 (define @t70 () (or @t47 @t69 @t65)) % 0.37/0.58 (define @t71 () (forall @t22 @t70)) % 0.37/0.58 (define @t72 () (_ @t11 @t4 @t9)) % 0.37/0.58 (define @t73 () (or @t47 @t69 @t72)) % 0.37/0.58 (define @t74 () (forall @t22 @t73)) % 0.37/0.58 (define @t75 () (lambda @t66 @t74)) % 0.37/0.58 (define @t76 () (_ @t11 @t10 @t9)) % 0.37/0.58 (define @t77 () (tptp.s @t27)) % 0.37/0.58 (define @t78 () (_ @t11 @t77 @t1)) % 0.37/0.58 (define @t79 () (forall @t6 (or (not @t38) (and @t78 @t59)))) % 0.37/0.58 (define @t80 () (@list @t3)) % 0.37/0.58 (define @t81 () (not @t79)) % 0.37/0.58 (define @t82 () (or @t47 @t81 @t76)) % 0.37/0.58 (define @t83 () (forall @t22 @t82)) % 0.37/0.58 (define @t84 () (lambda @t24 @t83)) % 0.37/0.58 (define @t85 () (_ @t11 @t3 @t9)) % 0.37/0.58 (define @t86 () (forall (@list @t41 @t1) (or (not (_ @t11 @t41 @t1)) (and (_ @t11 @t43 @t1) (_ @t11 @t42 @t26))))) % 0.37/0.58 (define @t87 () (not @t86)) % 0.37/0.58 (define @t88 () (or @t47 @t87 @t85)) % 0.37/0.58 (define @t89 () (forall @t22 @t88)) % 0.37/0.58 (define @t90 () (lambda @t66 @t89)) % 0.37/0.58 (define @t91 () (=> (_ (_ @t84 @t3) @t1) (_ (_ @t84 @t4) @t2))) % 0.37/0.58 (define @t92 () (forall @t6 @t91)) % 0.37/0.58 (define @t93 () (not @t19)) % 0.37/0.58 (define @t94 () (or @t93 @t81 @t12)) % 0.37/0.58 (define @t95 () (and @t19 @t79)) % 0.37/0.58 (define @t96 () (not @t17)) % 0.37/0.58 (define @t97 () (or @t96 @t16)) % 0.37/0.58 (define @t98 () (forall @t53 @t50)) % 0.37/0.58 (define @t99 () (@quantifiers_skolemize @t98 2)) % 0.37/0.58 (define @t100 () (_ @t99 tptp.c1 tptp.c1)) % 0.37/0.58 (define @t101 () (@quantifiers_skolemize @t98 1)) % 0.37/0.58 (define @t102 () (@quantifiers_skolemize @t98 0)) % 0.37/0.58 (define @t103 () (tptp.s @t102)) % 0.37/0.58 (define @t104 () (_ @t99 @t103 (tptp.s @t101))) % 0.37/0.58 (define @t105 () (forall @t35 (or (not (_ @t99 @t32 @t30)) (and (_ @t99 @t34 @t30) (_ @t99 @t33 @t31))))) % 0.37/0.58 (define @t106 () (not @t105)) % 0.37/0.58 (define @t107 () (not @t100)) % 0.37/0.58 (define @t108 () (forall @t22 (or @t47 @t45 (_ @t11 @t102 @t101)))) % 0.37/0.58 (define @t109 () (not @t108)) % 0.37/0.58 (define @t110 () (or @t109 @t107 @t106 @t104)) % 0.37/0.58 (define @t111 () (@list true)) % 0.37/0.58 (define @t112 () (@list @t110)) % 0.37/0.58 (define @t113 () (and (_ @t99 (tptp.s @t103) @t101) @t104)) % 0.37/0.58 (define @t114 () (not @t113)) % 0.37/0.58 (define @t115 () (_ @t99 @t102 @t101)) % 0.37/0.58 (define @t116 () (not @t115)) % 0.37/0.58 (define @t117 () (or @t116 @t113)) % 0.37/0.58 (define @t118 () (forall @t44 (or (not (_ @t99 @t41 @t39)) (and (_ @t99 @t43 @t39) (_ @t99 @t42 @t40))))) % 0.37/0.58 (define @t119 () (not @t118)) % 0.37/0.58 (define @t120 () (or @t107 @t119 @t115)) % 0.37/0.58 (assume @p1 @t8) % 0.37/0.58 (assume @p2 true) % 0.37/0.58 (step @p3 (= tptp.cCKB6_BLACK @t25) :rule refl :args (@t25)) % 0.37/0.58 (step @p4 :rule aci_norm :args ((= @t52 @t50))) % 0.37/0.58 (step @p5 :rule cong :premises (@p4) :args (@t54)) % 0.37/0.58 (step @p6 :rule quant-merge-prenex :args ((= (forall @t6 @t56) @t54))) % 0.37/0.58 (step @p7 :rule alpha_equiv :args (@t57 (@list @t28) (@list @t11))) % 0.37/0.58 (step @p8 :rule refl :args (@t49)) % 0.37/0.58 (step @p9 :rule nary_cong :premises (@p8 @p7) :args (@t58)) % 0.37/0.58 (step @p10 :rule quant-miniscope-or :args ((= @t56 @t58))) % 0.37/0.58 (step @p11 :rule trans :premises (@p10 @p9)) % 0.37/0.58 (step @p12 :rule symm :premises (@p11)) % 0.37/0.58 (step @p13 :rule cong :premises (@p12) :args ((forall @t6 (or @t49 @t61)))) % 0.37/0.58 (step @p14 :rule trans :premises (@p13 @p6)) % 0.37/0.58 (step @p15 :rule trans :premises (@p14 @p5)) % 0.37/0.58 (step @p16 :rule bool-impl-elim :args (@t48 @t61)) % 0.37/0.58 (step @p17 :rule cong :premises (@p16) :args ((forall @t6 (=> @t48 @t61)))) % 0.37/0.58 (step @p18 :rule trans :premises (@p17 @p15)) % 0.37/0.58 (step @p19 :rule refl :args (@t26)) % 0.37/0.58 (step @p20 :rule refl :args (@t2)) % 0.37/0.58 (step @p21 :rule cong :premises (@p20 @p19) :args ((= @t2 @t26))) % 0.37/0.58 (step @p22 :rule symm :premises (@p21)) % 0.37/0.58 (step @p23 :rule eq_resolve :premises (@p20 @p22)) % 0.37/0.58 (step @p24 :rule refl :args (@t27)) % 0.37/0.58 (step @p25 :rule cong :premises (@p24 @p23) :args (@t62)) % 0.37/0.58 (step @p26 :rule refl :args (@t60)) % 0.37/0.58 (step @p27 :rule refl :args (@t47)) % 0.37/0.58 (step @p28 :rule nary_cong :premises (@p27 @p26 @p25) :args (@t63)) % 0.37/0.58 (step @p29 :rule cong :premises (@p28) :args (@t64)) % 0.37/0.58 (step @p30 :rule beta-reduce :args ((= (_ (lambda @t66 (forall @t22 (or @t47 @t60 @t65))) @t2) @t64))) % 0.37/0.58 (step @p31 :rule trans :premises (@p30 @p29)) % 0.37/0.58 (step @p32 :rule refl :args (@t65)) % 0.37/0.58 (step @p33 :rule alpha_equiv :args (@t67 @t68 (@list @t30))) % 0.37/0.58 (step @p34 :rule cong :premises (@p33) :args (@t69)) % 0.37/0.58 (step @p35 :rule nary_cong :premises (@p27 @p34 @p32) :args (@t70)) % 0.37/0.58 (step @p36 :rule cong :premises (@p35) :args (@t71)) % 0.37/0.58 (step @p37 :rule cong :premises (@p36) :args ((lambda @t66 @t71))) % 0.37/0.58 (step @p38 :rule ho_cong :premises (@p37 @p20)) % 0.37/0.58 (step @p39 :rule trans :premises (@p38 @p31)) % 0.37/0.58 (step @p40 :rule refl :args (@t2)) % 0.37/0.58 (step @p41 :rule refl :args (@t9)) % 0.37/0.58 (step @p42 :rule refl :args (@t27)) % 0.37/0.58 (step @p43 :rule refl :args (@t4)) % 0.37/0.58 (step @p44 :rule cong :premises (@p43 @p42) :args ((= @t4 @t27))) % 0.37/0.58 (step @p45 :rule symm :premises (@p44)) % 0.37/0.58 (step @p46 :rule eq_resolve :premises (@p43 @p45)) % 0.37/0.58 (step @p47 :rule cong :premises (@p46 @p41) :args (@t72)) % 0.37/0.58 (step @p48 :rule refl :args (@t69)) % 0.37/0.58 (step @p49 :rule nary_cong :premises (@p27 @p48 @p47) :args (@t73)) % 0.37/0.58 (step @p50 :rule cong :premises (@p49) :args (@t74)) % 0.37/0.58 (step @p51 :rule cong :premises (@p50) :args (@t75)) % 0.37/0.58 (step @p52 :rule beta-reduce :args ((= (_ (lambda @t24 (forall @t22 (or @t47 @t69 @t76))) @t4) @t75))) % 0.37/0.58 (step @p53 :rule trans :premises (@p52 @p51)) % 0.37/0.58 (step @p54 :rule refl :args (@t76)) % 0.37/0.58 (step @p55 :rule alpha_equiv :args (@t79 @t80 (@list @t32))) % 0.37/0.58 (step @p56 :rule cong :premises (@p55) :args (@t81)) % 0.37/0.58 (step @p57 :rule nary_cong :premises (@p27 @p56 @p54) :args (@t82)) % 0.37/0.58 (step @p58 :rule cong :premises (@p57) :args (@t83)) % 0.37/0.58 (step @p59 :rule cong :premises (@p58) :args (@t84)) % 0.37/0.58 (step @p60 :rule ho_cong :premises (@p59 @p43)) % 0.37/0.58 (step @p61 :rule trans :premises (@p60 @p53)) % 0.37/0.58 (step @p62 :rule ho_cong :premises (@p61 @p40)) % 0.37/0.58 (step @p63 :rule trans :premises (@p62 @p39)) % 0.37/0.58 (step @p64 :rule beta-reduce :args ((= (_ (lambda @t66 (forall @t22 (or @t47 @t45 @t85))) @t1) @t48))) % 0.37/0.58 (step @p65 :rule refl :args (@t1)) % 0.37/0.58 (step @p66 :rule refl :args (@t85)) % 0.37/0.58 (step @p67 :rule alpha_equiv :args (@t86 @t68 (@list @t39))) % 0.37/0.58 (step @p68 :rule cong :premises (@p67) :args (@t87)) % 0.37/0.58 (step @p69 :rule nary_cong :premises (@p27 @p68 @p66) :args (@t88)) % 0.37/0.58 (step @p70 :rule cong :premises (@p69) :args (@t89)) % 0.37/0.58 (step @p71 :rule cong :premises (@p70) :args (@t90)) % 0.37/0.58 (step @p72 :rule ho_cong :premises (@p71 @p65)) % 0.37/0.58 (step @p73 :rule trans :premises (@p72 @p64)) % 0.37/0.58 (step @p74 :rule refl :args (@t1)) % 0.37/0.58 (step @p75 :rule beta-reduce :args ((= (_ (lambda @t24 (forall @t22 (or @t47 @t87 @t76))) @t3) @t90))) % 0.37/0.58 (step @p76 :rule refl :args (@t3)) % 0.37/0.58 (step @p77 :rule alpha_equiv :args (@t79 @t80 (@list @t41))) % 0.37/0.58 (step @p78 :rule cong :premises (@p77) :args (@t81)) % 0.37/0.58 (step @p79 :rule nary_cong :premises (@p27 @p78 @p54) :args (@t82)) % 0.37/0.58 (step @p80 :rule cong :premises (@p79) :args (@t83)) % 0.37/0.58 (step @p81 :rule cong :premises (@p80) :args (@t84)) % 0.37/0.58 (step @p82 :rule ho_cong :premises (@p81 @p76)) % 0.37/0.58 (step @p83 :rule trans :premises (@p82 @p75)) % 0.37/0.58 (step @p84 :rule ho_cong :premises (@p83 @p74)) % 0.37/0.58 (step @p85 :rule trans :premises (@p84 @p73)) % 0.37/0.58 (step @p86 :rule cong :premises (@p85 @p63) :args (@t91)) % 0.37/0.58 (step @p87 :rule cong :premises (@p86) :args (@t92)) % 0.37/0.58 (step @p88 :rule trans :premises (@p87 @p18)) % 0.37/0.58 (step @p89 :rule cong :premises (@p88) :args ((not @t92))) % 0.37/0.58 (step @p90 :rule refl :args (@t4)) % 0.37/0.58 (step @p91 :rule refl :args (@t76)) % 0.37/0.58 (step @p92 :rule refl :args (@t12)) % 0.37/0.58 (step @p93 :rule cong :premises (@p92 @p91) :args ((= @t12 @t76))) % 0.37/0.58 (step @p94 :rule symm :premises (@p93)) % 0.37/0.58 (step @p95 :rule eq_resolve :premises (@p92 @p94)) % 0.37/0.58 (step @p96 :rule refl :args (@t81)) % 0.37/0.58 (step @p97 :rule refl :args (@t46)) % 0.37/0.58 (step @p98 :rule refl :args (@t19)) % 0.37/0.58 (step @p99 :rule cong :premises (@p98 @p97) :args ((= @t19 @t46))) % 0.37/0.58 (step @p100 :rule symm :premises (@p99)) % 0.37/0.58 (step @p101 :rule eq_resolve :premises (@p98 @p100)) % 0.37/0.58 (step @p102 :rule cong :premises (@p101) :args (@t93)) % 0.37/0.58 (step @p103 :rule nary_cong :premises (@p102 @p96 @p95) :args (@t94)) % 0.37/0.58 (step @p104 :rule cong :premises (@p103) :args ((forall @t22 @t94))) % 0.37/0.58 (step @p105 :rule aci_norm :args ((= (or (or @t93 @t81) @t12) @t94))) % 0.37/0.58 (step @p106 :rule bool-and-de-morgan :args (@t19 @t79 true)) % 0.37/0.58 (step @p107 :rule nary_cong :premises (@p106 @p92) :args ((or (not @t95) @t12))) % 0.37/0.58 (step @p108 :rule trans :premises (@p107 @p105)) % 0.37/0.58 (step @p109 :rule bool-impl-elim :args (@t95 @t12)) % 0.37/0.58 (step @p110 :rule trans :premises (@p109 @p108)) % 0.37/0.58 (step @p111 :rule cong :premises (@p110) :args ((forall @t22 (=> @t95 @t12)))) % 0.37/0.58 (step @p112 :rule trans :premises (@p111 @p104)) % 0.37/0.58 (step @p113 :rule refl :args (@t12)) % 0.37/0.58 (step @p114 :rule refl :args ((_ @t11 @t4 @t2))) % 0.37/0.58 (step @p115 :rule cong :premises (@p42 @p19) :args (@t59)) % 0.37/0.58 (step @p116 :rule trans :premises (@p115 @p114)) % 0.37/0.58 (step @p117 :rule refl :args (@t11)) % 0.37/0.58 (step @p118 :rule ho_cong :premises (@p117 @p42)) % 0.37/0.58 (step @p119 :rule ho_cong :premises (@p118 @p19)) % 0.37/0.58 (step @p120 :rule cong :premises (@p119 @p116) :args ((= (_ (_ @t11 @t27) @t26) @t59))) % 0.37/0.58 (step @p121 :rule symm :premises (@p120)) % 0.37/0.58 (step @p122 :rule refl :args (@t13)) % 0.37/0.58 (step @p123 :rule eq_resolve :premises (@p122 @p121)) % 0.37/0.58 (step @p124 :rule ho_cong :premises (@p117 @p46)) % 0.37/0.58 (step @p125 :rule ho_cong :premises (@p124 @p23)) % 0.37/0.58 (step @p126 :rule trans :premises (@p125 @p123)) % 0.37/0.58 (step @p127 :rule refl :args ((_ @t11 @t14 @t1))) % 0.37/0.58 (step @p128 :rule refl :args ((tptp.s @t4))) % 0.37/0.58 (step @p129 :rule cong :premises (@p42) :args (@t77)) % 0.37/0.58 (step @p130 :rule trans :premises (@p129 @p128)) % 0.37/0.58 (step @p131 :rule cong :premises (@p130 @p65) :args (@t78)) % 0.37/0.58 (step @p132 :rule trans :premises (@p131 @p127)) % 0.37/0.58 (step @p133 :rule ho_cong :premises (@p117 @p130)) % 0.37/0.58 (step @p134 :rule ho_cong :premises (@p133 @p65)) % 0.37/0.58 (step @p135 :rule cong :premises (@p134 @p132) :args ((= (_ (_ @t11 @t77) @t1) @t78))) % 0.37/0.58 (step @p136 :rule symm :premises (@p135)) % 0.37/0.58 (step @p137 :rule refl :args (@t15)) % 0.37/0.58 (step @p138 :rule eq_resolve :premises (@p137 @p136)) % 0.37/0.58 (step @p139 :rule refl :args (tptp.s)) % 0.37/0.58 (step @p140 :rule ho_cong :premises (@p139 @p42)) % 0.37/0.58 (step @p141 :rule cong :premises (@p140 @p130) :args ((= (_ tptp.s @t27) @t77))) % 0.37/0.58 (step @p142 :rule symm :premises (@p141)) % 0.37/0.58 (step @p143 :rule refl :args (@t14)) % 0.37/0.58 (step @p144 :rule eq_resolve :premises (@p143 @p142)) % 0.37/0.58 (step @p145 :rule ho_cong :premises (@p139 @p46)) % 0.37/0.58 (step @p146 :rule trans :premises (@p145 @p144)) % 0.37/0.58 (step @p147 :rule ho_cong :premises (@p117 @p146)) % 0.37/0.58 (step @p148 :rule ho_cong :premises (@p147 @p65)) % 0.37/0.58 (step @p149 :rule trans :premises (@p148 @p138)) % 0.37/0.58 (step @p150 :rule nary_cong :premises (@p149 @p126) :args (@t16)) % 0.37/0.58 (step @p151 :rule refl :args (@t38)) % 0.37/0.58 (step @p152 :rule refl :args (@t17)) % 0.37/0.58 (step @p153 :rule cong :premises (@p152 @p151) :args ((= @t17 @t38))) % 0.37/0.58 (step @p154 :rule symm :premises (@p153)) % 0.37/0.58 (step @p155 :rule eq_resolve :premises (@p152 @p154)) % 0.37/0.58 (step @p156 :rule cong :premises (@p155) :args (@t96)) % 0.37/0.58 (step @p157 :rule nary_cong :premises (@p156 @p150) :args (@t97)) % 0.37/0.58 (step @p158 :rule cong :premises (@p157) :args ((forall @t6 @t97))) % 0.37/0.58 (step @p159 :rule bool-impl-elim :args (@t17 @t16)) % 0.37/0.58 (step @p160 :rule cong :premises (@p159) :args (@t18)) % 0.37/0.58 (step @p161 :rule trans :premises (@p160 @p158)) % 0.37/0.58 (step @p162 :rule refl :args (@t19)) % 0.37/0.58 (step @p163 :rule nary_cong :premises (@p162 @p161) :args (@t20)) % 0.37/0.58 (step @p164 :rule cong :premises (@p163 @p113) :args (@t21)) % 0.37/0.58 (step @p165 :rule cong :premises (@p164) :args (@t23)) % 0.37/0.58 (step @p166 :rule trans :premises (@p165 @p112)) % 0.37/0.58 (step @p167 :rule cong :premises (@p166) :args (@t25)) % 0.37/0.58 (step @p168 :rule trans :premises (@p3 @p167)) % 0.37/0.58 (step @p169 :rule ho_cong :premises (@p168 @p90)) % 0.37/0.58 (step @p170 :rule ho_cong :premises (@p169 @p40)) % 0.37/0.58 (step @p171 :rule refl :args (@t3)) % 0.37/0.58 (step @p172 :rule ho_cong :premises (@p168 @p171)) % 0.37/0.58 (step @p173 :rule ho_cong :premises (@p172 @p74)) % 0.37/0.58 (step @p174 :rule cong :premises (@p173 @p170) :args (@t5)) % 0.37/0.58 (step @p175 :rule cong :premises (@p174) :args (@t7)) % 0.37/0.58 (step @p176 :rule cong :premises (@p175) :args (@t8)) % 0.37/0.58 (step @p177 :rule trans :premises (@p176 @p89)) % 0.37/0.58 (step @p178 :rule eq_resolve :premises (@p1 @p177)) % 0.37/0.58 (step @p179 :rule skolemize :premises (@p178)) % 0.37/0.58 (step @p180 :rule bool-double-not-elim :args (@t100)) % 0.37/0.58 (step @p181 :rule refl :args (@t110)) % 0.37/0.58 (step @p182 :rule nary_cong :premises (@p181 @p180) :args ((or @t110 (not @t107)))) % 0.37/0.58 (step @p183 :rule cnf_or_neg :args (@t110 1)) % 0.37/0.58 (step @p184 :rule eq_resolve :premises (@p183 @p182)) % 0.37/0.58 (step @p185 :rule reordering :premises (@p184) :args ((or @t100 @t110))) % 0.37/0.58 (step @p186 :rule chain_m_resolution :premises (@p185 @p179) :args (@t100 @t111 @t112)) % 0.37/0.58 (step @p187 :rule bool-double-not-elim :args (@t105)) % 0.37/0.58 (step @p188 :rule nary_cong :premises (@p181 @p187) :args ((or @t110 (not @t106)))) % 0.37/0.58 (step @p189 :rule cnf_or_neg :args (@t110 2)) % 0.37/0.58 (step @p190 :rule eq_resolve :premises (@p189 @p188)) % 0.37/0.58 (step @p191 :rule reordering :premises (@p190) :args ((or @t105 @t110))) % 0.37/0.58 (step @p192 :rule chain_m_resolution :premises (@p191 @p179) :args (@t105 @t111 @t112)) % 0.37/0.58 (step @p193 :rule instantiate :premises (@p192) :args ((@list @t102 @t101))) % 0.37/0.58 (step @p194 :rule cnf_or_neg :args (@t110 3)) % 0.37/0.58 (step @p195 :rule chain_m_resolution :premises (@p194 @p179) :args ((not @t104) @t111 @t112)) % 0.37/0.58 (step @p196 :rule cnf_and_pos :args (@t113 1)) % 0.37/0.59 (step @p197 :rule reordering :premises (@p196) :args ((or @t104 @t114))) % 0.37/0.59 (step @p198 :rule chain_m_resolution :premises (@p197 @p195) :args (@t114 @t111 (@list @t104))) % 0.37/0.59 (step @p199 :rule cnf_or_pos :args (@t117)) % 0.37/0.59 (step @p200 :rule reordering :premises (@p199) :args ((or @t116 @t113 (not @t117)))) % 0.37/0.59 (step @p201 :rule chain_m_resolution :premises (@p200 @p198 @p193) :args (@t116 (@list true false) (@list @t113 @t117))) % 0.37/0.59 (step @p202 :rule alpha_equiv :args (@t105 (@list @t32 @t30) (@list @t41 @t39))) % 0.37/0.59 (step @p203 :rule equiv_elim1 :premises (@p202)) % 0.37/0.59 (step @p204 :rule chain_m_resolution :premises (@p203 @p192) :args (@t118 (@list false) (@list @t105))) % 0.37/0.59 (step @p205 :rule bool-double-not-elim :args (@t108)) % 0.37/0.59 (step @p206 :rule nary_cong :premises (@p181 @p205) :args ((or @t110 (not @t109)))) % 0.37/0.59 (step @p207 :rule cnf_or_neg :args (@t110 0)) % 0.37/0.59 (step @p208 :rule eq_resolve :premises (@p207 @p206)) % 0.37/0.59 (step @p209 :rule reordering :premises (@p208) :args ((or @t108 @t110))) % 0.37/0.59 (step @p210 :rule chain_m_resolution :premises (@p209 @p179) :args (@t108 @t111 @t112)) % 0.37/0.59 (step @p211 :rule instantiate :premises (@p210) :args ((@list @t99))) % 0.37/0.59 (step @p212 :rule cnf_or_pos :args (@t120)) % 0.37/0.59 (step @p213 :rule reordering :premises (@p212) :args ((or @t107 @t115 @t119 (not @t120)))) % 0.37/0.59 (step @p214 false :rule chain_m_resolution :premises (@p213 @p211 @p204 @p201 @p186) :args (false (@list false false true false) (@list @t120 @t118 @t115 @t100))) % 0.37/0.59 ) % 0.37/0.59 % SZS output end Proof % 0.37/0.59 % cvc5 exiting %------------------------------------------------------------------------------