%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : PUZ113^5 : 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 : n017.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 0.40s 0.62s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : PUZ113^5 : 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 % 0.16/0.34 % Computer : n017.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 13:17:16 EDT 2026 % 0.16/0.35 % CPUTime : % 0.33/0.49 %----Proving TH0 % 0.40/0.62 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.62 % SZS status Theorem % 0.40/0.62 % SZS output start Proof % 0.40/0.62 ( % 0.40/0.62 (declare-sort $$unsorted 0) % 0.40/0.62 (declare-const tptp.s (-> $$unsorted $$unsorted)) % 0.40/0.62 (declare-const tptp.c1 $$unsorted) % 0.40/0.62 (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))))))))))) % 0.40/0.62 (define @t1 () (@var "Xk" $$unsorted)) % 0.40/0.62 (define @t2 () (_ tptp.s @t1)) % 0.40/0.62 (define @t3 () (_ tptp.s @t2)) % 0.40/0.62 (define @t4 () (@var "Xj" $$unsorted)) % 0.40/0.62 (define @t5 () (_ tptp.s @t4)) % 0.40/0.62 (define @t6 () (_ tptp.s @t5)) % 0.40/0.62 (define @t7 () (=> (_ (_ tptp.cCKB6_BLACK @t4) @t1) (_ (_ tptp.cCKB6_BLACK @t6) @t3))) % 0.40/0.62 (define @t8 () (@list @t4 @t1)) % 0.40/0.62 (define @t9 () (forall @t8 @t7)) % 0.40/0.62 (define @t10 () (not @t9)) % 0.40/0.62 (define @t11 () (@var "Xv" $$unsorted)) % 0.40/0.62 (define @t12 () (@var "Xu" $$unsorted)) % 0.40/0.62 (define @t13 () (@var "Xw" (-> $$unsorted $$unsorted Bool))) % 0.40/0.62 (define @t14 () (_ (_ @t13 @t12) @t11)) % 0.40/0.62 (define @t15 () (_ (_ @t13 @t5) @t2)) % 0.40/0.62 (define @t16 () (_ (_ @t13 @t6) @t1)) % 0.40/0.62 (define @t17 () (and @t16 @t15)) % 0.40/0.62 (define @t18 () (_ (_ @t13 @t4) @t1)) % 0.40/0.62 (define @t19 () (forall @t8 (=> @t18 @t17))) % 0.40/0.62 (define @t20 () (_ (_ @t13 tptp.c1) tptp.c1)) % 0.40/0.62 (define @t21 () (and @t20 @t19)) % 0.40/0.62 (define @t22 () (=> @t21 @t14)) % 0.40/0.62 (define @t23 () (@list @t13)) % 0.40/0.62 (define @t24 () (forall @t23 @t22)) % 0.40/0.62 (define @t25 () (@list @t12 @t11)) % 0.40/0.62 (define @t26 () (lambda @t25 @t24)) % 0.40/0.62 (define @t27 () (tptp.s @t1)) % 0.40/0.62 (define @t28 () (tptp.s @t27)) % 0.40/0.62 (define @t29 () (tptp.s @t4)) % 0.40/0.62 (define @t30 () (tptp.s @t29)) % 0.40/0.62 (define @t31 () (@var "BOUND_VARIABLE_7597" (-> $$unsorted $$unsorted Bool))) % 0.40/0.62 (define @t32 () (_ @t31 @t30 @t28)) % 0.40/0.62 (define @t33 () (@var "BOUND_VARIABLE_7568" $$unsorted)) % 0.40/0.62 (define @t34 () (tptp.s @t33)) % 0.40/0.62 (define @t35 () (@var "BOUND_VARIABLE_7541" $$unsorted)) % 0.40/0.62 (define @t36 () (tptp.s @t35)) % 0.40/0.62 (define @t37 () (tptp.s @t36)) % 0.40/0.62 (define @t38 () (@list @t35 @t33)) % 0.40/0.62 (define @t39 () (not (forall @t38 (or (not (_ @t31 @t35 @t33)) (and (_ @t31 @t37 @t33) (_ @t31 @t36 @t34)))))) % 0.40/0.62 (define @t40 () (not (_ @t31 tptp.c1 tptp.c1))) % 0.40/0.62 (define @t41 () (_ @t13 @t4 @t1)) % 0.40/0.62 (define @t42 () (@var "BOUND_VARIABLE_7523" $$unsorted)) % 0.40/0.62 (define @t43 () (tptp.s @t42)) % 0.40/0.62 (define @t44 () (@var "BOUND_VARIABLE_7500" $$unsorted)) % 0.40/0.62 (define @t45 () (tptp.s @t44)) % 0.40/0.62 (define @t46 () (tptp.s @t45)) % 0.40/0.62 (define @t47 () (@list @t44 @t42)) % 0.40/0.62 (define @t48 () (not (forall @t47 (or (not (_ @t13 @t44 @t42)) (and (_ @t13 @t46 @t42) (_ @t13 @t45 @t43)))))) % 0.40/0.62 (define @t49 () (_ @t13 tptp.c1 tptp.c1)) % 0.40/0.62 (define @t50 () (not @t49)) % 0.40/0.62 (define @t51 () (forall @t23 (or @t50 @t48 @t41))) % 0.40/0.62 (define @t52 () (not @t51)) % 0.40/0.62 (define @t53 () (or @t52 @t40 @t39 @t32)) % 0.40/0.62 (define @t54 () (or @t40 @t39 @t32)) % 0.40/0.62 (define @t55 () (or @t52 @t54)) % 0.40/0.62 (define @t56 () (@list @t4 @t1 @t31)) % 0.40/0.62 (define @t57 () (forall @t56 @t55)) % 0.40/0.62 (define @t58 () (@list @t31)) % 0.40/0.62 (define @t59 () (forall @t58 @t55)) % 0.40/0.62 (define @t60 () (forall @t58 @t54)) % 0.40/0.62 (define @t61 () (or @t52 @t60)) % 0.40/0.62 (define @t62 () (not (forall @t38 (or (not (_ @t13 @t35 @t33)) (and (_ @t13 @t37 @t33) (_ @t13 @t36 @t34)))))) % 0.40/0.62 (define @t63 () (forall @t23 (or @t50 @t62 (_ @t13 @t30 @t28)))) % 0.40/0.62 (define @t64 () (_ @t13 @t30 @t3)) % 0.40/0.62 (define @t65 () (or @t50 @t62 @t64)) % 0.40/0.62 (define @t66 () (forall @t23 @t65)) % 0.40/0.62 (define @t67 () (_ @t13 @t30 @t11)) % 0.40/0.62 (define @t68 () (@list @t11)) % 0.40/0.62 (define @t69 () (forall (@list @t35 @t1) (or (not (_ @t13 @t35 @t1)) (and (_ @t13 @t37 @t1) (_ @t13 @t36 @t27))))) % 0.40/0.62 (define @t70 () (@list @t1)) % 0.40/0.62 (define @t71 () (not @t69)) % 0.40/0.62 (define @t72 () (or @t50 @t71 @t67)) % 0.40/0.62 (define @t73 () (forall @t23 @t72)) % 0.40/0.62 (define @t74 () (_ @t13 @t6 @t11)) % 0.40/0.62 (define @t75 () (or @t50 @t71 @t74)) % 0.40/0.62 (define @t76 () (forall @t23 @t75)) % 0.40/0.62 (define @t77 () (lambda @t68 @t76)) % 0.40/0.62 (define @t78 () (_ @t13 @t12 @t11)) % 0.40/0.62 (define @t79 () (_ @t13 @t29 @t27)) % 0.40/0.62 (define @t80 () (_ @t13 @t30 @t1)) % 0.40/0.62 (define @t81 () (forall @t8 (or (not @t41) (and @t80 @t79)))) % 0.40/0.62 (define @t82 () (@list @t4)) % 0.40/0.62 (define @t83 () (not @t81)) % 0.40/0.62 (define @t84 () (or @t50 @t83 @t78)) % 0.40/0.62 (define @t85 () (forall @t23 @t84)) % 0.40/0.62 (define @t86 () (lambda @t25 @t85)) % 0.40/0.62 (define @t87 () (_ @t13 @t4 @t11)) % 0.40/0.62 (define @t88 () (forall (@list @t44 @t1) (or (not (_ @t13 @t44 @t1)) (and (_ @t13 @t46 @t1) (_ @t13 @t45 @t27))))) % 0.40/0.62 (define @t89 () (not @t88)) % 0.40/0.62 (define @t90 () (or @t50 @t89 @t87)) % 0.40/0.62 (define @t91 () (forall @t23 @t90)) % 0.40/0.62 (define @t92 () (lambda @t68 @t91)) % 0.40/0.62 (define @t93 () (=> (_ (_ @t86 @t4) @t1) (_ (_ @t86 @t6) @t3))) % 0.40/0.62 (define @t94 () (forall @t8 @t93)) % 0.40/0.62 (define @t95 () (not @t20)) % 0.40/0.62 (define @t96 () (or @t95 @t83 @t14)) % 0.40/0.62 (define @t97 () (and @t20 @t81)) % 0.40/0.62 (define @t98 () (not @t18)) % 0.40/0.62 (define @t99 () (or @t98 @t17)) % 0.40/0.62 (define @t100 () (forall @t56 @t53)) % 0.40/0.62 (define @t101 () (@quantifiers_skolemize @t100 2)) % 0.40/0.62 (define @t102 () (_ @t101 tptp.c1 tptp.c1)) % 0.40/0.62 (define @t103 () (@quantifiers_skolemize @t100 1)) % 0.40/0.62 (define @t104 () (tptp.s @t103)) % 0.40/0.62 (define @t105 () (@quantifiers_skolemize @t100 0)) % 0.40/0.62 (define @t106 () (tptp.s @t105)) % 0.40/0.62 (define @t107 () (tptp.s @t106)) % 0.40/0.62 (define @t108 () (_ @t101 @t107 (tptp.s @t104))) % 0.40/0.62 (define @t109 () (forall @t38 (or (not (_ @t101 @t35 @t33)) (and (_ @t101 @t37 @t33) (_ @t101 @t36 @t34))))) % 0.40/0.62 (define @t110 () (not @t109)) % 0.40/0.62 (define @t111 () (not @t102)) % 0.40/0.62 (define @t112 () (forall @t23 (or @t50 @t48 (_ @t13 @t105 @t103)))) % 0.40/0.62 (define @t113 () (not @t112)) % 0.40/0.62 (define @t114 () (or @t113 @t111 @t110 @t108)) % 0.40/0.62 (define @t115 () (@list true)) % 0.40/0.62 (define @t116 () (@list @t114)) % 0.40/0.62 (define @t117 () (and (_ @t101 (tptp.s @t107) @t104) @t108)) % 0.40/0.62 (define @t118 () (not @t117)) % 0.40/0.62 (define @t119 () (_ @t101 @t106 @t104)) % 0.40/0.62 (define @t120 () (not @t119)) % 0.40/0.62 (define @t121 () (or @t120 @t117)) % 0.40/0.62 (define @t122 () (@list true false)) % 0.40/0.62 (define @t123 () (and (_ @t101 @t107 @t103) @t119)) % 0.40/0.62 (define @t124 () (not @t123)) % 0.40/0.62 (define @t125 () (_ @t101 @t105 @t103)) % 0.40/0.62 (define @t126 () (not @t125)) % 0.40/0.62 (define @t127 () (or @t126 @t123)) % 0.40/0.62 (define @t128 () (forall @t47 (or (not (_ @t101 @t44 @t42)) (and (_ @t101 @t46 @t42) (_ @t101 @t45 @t43))))) % 0.40/0.62 (define @t129 () (not @t128)) % 0.40/0.62 (define @t130 () (or @t111 @t129 @t125)) % 0.40/0.62 (assume @p1 @t10) % 0.40/0.62 (assume @p2 true) % 0.40/0.62 (step @p3 (= tptp.cCKB6_BLACK @t26) :rule refl :args (@t26)) % 0.40/0.62 (step @p4 :rule aci_norm :args ((= @t55 @t53))) % 0.40/0.62 (step @p5 :rule cong :premises (@p4) :args (@t57)) % 0.40/0.62 (step @p6 :rule quant-merge-prenex :args ((= (forall @t8 @t59) @t57))) % 0.40/0.62 (step @p7 :rule alpha_equiv :args (@t60 (@list @t31) (@list @t13))) % 0.40/0.62 (step @p8 :rule refl :args (@t52)) % 0.40/0.62 (step @p9 :rule nary_cong :premises (@p8 @p7) :args (@t61)) % 0.40/0.62 (step @p10 :rule quant-miniscope-or :args ((= @t59 @t61))) % 0.40/0.62 (step @p11 :rule trans :premises (@p10 @p9)) % 0.40/0.62 (step @p12 :rule symm :premises (@p11)) % 0.40/0.62 (step @p13 :rule cong :premises (@p12) :args ((forall @t8 (or @t52 @t63)))) % 0.40/0.62 (step @p14 :rule trans :premises (@p13 @p6)) % 0.40/0.62 (step @p15 :rule trans :premises (@p14 @p5)) % 0.40/0.62 (step @p16 :rule bool-impl-elim :args (@t51 @t63)) % 0.40/0.62 (step @p17 :rule cong :premises (@p16) :args ((forall @t8 (=> @t51 @t63)))) % 0.40/0.62 (step @p18 :rule trans :premises (@p17 @p15)) % 0.40/0.62 (step @p19 :rule refl :args ((tptp.s @t2))) % 0.40/0.62 (step @p20 :rule refl :args (@t27)) % 0.40/0.62 (step @p21 :rule cong :premises (@p20) :args (@t28)) % 0.40/0.62 (step @p22 :rule trans :premises (@p21 @p19)) % 0.40/0.62 (step @p23 :rule refl :args (tptp.s)) % 0.40/0.62 (step @p24 :rule ho_cong :premises (@p23 @p20)) % 0.40/0.62 (step @p25 :rule cong :premises (@p24 @p22) :args ((= (_ tptp.s @t27) @t28))) % 0.40/0.62 (step @p26 :rule symm :premises (@p25)) % 0.40/0.62 (step @p27 :rule refl :args (@t3)) % 0.40/0.62 (step @p28 :rule eq_resolve :premises (@p27 @p26)) % 0.40/0.62 (step @p29 :rule refl :args (@t2)) % 0.40/0.62 (step @p30 :rule cong :premises (@p29 @p20) :args ((= @t2 @t27))) % 0.40/0.62 (step @p31 :rule symm :premises (@p30)) % 0.40/0.62 (step @p32 :rule eq_resolve :premises (@p29 @p31)) % 0.40/0.62 (step @p33 :rule ho_cong :premises (@p23 @p32)) % 0.40/0.62 (step @p34 :rule trans :premises (@p33 @p28)) % 0.40/0.62 (step @p35 :rule refl :args (@t30)) % 0.40/0.62 (step @p36 :rule cong :premises (@p35 @p34) :args (@t64)) % 0.40/0.62 (step @p37 :rule refl :args (@t62)) % 0.40/0.62 (step @p38 :rule refl :args (@t50)) % 0.40/0.62 (step @p39 :rule nary_cong :premises (@p38 @p37 @p36) :args (@t65)) % 0.40/0.62 (step @p40 :rule cong :premises (@p39) :args (@t66)) % 0.40/0.62 (step @p41 :rule beta-reduce :args ((= (_ (lambda @t68 (forall @t23 (or @t50 @t62 @t67))) @t3) @t66))) % 0.40/0.62 (step @p42 :rule trans :premises (@p41 @p40)) % 0.40/0.62 (step @p43 :rule refl :args (@t67)) % 0.40/0.62 (step @p44 :rule alpha_equiv :args (@t69 @t70 (@list @t33))) % 0.40/0.62 (step @p45 :rule cong :premises (@p44) :args (@t71)) % 0.40/0.62 (step @p46 :rule nary_cong :premises (@p38 @p45 @p43) :args (@t72)) % 0.40/0.62 (step @p47 :rule cong :premises (@p46) :args (@t73)) % 0.40/0.62 (step @p48 :rule cong :premises (@p47) :args ((lambda @t68 @t73))) % 0.40/0.62 (step @p49 :rule ho_cong :premises (@p48 @p27)) % 0.40/0.62 (step @p50 :rule trans :premises (@p49 @p42)) % 0.40/0.62 (step @p51 :rule refl :args (@t3)) % 0.40/0.62 (step @p52 :rule refl :args (@t11)) % 0.40/0.62 (step @p53 :rule refl :args ((tptp.s @t5))) % 0.40/0.62 (step @p54 :rule refl :args (@t29)) % 0.40/0.62 (step @p55 :rule cong :premises (@p54) :args (@t30)) % 0.40/0.62 (step @p56 :rule trans :premises (@p55 @p53)) % 0.40/0.62 (step @p57 :rule ho_cong :premises (@p23 @p54)) % 0.40/0.62 (step @p58 :rule cong :premises (@p57 @p56) :args ((= (_ tptp.s @t29) @t30))) % 0.40/0.62 (step @p59 :rule symm :premises (@p58)) % 0.40/0.62 (step @p60 :rule refl :args (@t6)) % 0.40/0.62 (step @p61 :rule eq_resolve :premises (@p60 @p59)) % 0.40/0.62 (step @p62 :rule refl :args (@t5)) % 0.40/0.62 (step @p63 :rule cong :premises (@p62 @p54) :args ((= @t5 @t29))) % 0.40/0.62 (step @p64 :rule symm :premises (@p63)) % 0.40/0.62 (step @p65 :rule eq_resolve :premises (@p62 @p64)) % 0.40/0.62 (step @p66 :rule ho_cong :premises (@p23 @p65)) % 0.40/0.62 (step @p67 :rule trans :premises (@p66 @p61)) % 0.40/0.62 (step @p68 :rule cong :premises (@p67 @p52) :args (@t74)) % 0.40/0.62 (step @p69 :rule refl :args (@t71)) % 0.40/0.62 (step @p70 :rule nary_cong :premises (@p38 @p69 @p68) :args (@t75)) % 0.40/0.62 (step @p71 :rule cong :premises (@p70) :args (@t76)) % 0.40/0.62 (step @p72 :rule cong :premises (@p71) :args (@t77)) % 0.40/0.62 (step @p73 :rule beta-reduce :args ((= (_ (lambda @t25 (forall @t23 (or @t50 @t71 @t78))) @t6) @t77))) % 0.40/0.62 (step @p74 :rule trans :premises (@p73 @p72)) % 0.40/0.62 (step @p75 :rule refl :args (@t78)) % 0.40/0.62 (step @p76 :rule alpha_equiv :args (@t81 @t82 (@list @t35))) % 0.40/0.62 (step @p77 :rule cong :premises (@p76) :args (@t83)) % 0.40/0.62 (step @p78 :rule nary_cong :premises (@p38 @p77 @p75) :args (@t84)) % 0.40/0.62 (step @p79 :rule cong :premises (@p78) :args (@t85)) % 0.40/0.62 (step @p80 :rule cong :premises (@p79) :args (@t86)) % 0.40/0.62 (step @p81 :rule ho_cong :premises (@p80 @p60)) % 0.40/0.62 (step @p82 :rule trans :premises (@p81 @p74)) % 0.40/0.62 (step @p83 :rule ho_cong :premises (@p82 @p51)) % 0.40/0.62 (step @p84 :rule trans :premises (@p83 @p50)) % 0.40/0.62 (step @p85 :rule beta-reduce :args ((= (_ (lambda @t68 (forall @t23 (or @t50 @t48 @t87))) @t1) @t51))) % 0.40/0.62 (step @p86 :rule refl :args (@t1)) % 0.40/0.62 (step @p87 :rule refl :args (@t87)) % 0.40/0.62 (step @p88 :rule alpha_equiv :args (@t88 @t70 (@list @t42))) % 0.40/0.62 (step @p89 :rule cong :premises (@p88) :args (@t89)) % 0.40/0.62 (step @p90 :rule nary_cong :premises (@p38 @p89 @p87) :args (@t90)) % 0.40/0.62 (step @p91 :rule cong :premises (@p90) :args (@t91)) % 0.40/0.62 (step @p92 :rule cong :premises (@p91) :args (@t92)) % 0.40/0.62 (step @p93 :rule ho_cong :premises (@p92 @p86)) % 0.40/0.62 (step @p94 :rule trans :premises (@p93 @p85)) % 0.40/0.62 (step @p95 :rule refl :args (@t1)) % 0.40/0.62 (step @p96 :rule beta-reduce :args ((= (_ (lambda @t25 (forall @t23 (or @t50 @t89 @t78))) @t4) @t92))) % 0.40/0.62 (step @p97 :rule refl :args (@t4)) % 0.40/0.62 (step @p98 :rule alpha_equiv :args (@t81 @t82 (@list @t44))) % 0.40/0.62 (step @p99 :rule cong :premises (@p98) :args (@t83)) % 0.40/0.62 (step @p100 :rule nary_cong :premises (@p38 @p99 @p75) :args (@t84)) % 0.40/0.62 (step @p101 :rule cong :premises (@p100) :args (@t85)) % 0.40/0.62 (step @p102 :rule cong :premises (@p101) :args (@t86)) % 0.40/0.62 (step @p103 :rule ho_cong :premises (@p102 @p97)) % 0.40/0.62 (step @p104 :rule trans :premises (@p103 @p96)) % 0.40/0.62 (step @p105 :rule ho_cong :premises (@p104 @p95)) % 0.40/0.62 (step @p106 :rule trans :premises (@p105 @p94)) % 0.40/0.62 (step @p107 :rule cong :premises (@p106 @p84) :args (@t93)) % 0.40/0.62 (step @p108 :rule cong :premises (@p107) :args (@t94)) % 0.40/0.62 (step @p109 :rule trans :premises (@p108 @p18)) % 0.40/0.62 (step @p110 :rule cong :premises (@p109) :args ((not @t94))) % 0.40/0.62 (step @p111 :rule refl :args (@t6)) % 0.40/0.62 (step @p112 :rule refl :args (@t78)) % 0.40/0.62 (step @p113 :rule refl :args (@t14)) % 0.40/0.62 (step @p114 :rule cong :premises (@p113 @p112) :args ((= @t14 @t78))) % 0.40/0.62 (step @p115 :rule symm :premises (@p114)) % 0.40/0.62 (step @p116 :rule eq_resolve :premises (@p113 @p115)) % 0.40/0.62 (step @p117 :rule refl :args (@t83)) % 0.40/0.62 (step @p118 :rule refl :args (@t49)) % 0.40/0.62 (step @p119 :rule refl :args (@t20)) % 0.40/0.62 (step @p120 :rule cong :premises (@p119 @p118) :args ((= @t20 @t49))) % 0.40/0.62 (step @p121 :rule symm :premises (@p120)) % 0.40/0.62 (step @p122 :rule eq_resolve :premises (@p119 @p121)) % 0.40/0.62 (step @p123 :rule cong :premises (@p122) :args (@t95)) % 0.40/0.62 (step @p124 :rule nary_cong :premises (@p123 @p117 @p116) :args (@t96)) % 0.40/0.62 (step @p125 :rule cong :premises (@p124) :args ((forall @t23 @t96))) % 0.40/0.62 (step @p126 :rule aci_norm :args ((= (or (or @t95 @t83) @t14) @t96))) % 0.40/0.62 (step @p127 :rule bool-and-de-morgan :args (@t20 @t81 true)) % 0.40/0.62 (step @p128 :rule nary_cong :premises (@p127 @p113) :args ((or (not @t97) @t14))) % 0.40/0.62 (step @p129 :rule trans :premises (@p128 @p126)) % 0.40/0.62 (step @p130 :rule bool-impl-elim :args (@t97 @t14)) % 0.40/0.62 (step @p131 :rule trans :premises (@p130 @p129)) % 0.40/0.62 (step @p132 :rule cong :premises (@p131) :args ((forall @t23 (=> @t97 @t14)))) % 0.40/0.62 (step @p133 :rule trans :premises (@p132 @p125)) % 0.40/0.62 (step @p134 :rule refl :args (@t14)) % 0.40/0.62 (step @p135 :rule refl :args ((_ @t13 @t5 @t2))) % 0.40/0.62 (step @p136 :rule cong :premises (@p54 @p20) :args (@t79)) % 0.40/0.62 (step @p137 :rule trans :premises (@p136 @p135)) % 0.40/0.62 (step @p138 :rule refl :args (@t13)) % 0.40/0.62 (step @p139 :rule ho_cong :premises (@p138 @p54)) % 0.40/0.62 (step @p140 :rule ho_cong :premises (@p139 @p20)) % 0.40/0.62 (step @p141 :rule cong :premises (@p140 @p137) :args ((= (_ (_ @t13 @t29) @t27) @t79))) % 0.40/0.62 (step @p142 :rule symm :premises (@p141)) % 0.40/0.62 (step @p143 :rule refl :args (@t15)) % 0.40/0.62 (step @p144 :rule eq_resolve :premises (@p143 @p142)) % 0.40/0.62 (step @p145 :rule ho_cong :premises (@p138 @p65)) % 0.40/0.62 (step @p146 :rule ho_cong :premises (@p145 @p32)) % 0.40/0.62 (step @p147 :rule trans :premises (@p146 @p144)) % 0.40/0.62 (step @p148 :rule refl :args ((_ @t13 @t6 @t1))) % 0.40/0.62 (step @p149 :rule cong :premises (@p56 @p86) :args (@t80)) % 0.40/0.62 (step @p150 :rule trans :premises (@p149 @p148)) % 0.40/0.62 (step @p151 :rule ho_cong :premises (@p138 @p56)) % 0.40/0.62 (step @p152 :rule ho_cong :premises (@p151 @p86)) % 0.40/0.62 (step @p153 :rule cong :premises (@p152 @p150) :args ((= (_ (_ @t13 @t30) @t1) @t80))) % 0.40/0.62 (step @p154 :rule symm :premises (@p153)) % 0.40/0.62 (step @p155 :rule refl :args (@t16)) % 0.40/0.62 (step @p156 :rule eq_resolve :premises (@p155 @p154)) % 0.40/0.62 (step @p157 :rule ho_cong :premises (@p138 @p67)) % 0.40/0.62 (step @p158 :rule ho_cong :premises (@p157 @p86)) % 0.40/0.62 (step @p159 :rule trans :premises (@p158 @p156)) % 0.40/0.62 (step @p160 :rule nary_cong :premises (@p159 @p147) :args (@t17)) % 0.40/0.62 (step @p161 :rule refl :args (@t41)) % 0.40/0.62 (step @p162 :rule refl :args (@t18)) % 0.40/0.62 (step @p163 :rule cong :premises (@p162 @p161) :args ((= @t18 @t41))) % 0.40/0.62 (step @p164 :rule symm :premises (@p163)) % 0.40/0.62 (step @p165 :rule eq_resolve :premises (@p162 @p164)) % 0.40/0.62 (step @p166 :rule cong :premises (@p165) :args (@t98)) % 0.40/0.62 (step @p167 :rule nary_cong :premises (@p166 @p160) :args (@t99)) % 0.40/0.62 (step @p168 :rule cong :premises (@p167) :args ((forall @t8 @t99))) % 0.40/0.62 (step @p169 :rule bool-impl-elim :args (@t18 @t17)) % 0.40/0.62 (step @p170 :rule cong :premises (@p169) :args (@t19)) % 0.40/0.62 (step @p171 :rule trans :premises (@p170 @p168)) % 0.40/0.62 (step @p172 :rule refl :args (@t20)) % 0.40/0.62 (step @p173 :rule nary_cong :premises (@p172 @p171) :args (@t21)) % 0.40/0.62 (step @p174 :rule cong :premises (@p173 @p134) :args (@t22)) % 0.40/0.62 (step @p175 :rule cong :premises (@p174) :args (@t24)) % 0.40/0.62 (step @p176 :rule trans :premises (@p175 @p133)) % 0.40/0.62 (step @p177 :rule cong :premises (@p176) :args (@t26)) % 0.40/0.62 (step @p178 :rule trans :premises (@p3 @p177)) % 0.40/0.62 (step @p179 :rule ho_cong :premises (@p178 @p111)) % 0.40/0.62 (step @p180 :rule ho_cong :premises (@p179 @p51)) % 0.40/0.62 (step @p181 :rule refl :args (@t4)) % 0.40/0.62 (step @p182 :rule ho_cong :premises (@p178 @p181)) % 0.40/0.62 (step @p183 :rule ho_cong :premises (@p182 @p95)) % 0.40/0.62 (step @p184 :rule cong :premises (@p183 @p180) :args (@t7)) % 0.40/0.62 (step @p185 :rule cong :premises (@p184) :args (@t9)) % 0.40/0.62 (step @p186 :rule cong :premises (@p185) :args (@t10)) % 0.40/0.62 (step @p187 :rule trans :premises (@p186 @p110)) % 0.40/0.62 (step @p188 :rule eq_resolve :premises (@p1 @p187)) % 0.40/0.62 (step @p189 :rule skolemize :premises (@p188)) % 0.40/0.62 (step @p190 :rule bool-double-not-elim :args (@t102)) % 0.40/0.62 (step @p191 :rule refl :args (@t114)) % 0.40/0.62 (step @p192 :rule nary_cong :premises (@p191 @p190) :args ((or @t114 (not @t111)))) % 0.40/0.62 (step @p193 :rule cnf_or_neg :args (@t114 1)) % 0.40/0.62 (step @p194 :rule eq_resolve :premises (@p193 @p192)) % 0.40/0.62 (step @p195 :rule reordering :premises (@p194) :args ((or @t102 @t114))) % 0.40/0.62 (step @p196 :rule chain_m_resolution :premises (@p195 @p189) :args (@t102 @t115 @t116)) % 0.40/0.62 (step @p197 :rule bool-double-not-elim :args (@t109)) % 0.40/0.62 (step @p198 :rule nary_cong :premises (@p191 @p197) :args ((or @t114 (not @t110)))) % 0.40/0.62 (step @p199 :rule cnf_or_neg :args (@t114 2)) % 0.40/0.62 (step @p200 :rule eq_resolve :premises (@p199 @p198)) % 0.40/0.62 (step @p201 :rule reordering :premises (@p200) :args ((or @t109 @t114))) % 0.40/0.62 (step @p202 :rule chain_m_resolution :premises (@p201 @p189) :args (@t109 @t115 @t116)) % 0.40/0.62 (step @p203 :rule instantiate :premises (@p202) :args ((@list @t105 @t103))) % 0.40/0.62 (step @p204 :rule instantiate :premises (@p202) :args ((@list @t106 @t104))) % 0.40/0.62 (step @p205 :rule cnf_or_neg :args (@t114 3)) % 0.40/0.62 (step @p206 :rule chain_m_resolution :premises (@p205 @p189) :args ((not @t108) @t115 @t116)) % 0.40/0.62 (step @p207 :rule cnf_and_pos :args (@t117 1)) % 0.40/0.62 (step @p208 :rule reordering :premises (@p207) :args ((or @t108 @t118))) % 0.40/0.62 (step @p209 :rule chain_m_resolution :premises (@p208 @p206) :args (@t118 @t115 (@list @t108))) % 0.40/0.62 (step @p210 :rule cnf_or_pos :args (@t121)) % 0.40/0.62 (step @p211 :rule reordering :premises (@p210) :args ((or @t120 @t117 (not @t121)))) % 0.40/0.62 (step @p212 :rule chain_m_resolution :premises (@p211 @p209 @p204) :args (@t120 @t122 (@list @t117 @t121))) % 0.40/0.62 (step @p213 :rule cnf_and_pos :args (@t123 1)) % 0.40/0.62 (step @p214 :rule reordering :premises (@p213) :args ((or @t119 @t124))) % 0.40/0.62 (step @p215 :rule chain_m_resolution :premises (@p214 @p212) :args (@t124 @t115 (@list @t119))) % 0.40/0.62 (step @p216 :rule cnf_or_pos :args (@t127)) % 0.40/0.62 (step @p217 :rule reordering :premises (@p216) :args ((or @t126 @t123 (not @t127)))) % 0.40/0.62 (step @p218 :rule chain_m_resolution :premises (@p217 @p215 @p203) :args (@t126 @t122 (@list @t123 @t127))) % 0.40/0.62 (step @p219 :rule alpha_equiv :args (@t109 (@list @t35 @t33) (@list @t44 @t42))) % 0.40/0.62 (step @p220 :rule equiv_elim1 :premises (@p219)) % 0.40/0.62 (step @p221 :rule chain_m_resolution :premises (@p220 @p202) :args (@t128 (@list false) (@list @t109))) % 0.40/0.62 (step @p222 :rule bool-double-not-elim :args (@t112)) % 0.40/0.62 (step @p223 :rule nary_cong :premises (@p191 @p222) :args ((or @t114 (not @t113)))) % 0.40/0.62 (step @p224 :rule cnf_or_neg :args (@t114 0)) % 0.40/0.62 (step @p225 :rule eq_resolve :premises (@p224 @p223)) % 0.40/0.62 (step @p226 :rule reordering :premises (@p225) :args ((or @t112 @t114))) % 0.40/0.62 (step @p227 :rule chain_m_resolution :premises (@p226 @p189) :args (@t112 @t115 @t116)) % 0.40/0.62 (step @p228 :rule instantiate :premises (@p227) :args ((@list @t101))) % 0.40/0.62 (step @p229 :rule cnf_or_pos :args (@t130)) % 0.40/0.62 (step @p230 :rule reordering :premises (@p229) :args ((or @t111 @t125 @t129 (not @t130)))) % 0.40/0.62 (step @p231 false :rule chain_m_resolution :premises (@p230 @p228 @p221 @p218 @p196) :args (false (@list false false true false) (@list @t130 @t128 @t125 @t102))) % 0.40/0.62 ) % 0.40/0.62 % SZS output end Proof % 0.40/0.62 % cvc5 exiting %------------------------------------------------------------------------------