%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO241^5 : 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 : n003.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 09:12:17 AM UTC 2026 % Result : Theorem 0.44s 0.65s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO241^5 : TPTP v9.2.1. Released v4.0.0. % 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 : n003.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 : Wed Jun 3 00:00:59 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.49 %----Proving TH0 % 0.44/0.65 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.44/0.65 % SZS status Theorem % 0.44/0.65 % SZS output start Proof % 0.44/0.65 ( % 0.44/0.65 (declare-sort $$unsorted 0) % 0.44/0.65 (define @t1 () (@var "Xt" (-> $$unsorted Bool))) % 0.44/0.65 (define @t2 () (@var "Xh" (-> (-> $$unsorted Bool) $$unsorted))) % 0.44/0.65 (define @t3 () (_ @t2 @t1)) % 0.44/0.65 (define @t4 () (@var "Xt0" (-> $$unsorted Bool))) % 0.44/0.65 (define @t5 () (_ @t2 @t4)) % 0.44/0.65 (define @t6 () (@var "Xz" $$unsorted)) % 0.44/0.65 (define @t7 () (= @t6 @t5)) % 0.44/0.65 (define @t8 () (_ @t4 @t5)) % 0.44/0.65 (define @t9 () (not @t8)) % 0.44/0.65 (define @t10 () (and @t9 @t7)) % 0.44/0.65 (define @t11 () (@list @t4)) % 0.44/0.65 (define @t12 () (exists @t11 @t10)) % 0.44/0.65 (define @t13 () (@list @t6)) % 0.44/0.65 (define @t14 () (lambda @t13 @t12)) % 0.44/0.65 (define @t15 () (= (_ @t2 @t14) @t3)) % 0.44/0.65 (define @t16 () (_ @t1 @t3)) % 0.44/0.65 (define @t17 () (not @t16)) % 0.44/0.65 (define @t18 () (and @t17 @t15)) % 0.44/0.65 (define @t19 () (@list @t1)) % 0.44/0.65 (define @t20 () (exists @t19 @t18)) % 0.44/0.65 (define @t21 () (not @t20)) % 0.44/0.65 (define @t22 () (@var "Xq" (-> $$unsorted Bool))) % 0.44/0.65 (define @t23 () (@var "Xp" (-> $$unsorted Bool))) % 0.44/0.65 (define @t24 () (= @t23 @t22)) % 0.44/0.65 (define @t25 () (_ @t2 @t22)) % 0.44/0.65 (define @t26 () (_ @t2 @t23)) % 0.44/0.65 (define @t27 () (= @t26 @t25)) % 0.44/0.65 (define @t28 () (@list @t23 @t22)) % 0.44/0.65 (define @t29 () (forall @t28 (=> @t27 @t24))) % 0.44/0.65 (define @t30 () (=> @t29 @t21)) % 0.44/0.65 (define @t31 () (@list @t2)) % 0.44/0.65 (define @t32 () (forall @t31 @t30)) % 0.44/0.65 (define @t33 () (not @t32)) % 0.44/0.65 (define @t34 () (@var "BOUND_VARIABLE_7493" (-> $$unsorted Bool))) % 0.44/0.65 (define @t35 () (_ @t2 @t34)) % 0.44/0.65 (define @t36 () (_ @t2 @t4)) % 0.44/0.65 (define @t37 () (= @t6 @t36)) % 0.44/0.65 (define @t38 () (not @t37)) % 0.44/0.65 (define @t39 () (_ @t4 @t36)) % 0.44/0.65 (define @t40 () (or @t39 @t38)) % 0.44/0.65 (define @t41 () (forall @t11 @t40)) % 0.44/0.65 (define @t42 () (not @t41)) % 0.44/0.65 (define @t43 () (lambda @t13 @t42)) % 0.44/0.65 (define @t44 () (_ @t2 @t43)) % 0.44/0.65 (define @t45 () (_ @t34 @t35)) % 0.44/0.65 (define @t46 () (_ @t2 @t22)) % 0.44/0.65 (define @t47 () (_ @t2 @t23)) % 0.44/0.65 (define @t48 () (forall @t28 (or (not (= @t47 @t46)) @t24))) % 0.44/0.65 (define @t49 () (not @t48)) % 0.44/0.65 (define @t50 () (@list @t2 @t34)) % 0.44/0.65 (define @t51 () (forall @t50 (or @t49 @t45 (not (= @t44 @t35))))) % 0.44/0.65 (define @t52 () (@quantifiers_skolemize @t51 0)) % 0.44/0.65 (define @t53 () (_ @t52 @t4)) % 0.44/0.65 (define @t54 () (_ @t4 @t53)) % 0.44/0.65 (define @t55 () (not (forall @t11 (or @t54 (not (= @t6 @t53)))))) % 0.44/0.65 (define @t56 () (lambda @t13 @t55)) % 0.44/0.65 (define @t57 () (@purify @t56)) % 0.44/0.65 (define @t58 () (_ @t57 @t6)) % 0.44/0.65 (define @t59 () (_ @t56 @t6)) % 0.44/0.65 (define @t60 () (= @t58 @t59)) % 0.44/0.65 (define @t61 () (forall @t13 @t60)) % 0.44/0.65 (define @t62 () (_ @t52 @t57)) % 0.44/0.65 (define @t63 () (forall @t11 (or @t54 (not (= @t53 @t62))))) % 0.44/0.65 (define @t64 () (not @t63)) % 0.44/0.65 (define @t65 () (_ @t57 @t62)) % 0.44/0.65 (define @t66 () (not (= @t62 @t53))) % 0.44/0.65 (define @t67 () (or @t54 @t66)) % 0.44/0.65 (define @t68 () (forall @t11 @t67)) % 0.44/0.65 (define @t69 () (not @t68)) % 0.44/0.65 (define @t70 () (= @t69 @t65)) % 0.44/0.65 (define @t71 () (forall @t13 (= @t55 @t58))) % 0.44/0.65 (define @t72 () (= @t65 @t64)) % 0.44/0.65 (define @t73 () (not (= @t35 @t44))) % 0.44/0.65 (define @t74 () (or @t49 @t45 @t73)) % 0.44/0.65 (define @t75 () (or @t45 @t73)) % 0.44/0.65 (define @t76 () (or @t49 @t75)) % 0.44/0.65 (define @t77 () (forall @t50 @t76)) % 0.44/0.65 (define @t78 () (@list @t34)) % 0.44/0.65 (define @t79 () (forall @t78 @t76)) % 0.44/0.65 (define @t80 () (forall @t78 @t75)) % 0.44/0.65 (define @t81 () (or @t49 @t80)) % 0.44/0.65 (define @t82 () (_ @t2 @t1)) % 0.44/0.65 (define @t83 () (_ @t1 @t82)) % 0.44/0.65 (define @t84 () (forall @t19 (or @t83 (not (= @t82 @t44))))) % 0.44/0.65 (define @t85 () (not @t7)) % 0.44/0.65 (define @t86 () (or @t8 @t85)) % 0.44/0.65 (define @t87 () (forall @t11 @t86)) % 0.44/0.65 (define @t88 () (lambda @t13 (not @t87))) % 0.44/0.65 (define @t89 () (_ @t2 @t43)) % 0.44/0.65 (define @t90 () (= @t3 @t89)) % 0.44/0.65 (define @t91 () (not @t90)) % 0.44/0.65 (define @t92 () (or @t16 @t91)) % 0.44/0.65 (define @t93 () (and @t17 @t90)) % 0.44/0.65 (define @t94 () (forall @t19 (not @t93))) % 0.44/0.65 (define @t95 () (not @t94)) % 0.44/0.65 (define @t96 () (forall @t11 (not @t10))) % 0.44/0.65 (define @t97 () (not @t96)) % 0.44/0.65 (define @t98 () (not @t27)) % 0.44/0.65 (define @t99 () (or @t98 @t24)) % 0.44/0.65 (define @t100 () (@quantifiers_skolemize @t51 1)) % 0.44/0.65 (define @t101 () (_ @t52 @t100)) % 0.44/0.65 (define @t102 () (= @t101 @t62)) % 0.44/0.65 (define @t103 () (not @t102)) % 0.44/0.65 (define @t104 () (_ @t100 @t101)) % 0.44/0.65 (define @t105 () (forall @t28 (or (not (= (_ @t52 @t23) (_ @t52 @t22))) @t24))) % 0.44/0.65 (define @t106 () (not @t105)) % 0.44/0.65 (define @t107 () (or @t106 @t104 @t103)) % 0.44/0.65 (define @t108 () (not @t107)) % 0.44/0.65 (define @t109 () (not @t51)) % 0.44/0.65 (define @t110 () (_ @t52 @t56)) % 0.44/0.65 (define @t111 () (= @t101 @t110)) % 0.44/0.65 (define @t112 () (not @t111)) % 0.44/0.65 (define @t113 () (or @t106 @t104 @t112)) % 0.44/0.65 (define @t114 () (not @t113)) % 0.44/0.65 (define @t115 () (not (= @t110 @t101))) % 0.44/0.65 (define @t116 () (or @t106 @t104 @t115)) % 0.44/0.65 (define @t117 () (not @t116)) % 0.44/0.65 (define @t118 () (@list true)) % 0.44/0.65 (define @t119 () (@list @t107)) % 0.44/0.65 (define @t120 () (= @t100 @t57)) % 0.44/0.65 (define @t121 () (or @t103 @t120)) % 0.44/0.65 (define @t122 () (not @t72)) % 0.44/0.65 (define @t123 () (@list true false)) % 0.44/0.65 (define @t124 () (or @t104 @t103)) % 0.44/0.65 (define @t125 () (not @t124)) % 0.44/0.65 (assume @p1 @t33) % 0.44/0.65 (assume @p2 true) % 0.44/0.65 (step @p3 :rule eq-symm :args (@t58 @t55)) % 0.44/0.65 (step @p4 :rule beta-reduce :args ((= @t59 @t55))) % 0.44/0.65 (step @p5 :rule refl :args (@t58)) % 0.44/0.65 (step @p6 :rule cong :premises (@p5 @p4) :args (@t60)) % 0.44/0.65 (step @p7 :rule trans :premises (@p6 @p3)) % 0.44/0.65 (step @p8 :rule cong :premises (@p7) :args (@t61)) % 0.44/0.65 (step @p9 :rule quant-unused-vars :args ((= (forall @t13 true) true))) % 0.44/0.65 (step @p10 :rule eq-refl :args (@t59)) % 0.44/0.65 (step @p11 :rule cong :premises (@p10) :args ((forall @t13 (= @t59 @t59)))) % 0.44/0.65 (step @p12 :rule trans :premises (@p11 @p9)) % 0.44/0.65 (step @p13 :rule refl :args (@t59)) % 0.44/0.65 (step @p14 :rule refl :args (@t6)) % 0.44/0.65 (step @p15 :rule skolem_intro :args (@t57)) % 0.44/0.65 (step @p16 :rule ho_cong :premises (@p15 @p14)) % 0.44/0.65 (step @p17 :rule cong :premises (@p16 @p13) :args (@t60)) % 0.44/0.65 (step @p18 :rule cong :premises (@p17) :args (@t61)) % 0.44/0.65 (step @p19 :rule trans :premises (@p18 @p12)) % 0.44/0.65 (step @p20 :rule true_elim :premises (@p19)) % 0.44/0.65 (step @p21 :rule eq_resolve :premises (@p20 @p8)) % 0.44/0.65 (step @p22 :rule eq-symm :args (@t64 @t65)) % 0.44/0.65 (step @p23 :rule refl :args (@t65)) % 0.44/0.65 (step @p24 :rule eq-symm :args (@t62 @t53)) % 0.44/0.65 (step @p25 :rule cong :premises (@p24) :args (@t66)) % 0.44/0.65 (step @p26 :rule refl :args (@t54)) % 0.44/0.65 (step @p27 :rule nary_cong :premises (@p26 @p25) :args (@t67)) % 0.44/0.65 (step @p28 :rule cong :premises (@p27) :args (@t68)) % 0.44/0.65 (step @p29 :rule cong :premises (@p28) :args (@t69)) % 0.44/0.65 (step @p30 :rule cong :premises (@p29 @p23) :args (@t70)) % 0.44/0.65 (step @p31 :rule trans :premises (@p30 @p22)) % 0.44/0.65 (step @p32 :rule refl :args (@t71)) % 0.44/0.65 (step @p33 :rule cong :premises (@p32 @p31) :args ((=> @t71 @t70))) % 0.44/0.65 (assume-push @p248 @t71) % 0.44/0.65 (step @p35 :rule instantiate :premises (@p21) :args ((@list @t62))) % 0.44/0.65 (step-pop @p249 :rule scope :premises (@p35)) % 0.44/0.65 (step @p36 :rule process_scope :premises (@p249) :args (@t70)) % 0.44/0.65 (step @p38 :rule eq_resolve :premises (@p36 @p33)) % 0.44/0.65 (step @p39 :rule implies_elim :premises (@p38)) % 0.44/0.65 (step @p40 :rule chain_m_resolution :premises (@p39 @p21) :args (@t72 (@list false) (@list @t71))) % 0.44/0.65 (step @p41 :rule eq-symm :args (@t35 @t44)) % 0.44/0.65 (step @p42 :rule cong :premises (@p41) :args (@t73)) % 0.44/0.65 (step @p43 :rule refl :args (@t45)) % 0.44/0.65 (step @p44 :rule refl :args (@t49)) % 0.44/0.65 (step @p45 :rule nary_cong :premises (@p44 @p43 @p42) :args (@t74)) % 0.44/0.65 (step @p46 :rule aci_norm :args ((= @t76 @t74))) % 0.44/0.65 (step @p47 :rule trans :premises (@p46 @p45)) % 0.44/0.65 (step @p48 :rule cong :premises (@p47) :args (@t77)) % 0.44/0.65 (step @p49 :rule quant-merge-prenex :args ((= (forall @t31 @t79) @t77))) % 0.44/0.65 (step @p50 :rule alpha_equiv :args (@t80 (@list @t34) (@list @t1))) % 0.44/0.65 (step @p51 :rule refl :args (@t49)) % 0.44/0.65 (step @p52 :rule nary_cong :premises (@p51 @p50) :args (@t81)) % 0.44/0.65 (step @p53 :rule quant-miniscope-or :args ((= @t79 @t81))) % 0.44/0.65 (step @p54 :rule trans :premises (@p53 @p52)) % 0.44/0.65 (step @p55 :rule symm :premises (@p54)) % 0.44/0.65 (step @p56 :rule cong :premises (@p55) :args ((forall @t31 (or @t49 @t84)))) % 0.44/0.65 (step @p57 :rule trans :premises (@p56 @p49)) % 0.44/0.65 (step @p58 :rule trans :premises (@p57 @p48)) % 0.44/0.65 (step @p59 :rule bool-impl-elim :args (@t48 @t84)) % 0.44/0.65 (step @p60 :rule cong :premises (@p59) :args ((forall @t31 (=> @t48 @t84)))) % 0.44/0.65 (step @p61 :rule trans :premises (@p60 @p58)) % 0.44/0.65 (step @p62 :rule bool-double-not-elim :args (@t84)) % 0.44/0.65 (step @p63 :rule refl :args ((_ @t2 @t88))) % 0.44/0.65 (step @p64 :rule refl :args (@t36)) % 0.44/0.65 (step @p65 :rule refl :args (@t6)) % 0.44/0.65 (step @p66 :rule cong :premises (@p65 @p64) :args (@t37)) % 0.44/0.65 (step @p67 :rule cong :premises (@p66) :args (@t38)) % 0.44/0.65 (step @p68 :rule refl :args ((_ @t4 @t5))) % 0.44/0.65 (step @p69 :rule cong :premises (@p64) :args (@t39)) % 0.44/0.65 (step @p70 :rule trans :premises (@p69 @p68)) % 0.44/0.65 (step @p71 :rule nary_cong :premises (@p70 @p67) :args (@t40)) % 0.44/0.65 (step @p72 :rule cong :premises (@p71) :args (@t41)) % 0.44/0.65 (step @p73 :rule cong :premises (@p72) :args (@t42)) % 0.44/0.65 (step @p74 :rule cong :premises (@p73) :args (@t43)) % 0.44/0.65 (step @p75 :rule cong :premises (@p74) :args (@t44)) % 0.44/0.65 (step @p76 :rule trans :premises (@p75 @p63)) % 0.44/0.65 (step @p77 :rule refl :args (@t2)) % 0.44/0.65 (step @p78 :rule ho_cong :premises (@p77 @p74)) % 0.44/0.65 (step @p79 :rule cong :premises (@p78 @p76) :args ((= @t89 @t44))) % 0.44/0.65 (step @p80 :rule symm :premises (@p79)) % 0.44/0.65 (step @p81 :rule refl :args ((_ @t2 @t88))) % 0.44/0.65 (step @p82 :rule eq_resolve :premises (@p81 @p80)) % 0.44/0.65 (step @p83 :rule refl :args (@t82)) % 0.44/0.65 (step @p84 :rule refl :args (@t3)) % 0.44/0.65 (step @p85 :rule cong :premises (@p84 @p83) :args ((= @t3 @t82))) % 0.44/0.65 (step @p86 :rule symm :premises (@p85)) % 0.44/0.65 (step @p87 :rule eq_resolve :premises (@p84 @p86)) % 0.44/0.65 (step @p88 :rule cong :premises (@p87 @p82) :args (@t90)) % 0.44/0.65 (step @p89 :rule cong :premises (@p88) :args (@t91)) % 0.44/0.65 (step @p90 :rule refl :args ((_ @t1 @t3))) % 0.44/0.65 (step @p91 :rule cong :premises (@p83) :args (@t83)) % 0.44/0.65 (step @p92 :rule trans :premises (@p91 @p90)) % 0.44/0.65 (step @p93 :rule refl :args (@t1)) % 0.44/0.65 (step @p94 :rule ho_cong :premises (@p93 @p83)) % 0.44/0.65 (step @p95 :rule cong :premises (@p94 @p92) :args ((= (_ @t1 @t82) @t83))) % 0.44/0.65 (step @p96 :rule symm :premises (@p95)) % 0.44/0.65 (step @p97 :rule refl :args (@t16)) % 0.44/0.65 (step @p98 :rule eq_resolve :premises (@p97 @p96)) % 0.44/0.65 (step @p99 :rule ho_cong :premises (@p93 @p87)) % 0.44/0.65 (step @p100 :rule trans :premises (@p99 @p98)) % 0.44/0.65 (step @p101 :rule nary_cong :premises (@p100 @p89) :args (@t92)) % 0.44/0.65 (step @p102 :rule cong :premises (@p101) :args ((forall @t19 @t92))) % 0.44/0.65 (step @p103 :rule refl :args (@t91)) % 0.44/0.65 (step @p104 :rule bool-double-not-elim :args (@t16)) % 0.44/0.65 (step @p105 :rule nary_cong :premises (@p104 @p103) :args ((or (not @t17) @t91))) % 0.44/0.65 (step @p106 :rule bool-and-de-morgan :args (@t17 @t90 true)) % 0.44/0.65 (step @p107 :rule trans :premises (@p106 @p105)) % 0.44/0.65 (step @p108 :rule cong :premises (@p107) :args (@t94)) % 0.44/0.65 (step @p109 :rule trans :premises (@p108 @p102)) % 0.44/0.65 (step @p110 :rule cong :premises (@p109) :args (@t95)) % 0.44/0.65 (step @p111 :rule exists-elim :args ((= (exists @t19 @t93) @t95))) % 0.44/0.65 (step @p112 :rule trans :premises (@p111 @p110)) % 0.44/0.65 (step @p113 :rule eq-symm :args (@t89 @t3)) % 0.44/0.65 (step @p114 :rule refl :args (@t3)) % 0.44/0.65 (step @p115 :rule refl :args (@t5)) % 0.44/0.65 (step @p116 :rule cong :premises (@p115 @p64) :args ((= @t5 @t36))) % 0.44/0.65 (step @p117 :rule symm :premises (@p116)) % 0.44/0.65 (step @p118 :rule eq_resolve :premises (@p115 @p117)) % 0.44/0.65 (step @p119 :rule cong :premises (@p65 @p118) :args (@t7)) % 0.44/0.65 (step @p120 :rule cong :premises (@p119) :args (@t85)) % 0.44/0.65 (step @p121 :rule refl :args (@t4)) % 0.44/0.65 (step @p122 :rule ho_cong :premises (@p121 @p64)) % 0.44/0.65 (step @p123 :rule cong :premises (@p122 @p70) :args ((= (_ @t4 @t36) @t39))) % 0.44/0.65 (step @p124 :rule symm :premises (@p123)) % 0.44/0.65 (step @p125 :rule refl :args (@t8)) % 0.44/0.65 (step @p126 :rule eq_resolve :premises (@p125 @p124)) % 0.44/0.65 (step @p127 :rule ho_cong :premises (@p121 @p118)) % 0.44/0.65 (step @p128 :rule trans :premises (@p127 @p126)) % 0.44/0.65 (step @p129 :rule nary_cong :premises (@p128 @p120) :args (@t86)) % 0.44/0.65 (step @p130 :rule cong :premises (@p129) :args (@t87)) % 0.44/0.65 (step @p131 :rule refl :args (@t85)) % 0.44/0.65 (step @p132 :rule bool-double-not-elim :args (@t8)) % 0.44/0.65 (step @p133 :rule nary_cong :premises (@p132 @p131) :args ((or (not @t9) @t85))) % 0.44/0.65 (step @p134 :rule bool-and-de-morgan :args (@t9 @t7 true)) % 0.44/0.65 (step @p135 :rule trans :premises (@p134 @p133)) % 0.44/0.65 (step @p136 :rule cong :premises (@p135) :args (@t96)) % 0.44/0.65 (step @p137 :rule trans :premises (@p136 @p130)) % 0.44/0.65 (step @p138 :rule cong :premises (@p137) :args (@t97)) % 0.44/0.65 (step @p139 :rule exists-elim :args ((= @t12 @t97))) % 0.44/0.65 (step @p140 :rule trans :premises (@p139 @p138)) % 0.44/0.65 (step @p141 :rule cong :premises (@p140) :args (@t14)) % 0.44/0.65 (step @p142 :rule refl :args (@t2)) % 0.44/0.65 (step @p143 :rule ho_cong :premises (@p142 @p141)) % 0.44/0.65 (step @p144 :rule cong :premises (@p143 @p114) :args (@t15)) % 0.44/0.65 (step @p145 :rule trans :premises (@p144 @p113)) % 0.44/0.65 (step @p146 :rule refl :args (@t17)) % 0.44/0.65 (step @p147 :rule nary_cong :premises (@p146 @p145) :args (@t18)) % 0.44/0.65 (step @p148 :rule cong :premises (@p147) :args (@t20)) % 0.44/0.65 (step @p149 :rule trans :premises (@p148 @p112)) % 0.44/0.65 (step @p150 :rule cong :premises (@p149) :args (@t21)) % 0.44/0.65 (step @p151 :rule trans :premises (@p150 @p62)) % 0.44/0.65 (step @p152 :rule refl :args (@t24)) % 0.44/0.65 (step @p153 :rule refl :args (@t46)) % 0.44/0.65 (step @p154 :rule refl :args (@t25)) % 0.44/0.65 (step @p155 :rule cong :premises (@p154 @p153) :args ((= @t25 @t46))) % 0.44/0.65 (step @p156 :rule symm :premises (@p155)) % 0.44/0.65 (step @p157 :rule eq_resolve :premises (@p154 @p156)) % 0.44/0.65 (step @p158 :rule refl :args (@t47)) % 0.44/0.65 (step @p159 :rule refl :args (@t26)) % 0.44/0.65 (step @p160 :rule cong :premises (@p159 @p158) :args ((= @t26 @t47))) % 0.44/0.65 (step @p161 :rule symm :premises (@p160)) % 0.44/0.65 (step @p162 :rule eq_resolve :premises (@p159 @p161)) % 0.44/0.65 (step @p163 :rule cong :premises (@p162 @p157) :args (@t27)) % 0.44/0.65 (step @p164 :rule cong :premises (@p163) :args (@t98)) % 0.44/0.65 (step @p165 :rule nary_cong :premises (@p164 @p152) :args (@t99)) % 0.44/0.65 (step @p166 :rule cong :premises (@p165) :args ((forall @t28 @t99))) % 0.44/0.65 (step @p167 :rule bool-impl-elim :args (@t27 @t24)) % 0.44/0.65 (step @p168 :rule cong :premises (@p167) :args (@t29)) % 0.44/0.65 (step @p169 :rule trans :premises (@p168 @p166)) % 0.44/0.65 (step @p170 :rule cong :premises (@p169 @p151) :args (@t30)) % 0.44/0.65 (step @p171 :rule cong :premises (@p170) :args (@t32)) % 0.44/0.65 (step @p172 :rule trans :premises (@p171 @p61)) % 0.44/0.65 (step @p173 :rule cong :premises (@p172) :args (@t33)) % 0.44/0.65 (step @p174 :rule eq_resolve :premises (@p1 @p173)) % 0.44/0.65 (step @p175 :rule refl :args (@t108)) % 0.44/0.65 (step @p176 :rule bool-double-not-elim :args (@t51)) % 0.44/0.65 (step @p177 :rule nary_cong :premises (@p176 @p175) :args ((or (not @t109) @t108))) % 0.44/0.65 (step @p178 :rule eq-refl :args (@t56)) % 0.44/0.65 (step @p179 :rule refl :args (@t56)) % 0.44/0.65 (step @p180 :rule cong :premises (@p179 @p15) :args ((= @t56 @t57))) % 0.44/0.65 (step @p181 :rule trans :premises (@p180 @p178)) % 0.44/0.65 (step @p182 :rule true_elim :premises (@p181)) % 0.44/0.65 (step @p183 :rule cong :premises (@p182) :args (@t110)) % 0.44/0.65 (step @p184 :rule refl :args (@t101)) % 0.44/0.65 (step @p185 :rule cong :premises (@p184 @p183) :args (@t111)) % 0.44/0.65 (step @p186 :rule cong :premises (@p185) :args (@t112)) % 0.44/0.65 (step @p187 :rule refl :args (@t104)) % 0.44/0.65 (step @p188 :rule refl :args (@t106)) % 0.44/0.65 (step @p189 :rule nary_cong :premises (@p188 @p187 @p186) :args (@t113)) % 0.44/0.65 (step @p190 :rule cong :premises (@p189) :args (@t114)) % 0.44/0.65 (step @p191 :rule refl :args (@t109)) % 0.44/0.65 (step @p192 :rule cong :premises (@p191 @p190) :args ((=> @t109 @t114))) % 0.44/0.65 (step @p193 :rule eq-symm :args (@t110 @t101)) % 0.44/0.65 (step @p194 :rule cong :premises (@p193) :args (@t115)) % 0.44/0.65 (step @p195 :rule nary_cong :premises (@p188 @p187 @p194) :args (@t116)) % 0.44/0.65 (step @p196 :rule cong :premises (@p195) :args (@t117)) % 0.44/0.65 (step @p197 :rule cong :premises (@p191 @p196) :args ((=> @t109 @t117))) % 0.44/0.65 (step @p198 :rule trans :premises (@p197 @p192)) % 0.44/0.65 (assume-push @p250 @t109) % 0.44/0.65 (step @p200 :rule skolemize :premises (@p174)) % 0.44/0.65 (step-pop @p251 :rule scope :premises (@p200)) % 0.44/0.65 (step @p201 :rule process_scope :premises (@p251) :args (@t117)) % 0.44/0.65 (step @p203 :rule eq_resolve :premises (@p201 @p198)) % 0.44/0.65 (step @p204 :rule implies_elim :premises (@p203)) % 0.44/0.65 (step @p205 :rule eq_resolve :premises (@p204 @p177)) % 0.44/0.65 (step @p206 :rule chain_m_resolution :premises (@p205 @p174) :args (@t108 @t118 (@list @t51))) % 0.44/0.65 (step @p207 :rule cnf_or_neg :args (@t107 1)) % 0.44/0.65 (step @p208 :rule chain_m_resolution :premises (@p207 @p206) :args ((not @t104) @t118 @t119)) % 0.44/0.65 (step @p209 :rule false_intro :premises (@p208)) % 0.44/0.65 (step @p210 :rule bool-double-not-elim :args (@t102)) % 0.44/0.65 (step @p211 :rule refl :args (@t107)) % 0.44/0.65 (step @p212 :rule nary_cong :premises (@p211 @p210) :args ((or @t107 (not @t103)))) % 0.44/0.65 (step @p213 :rule cnf_or_neg :args (@t107 2)) % 0.44/0.65 (step @p214 :rule eq_resolve :premises (@p213 @p212)) % 0.44/0.65 (step @p215 :rule reordering :premises (@p214) :args ((or @t102 @t107))) % 0.44/0.65 (step @p216 :rule chain_m_resolution :premises (@p215 @p206) :args (@t102 @t118 @t119)) % 0.44/0.65 (step @p217 :rule symm :premises (@p216)) % 0.44/0.65 (step @p218 :rule bool-double-not-elim :args (@t105)) % 0.44/0.65 (step @p219 :rule nary_cong :premises (@p211 @p218) :args ((or @t107 (not @t106)))) % 0.44/0.65 (step @p220 :rule cnf_or_neg :args (@t107 0)) % 0.44/0.65 (step @p221 :rule eq_resolve :premises (@p220 @p219)) % 0.44/0.65 (step @p222 :rule reordering :premises (@p221) :args ((or @t105 @t107))) % 0.44/0.65 (step @p223 :rule chain_m_resolution :premises (@p222 @p206) :args (@t105 @t118 @t119)) % 0.44/0.65 (step @p224 :rule instantiate :premises (@p223) :args ((@list @t100 @t57))) % 0.44/0.65 (step @p225 :rule cnf_or_pos :args (@t121)) % 0.44/0.65 (step @p226 :rule reordering :premises (@p225) :args ((or @t103 @t120 (not @t121)))) % 0.44/0.65 (step @p227 :rule chain_m_resolution :premises (@p226 @p216 @p224) :args (@t120 (@list false false) (@list @t102 @t121))) % 0.44/0.65 (step @p228 :rule symm :premises (@p227)) % 0.44/0.65 (step @p229 :rule ho_cong :premises (@p228 @p217)) % 0.44/0.65 (step @p230 :rule trans :premises (@p229 @p209)) % 0.44/0.65 (step @p231 :rule false_elim :premises (@p230)) % 0.44/0.65 (step @p232 :rule bool-double-not-elim :args (@t63)) % 0.44/0.65 (step @p233 :rule refl :args (@t122)) % 0.44/0.65 (step @p234 :rule nary_cong :premises (@p233 @p23 @p232) :args ((or @t122 @t65 (not @t64)))) % 0.44/0.65 (step @p235 :rule cnf_equiv_pos2 :args (@t72)) % 0.44/0.65 (step @p236 :rule eq_resolve :premises (@p235 @p234)) % 0.44/0.65 (step @p237 :rule reordering :premises (@p236) :args ((or @t65 @t63 @t122))) % 0.44/0.65 (step @p238 :rule chain_m_resolution :premises (@p237 @p231 @p40) :args (@t63 @t123 (@list @t65 @t72))) % 0.44/0.65 (step @p239 :rule cnf_or_pos :args (@t124)) % 0.44/0.65 (step @p240 :rule reordering :premises (@p239) :args ((or @t104 @t103 @t125))) % 0.44/0.65 (step @p241 :rule chain_m_resolution :premises (@p240 @p208 @p216) :args (@t125 @t123 (@list @t104 @t102))) % 0.44/0.65 (assume-push @p252 @t63) % 0.44/0.65 (step @p243 :rule instantiate :premises (@p238) :args ((@list @t100))) % 0.44/0.65 (step-pop @p253 :rule scope :premises (@p243)) % 0.44/0.65 (step @p244 :rule process_scope :premises (@p253) :args (@t124)) % 0.44/0.65 (step @p246 :rule implies_elim :premises (@p244)) % 0.44/0.65 (step @p247 false :rule chain_m_resolution :premises (@p246 @p241 @p238) :args (false @t123 (@list @t124 @t63))) % 0.44/0.65 ) % 0.44/0.65 % SZS output end Proof % 0.44/0.65 % cvc5 exiting %------------------------------------------------------------------------------