%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU827^1 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n005.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 08:53:23 AM UTC 2026 % Result : Theorem 0.37s 0.57s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU827^1 : TPTP v9.2.1. Released v3.7.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n005.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 17:54:48 EDT 2026 % 0.16/0.34 % CPUTime : % 0.27/0.49 %----Proving TH0 % 0.37/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.57 % SZS status Theorem % 0.37/0.57 % SZS output start Proof % 0.37/0.57 ( % 0.37/0.57 (declare-sort $$unsorted 0) % 0.37/0.57 (declare-const tptp.b (-> $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.a (-> $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.c (-> $$unsorted Bool)) % 0.37/0.57 (define tptp.leibeq () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "P" (-> (-> $$unsorted Bool) Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ _let_2 _let_3) (_ _let_2 _let_1)))))))) % 0.37/0.57 (define tptp.u () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.57 (define tptp.n () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.57 (define @t1 () (_ tptp.u tptp.a)) % 0.37/0.57 (define @t2 () (not (_ (_ tptp.leibeq (_ @t1 (_ (_ tptp.n tptp.b) tptp.c))) (_ (_ tptp.n (_ @t1 tptp.b)) (_ @t1 tptp.c))))) % 0.37/0.57 (define @t3 () (@var "Y" (-> $$unsorted Bool))) % 0.37/0.57 (define @t4 () (@var "P" (-> (-> $$unsorted Bool) Bool))) % 0.37/0.57 (define @t5 () (_ @t4 @t3)) % 0.37/0.57 (define @t6 () (@var "X" (-> $$unsorted Bool))) % 0.37/0.57 (define @t7 () (_ @t4 @t6)) % 0.37/0.57 (define @t8 () (@list @t4)) % 0.37/0.57 (define @t9 () (forall @t8 (=> @t7 @t5))) % 0.37/0.57 (define @t10 () (@list @t6 @t3)) % 0.37/0.57 (define @t11 () (lambda @t10 @t9)) % 0.37/0.57 (define @t12 () (@var "U" $$unsorted)) % 0.37/0.57 (define @t13 () (_ @t3 @t12)) % 0.37/0.57 (define @t14 () (_ @t6 @t12)) % 0.37/0.57 (define @t15 () (@list @t6 @t3 @t12)) % 0.37/0.57 (define @t16 () (lambda @t15 (or @t14 @t13))) % 0.37/0.57 (define @t17 () (lambda @t15 (and @t14 @t13))) % 0.37/0.57 (define @t18 () (tptp.c @t12)) % 0.37/0.57 (define @t19 () (tptp.a @t12)) % 0.37/0.57 (define @t20 () (tptp.b @t12)) % 0.37/0.57 (define @t21 () (and (or @t19 @t20) (or @t19 @t18))) % 0.37/0.57 (define @t22 () (@list @t12)) % 0.37/0.57 (define @t23 () (lambda @t22 @t21)) % 0.37/0.57 (define @t24 () (@purify @t23)) % 0.37/0.57 (define @t25 () (_ @t24 @t12)) % 0.37/0.57 (define @t26 () (_ @t23 @t12)) % 0.37/0.57 (define @t27 () (= @t25 @t26)) % 0.37/0.57 (define @t28 () (forall @t22 @t27)) % 0.37/0.57 (define @t29 () (@const 0 $$unsorted)) % 0.37/0.57 (define @t30 () (tptp.c @t29)) % 0.37/0.57 (define @t31 () (tptp.a @t29)) % 0.37/0.57 (define @t32 () (or @t31 @t30)) % 0.37/0.57 (define @t33 () (tptp.b @t29)) % 0.37/0.57 (define @t34 () (or @t31 @t33)) % 0.37/0.57 (define @t35 () (and @t34 @t32)) % 0.37/0.57 (define @t36 () (_ @t24 @t29)) % 0.37/0.57 (define @t37 () (forall @t22 (= @t21 @t25))) % 0.37/0.57 (define @t38 () (= @t35 @t36)) % 0.37/0.57 (define @t39 () (@list @t29)) % 0.37/0.57 (define @t40 () (= @t36 @t35)) % 0.37/0.57 (define @t41 () (@list false)) % 0.37/0.57 (define @t42 () (_ tptp.c @t12)) % 0.37/0.57 (define @t43 () (_ tptp.a @t12)) % 0.37/0.57 (define @t44 () (or @t43 @t42)) % 0.37/0.57 (define @t45 () (_ tptp.b @t12)) % 0.37/0.57 (define @t46 () (or @t43 @t45)) % 0.37/0.57 (define @t47 () (and @t46 @t44)) % 0.37/0.57 (define @t48 () (lambda @t22 @t47)) % 0.37/0.57 (define @t49 () (_ @t4 @t48)) % 0.37/0.57 (define @t50 () (or @t19 (and @t20 @t18))) % 0.37/0.57 (define @t51 () (lambda @t22 @t50)) % 0.37/0.57 (define @t52 () (not (_ @t4 @t51))) % 0.37/0.57 (define @t53 () (or @t52 @t49)) % 0.37/0.57 (define @t54 () (forall @t8 @t53)) % 0.37/0.57 (define @t55 () (_ @t4 @t3)) % 0.37/0.57 (define @t56 () (@list @t3)) % 0.37/0.57 (define @t57 () (lambda @t22 @t44)) % 0.37/0.57 (define @t58 () (_ @t57 @t12)) % 0.37/0.57 (define @t59 () (and @t46 @t58)) % 0.37/0.57 (define @t60 () (lambda @t22 @t59)) % 0.37/0.57 (define @t61 () (@list @t3 @t12)) % 0.37/0.57 (define @t62 () (lambda @t61 (or @t43 @t13))) % 0.37/0.57 (define @t63 () (_ @t16 tptp.a)) % 0.37/0.57 (define @t64 () (lambda @t22 @t46)) % 0.37/0.57 (define @t65 () (_ @t64 @t12)) % 0.37/0.57 (define @t66 () (and @t65 @t13)) % 0.37/0.57 (define @t67 () (lambda @t61 @t66)) % 0.37/0.57 (define @t68 () (and @t45 @t42)) % 0.37/0.57 (define @t69 () (or @t43 @t68)) % 0.37/0.57 (define @t70 () (lambda @t22 @t69)) % 0.37/0.57 (define @t71 () (_ @t4 @t70)) % 0.37/0.57 (define @t72 () (not @t71)) % 0.37/0.57 (define @t73 () (or @t72 @t55)) % 0.37/0.57 (define @t74 () (forall @t8 @t73)) % 0.37/0.57 (define @t75 () (lambda @t56 @t74)) % 0.37/0.57 (define @t76 () (_ @t4 @t6)) % 0.37/0.57 (define @t77 () (lambda @t10 (forall @t8 (or (not @t76) @t55)))) % 0.37/0.57 (define @t78 () (lambda @t22 @t68)) % 0.37/0.57 (define @t79 () (_ @t78 @t12)) % 0.37/0.57 (define @t80 () (or @t43 @t79)) % 0.37/0.57 (define @t81 () (lambda @t22 @t80)) % 0.37/0.57 (define @t82 () (lambda @t61 (and @t45 @t13))) % 0.37/0.57 (define @t83 () (_ @t17 tptp.b)) % 0.37/0.57 (define @t84 () (not @t7)) % 0.37/0.57 (define @t85 () (or @t84 @t5)) % 0.37/0.57 (define @t86 () (forall @t8 (or @t52 (_ @t4 @t23)))) % 0.37/0.57 (define @t87 () (@quantifiers_skolemize @t86 0)) % 0.37/0.57 (define @t88 () (_ @t87 @t24)) % 0.37/0.57 (define @t89 () (@purify @t51)) % 0.37/0.57 (define @t90 () (_ @t87 @t89)) % 0.37/0.57 (define @t91 () (not @t90)) % 0.37/0.57 (define @t92 () (or @t91 @t88)) % 0.37/0.57 (define @t93 () (not @t92)) % 0.37/0.57 (define @t94 () (not @t86)) % 0.37/0.57 (define @t95 () (_ @t87 @t23)) % 0.37/0.57 (define @t96 () (_ @t87 @t51)) % 0.37/0.57 (define @t97 () (not @t96)) % 0.37/0.57 (define @t98 () (or @t97 @t95)) % 0.37/0.57 (define @t99 () (not @t98)) % 0.37/0.57 (define @t100 () (@list true)) % 0.37/0.57 (define @t101 () (@list @t92)) % 0.37/0.57 (define @t102 () (not @t88)) % 0.37/0.57 (define @t103 () (= @t24 @t89)) % 0.37/0.57 (define @t104 () (not @t103)) % 0.37/0.57 (define @t105 () (and @t102 @t103 @t90)) % 0.37/0.57 (define @t106 () (@list true false)) % 0.37/0.57 (define @t107 () (_ @t89 @t29)) % 0.37/0.57 (define @t108 () (= @t36 @t107)) % 0.37/0.57 (define @t109 () (not @t108)) % 0.37/0.57 (define @t110 () (not @t40)) % 0.37/0.57 (define @t111 () (not @t36)) % 0.37/0.57 (define @t112 () (_ @t89 @t12)) % 0.37/0.57 (define @t113 () (_ @t51 @t12)) % 0.37/0.57 (define @t114 () (= @t112 @t113)) % 0.37/0.57 (define @t115 () (forall @t22 @t114)) % 0.37/0.57 (define @t116 () (and @t33 @t30)) % 0.37/0.57 (define @t117 () (or @t31 @t116)) % 0.37/0.57 (define @t118 () (forall @t22 (= @t50 @t112))) % 0.37/0.57 (define @t119 () (= @t117 @t107)) % 0.37/0.57 (define @t120 () (= @t107 @t117)) % 0.37/0.57 (define @t121 () (not @t120)) % 0.37/0.57 (define @t122 () (not @t117)) % 0.37/0.57 (define @t123 () (not @t35)) % 0.37/0.57 (define @t124 () (not @t116)) % 0.37/0.57 (define @t125 () (@list @t31)) % 0.37/0.57 (assume @p1 @t2) % 0.37/0.57 (assume @p2 true) % 0.37/0.57 (step @p3 (= tptp.leibeq @t11) :rule refl :args (@t11)) % 0.37/0.57 (step @p4 (= tptp.u @t16) :rule refl :args (@t16)) % 0.37/0.57 (step @p5 (= tptp.n @t17) :rule refl :args (@t17)) % 0.37/0.57 (step @p6 :rule eq-symm :args (@t25 @t21)) % 0.37/0.57 (step @p7 :rule beta-reduce :args ((= @t26 @t21))) % 0.37/0.57 (step @p8 :rule refl :args (@t25)) % 0.37/0.57 (step @p9 :rule cong :premises (@p8 @p7) :args (@t27)) % 0.37/0.57 (step @p10 :rule trans :premises (@p9 @p6)) % 0.37/0.57 (step @p11 :rule cong :premises (@p10) :args (@t28)) % 0.37/0.57 (step @p12 :rule quant-unused-vars :args ((= (forall @t22 true) true))) % 0.37/0.57 (step @p13 :rule eq-refl :args (@t26)) % 0.37/0.57 (step @p14 :rule cong :premises (@p13) :args ((forall @t22 (= @t26 @t26)))) % 0.37/0.57 (step @p15 :rule trans :premises (@p14 @p12)) % 0.37/0.57 (step @p16 :rule refl :args (@t26)) % 0.37/0.57 (step @p17 :rule refl :args (@t12)) % 0.37/0.57 (step @p18 :rule skolem_intro :args (@t24)) % 0.37/0.57 (step @p19 :rule ho_cong :premises (@p18 @p17)) % 0.37/0.57 (step @p20 :rule cong :premises (@p19 @p16) :args (@t27)) % 0.37/0.57 (step @p21 :rule cong :premises (@p20) :args (@t28)) % 0.37/0.57 (step @p22 :rule trans :premises (@p21 @p15)) % 0.37/0.57 (step @p23 :rule true_elim :premises (@p22)) % 0.37/0.57 (step @p24 :rule eq_resolve :premises (@p23 @p11)) % 0.37/0.57 (step @p25 :rule eq-symm :args (@t35 @t36)) % 0.37/0.57 (step @p26 :rule refl :args (@t37)) % 0.37/0.57 (step @p27 :rule cong :premises (@p26 @p25) :args ((=> @t37 @t38))) % 0.37/0.57 (assume-push @p288 @t37) % 0.37/0.57 (step @p29 :rule instantiate :premises (@p24) :args (@t39)) % 0.37/0.57 (step-pop @p289 :rule scope :premises (@p29)) % 0.37/0.57 (step @p30 :rule process_scope :premises (@p289) :args (@t38)) % 0.37/0.57 (step @p32 :rule eq_resolve :premises (@p30 @p27)) % 0.37/0.57 (step @p33 :rule implies_elim :premises (@p32)) % 0.37/0.57 (step @p34 :rule chain_m_resolution :premises (@p33 @p24) :args (@t40 @t41 (@list @t37))) % 0.37/0.57 (step @p35 :rule refl :args (@t18)) % 0.37/0.57 (step @p36 :rule refl :args (@t42)) % 0.37/0.57 (step @p37 :rule cong :premises (@p36 @p35) :args ((= @t42 @t18))) % 0.37/0.57 (step @p38 :rule symm :premises (@p37)) % 0.37/0.57 (step @p39 :rule eq_resolve :premises (@p36 @p38)) % 0.37/0.57 (step @p40 :rule refl :args (@t19)) % 0.37/0.57 (step @p41 :rule refl :args (@t43)) % 0.37/0.57 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t43 @t19))) % 0.37/0.57 (step @p43 :rule symm :premises (@p42)) % 0.37/0.57 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 0.37/0.57 (step @p45 :rule nary_cong :premises (@p44 @p39) :args (@t44)) % 0.37/0.57 (step @p46 :rule refl :args (@t20)) % 0.37/0.57 (step @p47 :rule refl :args (@t45)) % 0.37/0.57 (step @p48 :rule cong :premises (@p47 @p46) :args ((= @t45 @t20))) % 0.37/0.57 (step @p49 :rule symm :premises (@p48)) % 0.37/0.57 (step @p50 :rule eq_resolve :premises (@p47 @p49)) % 0.37/0.57 (step @p51 :rule nary_cong :premises (@p44 @p50) :args (@t46)) % 0.37/0.57 (step @p52 :rule nary_cong :premises (@p51 @p45) :args (@t47)) % 0.37/0.57 (step @p53 :rule cong :premises (@p52) :args (@t48)) % 0.37/0.57 (step @p54 :rule cong :premises (@p53) :args (@t49)) % 0.37/0.57 (step @p55 :rule refl :args (@t52)) % 0.37/0.57 (step @p56 :rule nary_cong :premises (@p55 @p54) :args (@t53)) % 0.37/0.57 (step @p57 :rule cong :premises (@p56) :args (@t54)) % 0.37/0.57 (step @p58 :rule beta-reduce :args ((= (_ (lambda @t56 (forall @t8 (or @t52 @t55))) @t48) @t54))) % 0.37/0.57 (step @p59 :rule trans :premises (@p58 @p57)) % 0.37/0.57 (step @p60 :rule beta-reduce :args ((= @t58 @t44))) % 0.37/0.57 (step @p61 :rule refl :args (@t46)) % 0.37/0.57 (step @p62 :rule nary_cong :premises (@p61 @p60) :args (@t59)) % 0.37/0.57 (step @p63 :rule cong :premises (@p62) :args (@t60)) % 0.37/0.57 (step @p64 :rule beta-reduce :args ((= (_ (lambda @t61 (and @t46 @t13)) @t57) @t60))) % 0.37/0.57 (step @p65 :rule trans :premises (@p64 @p63)) % 0.37/0.57 (step @p66 :rule beta-reduce :args ((= (_ @t62 tptp.c) @t57))) % 0.37/0.57 (step @p67 :rule refl :args (tptp.c)) % 0.37/0.57 (step @p68 :rule beta-reduce :args ((= @t63 @t62))) % 0.37/0.57 (step @p69 :rule ho_cong :premises (@p68 @p67)) % 0.37/0.57 (step @p70 :rule trans :premises (@p69 @p66)) % 0.37/0.57 (step @p71 :rule refl :args (@t13)) % 0.37/0.57 (step @p72 :rule beta-reduce :args ((= @t65 @t46))) % 0.37/0.57 (step @p73 :rule nary_cong :premises (@p72 @p71) :args (@t66)) % 0.37/0.57 (step @p74 :rule cong :premises (@p73) :args (@t67)) % 0.37/0.57 (step @p75 :rule beta-reduce :args ((= (_ @t17 @t64) @t67))) % 0.37/0.57 (step @p76 :rule trans :premises (@p75 @p74)) % 0.37/0.57 (step @p77 :rule beta-reduce :args ((= (_ @t62 tptp.b) @t64))) % 0.37/0.57 (step @p78 :rule refl :args (tptp.b)) % 0.37/0.57 (step @p79 :rule ho_cong :premises (@p68 @p78)) % 0.37/0.57 (step @p80 :rule trans :premises (@p79 @p77)) % 0.37/0.57 (step @p81 :rule refl :args (@t17)) % 0.37/0.57 (step @p82 :rule ho_cong :premises (@p81 @p80)) % 0.37/0.57 (step @p83 :rule trans :premises (@p82 @p76)) % 0.37/0.57 (step @p84 :rule ho_cong :premises (@p83 @p70)) % 0.37/0.57 (step @p85 :rule trans :premises (@p84 @p65)) % 0.37/0.57 (step @p86 :rule refl :args (@t55)) % 0.37/0.57 (step @p87 :rule nary_cong :premises (@p50 @p39) :args (@t68)) % 0.37/0.57 (step @p88 :rule nary_cong :premises (@p44 @p87) :args (@t69)) % 0.37/0.57 (step @p89 :rule cong :premises (@p88) :args (@t70)) % 0.37/0.57 (step @p90 :rule cong :premises (@p89) :args (@t71)) % 0.37/0.57 (step @p91 :rule cong :premises (@p90) :args (@t72)) % 0.37/0.57 (step @p92 :rule nary_cong :premises (@p91 @p86) :args (@t73)) % 0.37/0.57 (step @p93 :rule cong :premises (@p92) :args (@t74)) % 0.37/0.57 (step @p94 :rule cong :premises (@p93) :args (@t75)) % 0.37/0.57 (step @p95 :rule beta-reduce :args ((= (_ @t77 @t70) @t75))) % 0.37/0.57 (step @p96 :rule trans :premises (@p95 @p94)) % 0.37/0.57 (step @p97 :rule beta-reduce :args ((= @t79 @t68))) % 0.37/0.57 (step @p98 :rule refl :args (@t43)) % 0.37/0.57 (step @p99 :rule nary_cong :premises (@p98 @p97) :args (@t80)) % 0.37/0.57 (step @p100 :rule cong :premises (@p99) :args (@t81)) % 0.37/0.57 (step @p101 :rule beta-reduce :args ((= (_ @t62 @t78) @t81))) % 0.37/0.57 (step @p102 :rule trans :premises (@p101 @p100)) % 0.37/0.57 (step @p103 :rule beta-reduce :args ((= (_ @t82 tptp.c) @t78))) % 0.37/0.57 (step @p104 :rule beta-reduce :args ((= @t83 @t82))) % 0.37/0.57 (step @p105 :rule ho_cong :premises (@p104 @p67)) % 0.37/0.57 (step @p106 :rule trans :premises (@p105 @p103)) % 0.37/0.57 (step @p107 :rule ho_cong :premises (@p68 @p106)) % 0.37/0.57 (step @p108 :rule trans :premises (@p107 @p102)) % 0.37/0.57 (step @p109 :rule refl :args (@t77)) % 0.37/0.57 (step @p110 :rule ho_cong :premises (@p109 @p108)) % 0.37/0.57 (step @p111 :rule trans :premises (@p110 @p96)) % 0.37/0.57 (step @p112 :rule ho_cong :premises (@p111 @p85)) % 0.37/0.57 (step @p113 :rule trans :premises (@p112 @p59)) % 0.37/0.57 (step @p114 :rule cong :premises (@p113) :args ((not (_ (_ @t77 (_ @t63 (_ @t83 tptp.c))) (_ (_ @t17 (_ @t63 tptp.b)) (_ @t63 tptp.c)))))) % 0.37/0.57 (step @p115 :rule refl :args (tptp.a)) % 0.37/0.57 (step @p116 :rule ho_cong :premises (@p4 @p115)) % 0.37/0.57 (step @p117 :rule ho_cong :premises (@p116 @p67)) % 0.37/0.57 (step @p118 :rule ho_cong :premises (@p116 @p78)) % 0.37/0.57 (step @p119 :rule ho_cong :premises (@p5 @p118)) % 0.37/0.57 (step @p120 :rule ho_cong :premises (@p119 @p117)) % 0.37/0.57 (step @p121 :rule ho_cong :premises (@p5 @p78)) % 0.37/0.57 (step @p122 :rule ho_cong :premises (@p121 @p67)) % 0.37/0.57 (step @p123 :rule ho_cong :premises (@p116 @p122)) % 0.37/0.57 (step @p124 :rule refl :args (@t55)) % 0.37/0.57 (step @p125 :rule refl :args (@t5)) % 0.37/0.57 (step @p126 :rule cong :premises (@p125 @p124) :args ((= @t5 @t55))) % 0.37/0.57 (step @p127 :rule symm :premises (@p126)) % 0.37/0.57 (step @p128 :rule eq_resolve :premises (@p125 @p127)) % 0.37/0.57 (step @p129 :rule refl :args (@t76)) % 0.37/0.57 (step @p130 :rule refl :args (@t7)) % 0.37/0.57 (step @p131 :rule cong :premises (@p130 @p129) :args ((= @t7 @t76))) % 0.37/0.57 (step @p132 :rule symm :premises (@p131)) % 0.37/0.57 (step @p133 :rule 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nary_cong :premises (@p163 @p155) :args (@t98)) % 0.37/0.57 (step @p165 :rule cong :premises (@p164) :args (@t99)) % 0.37/0.57 (step @p166 :rule refl :args (@t94)) % 0.37/0.57 (step @p167 :rule cong :premises (@p166 @p165) :args ((=> @t94 @t99))) % 0.37/0.57 (assume-push @p290 @t94) % 0.37/0.57 (step @p169 :rule skolemize :premises (@p146)) % 0.37/0.57 (step-pop @p291 :rule scope :premises (@p169)) % 0.37/0.57 (step @p170 :rule process_scope :premises (@p291) :args (@t99)) % 0.37/0.57 (step @p172 :rule eq_resolve :premises (@p170 @p167)) % 0.37/0.57 (step @p173 :rule implies_elim :premises (@p172)) % 0.37/0.57 (step @p174 :rule eq_resolve :premises (@p173 @p149)) % 0.37/0.57 (step @p175 :rule chain_m_resolution :premises (@p174 @p146) :args (@t93 @t100 (@list @t86))) % 0.37/0.57 (step @p176 :rule bool-double-not-elim :args (@t90)) % 0.37/0.57 (step @p177 :rule refl :args (@t92)) % 0.37/0.57 (step @p178 :rule nary_cong :premises (@p177 @p176) :args ((or @t92 (not @t91)))) % 0.37/0.57 (step @p179 :rule cnf_or_neg :args (@t92 0)) % 0.37/0.57 (step @p180 :rule eq_resolve :premises (@p179 @p178)) % 0.37/0.57 (step @p181 :rule reordering :premises (@p180) :args ((or @t90 @t92))) % 0.37/0.57 (step @p182 :rule chain_m_resolution :premises (@p181 @p175) :args (@t90 @t100 @t101)) % 0.37/0.57 (step @p183 :rule cnf_or_neg :args (@t92 1)) % 0.37/0.57 (step @p184 :rule chain_m_resolution :premises (@p183 @p175) :args (@t102 @t100 @t101)) % 0.37/0.57 (step @p185 :rule refl :args (@t104)) % 0.37/0.57 (step @p186 :rule bool-double-not-elim :args (@t88)) % 0.37/0.57 (step @p187 :rule refl :args (@t91)) % 0.37/0.57 (step @p188 :rule nary_cong :premises (@p187 @p186 @p185) :args ((or @t91 (not @t102) @t104))) % 0.37/0.57 (assume-push @p292 @t102) % 0.37/0.57 (assume-push @p293 @t103) % 0.37/0.57 (assume-push @p294 @t90) % 0.37/0.57 (step @p192 :rule evaluate :args ((= true false))) % 0.37/0.57 (step @p193 :rule false_intro :premises (@p184)) % 0.37/0.57 (step @p194 :rule symm :premises (@p293)) % 0.37/0.57 (step @p195 :rule cong :premises (@p194) :args (@t90)) % 0.37/0.57 (step @p196 :rule true_intro :premises (@p182)) % 0.37/0.57 (step @p197 :rule symm :premises (@p196)) % 0.37/0.57 (step @p198 :rule trans :premises (@p197 @p195 @p193)) % 0.37/0.57 (step @p199 false :rule eq_resolve :premises (@p198 @p192)) % 0.37/0.57 (step-pop @p295 :rule scope :premises (@p199)) % 0.37/0.57 (step-pop @p296 :rule scope :premises (@p295)) % 0.37/0.57 (step-pop @p297 :rule scope :premises (@p296)) % 0.37/0.57 (step @p200 :rule process_scope :premises (@p297) :args (false)) % 0.37/0.57 (assume-push @p298 @t90) % 0.37/0.57 (assume-push @p299 @t102) % 0.37/0.57 (assume-push @p300 @t103) % 0.37/0.57 (step @p207 :rule and_intro :premises (@p184 @p300 @p182)) % 0.37/0.57 (step-pop @p301 :rule scope :premises (@p207)) % 0.37/0.57 (step-pop @p302 :rule scope :premises (@p301)) % 0.37/0.57 (step-pop @p303 :rule scope :premises (@p302)) % 0.37/0.57 (step @p208 :rule process_scope :premises (@p303) :args (@t105)) % 0.37/0.57 (step @p212 :rule implies_elim :premises (@p208)) % 0.37/0.57 (step @p213 :rule resolution :premises (@p212 @p200) :args (true @t105)) % 0.37/0.57 (step @p214 :rule not_and :premises (@p213)) % 0.37/0.57 (step @p215 :rule eq_resolve :premises (@p214 @p188)) % 0.37/0.57 (step @p216 :rule reordering :premises (@p215) :args ((or @t88 @t91 @t104))) % 0.37/0.57 (step @p217 :rule chain_m_resolution :premises (@p216 @p184 @p182) :args (@t104 @t106 (@list @t88 @t90))) % 0.37/0.57 ; WARNING: add trust step for TRUST % 0.37/0.57 ; trust TRUST THEORY_LEMMA % 0.37/0.57 (step @p218 :rule trust :premises () :args ((or @t103 @t109))) % 0.37/0.57 (step @p219 :rule chain_m_resolution :premises (@p218 @p217) :args (@t109 @t100 (@list @t103))) % 0.37/0.57 (step @p220 :rule cnf_equiv_neg2 :args (@t108)) % 0.37/0.57 (step @p221 :rule cnf_equiv_pos1 :args (@t40)) % 0.37/0.57 (step @p222 :rule reordering :premises (@p221) :args ((or @t111 @t35 @t110))) % 0.37/0.57 (step @p223 :rule eq-symm :args (@t112 @t50)) % 0.37/0.57 (step @p224 :rule beta-reduce :args ((= @t113 @t50))) % 0.37/0.57 (step @p225 :rule refl :args (@t112)) % 0.37/0.57 (step @p226 :rule cong :premises (@p225 @p224) :args (@t114)) % 0.37/0.57 (step @p227 :rule trans :premises (@p226 @p223)) % 0.37/0.57 (step @p228 :rule cong :premises (@p227) :args (@t115)) % 0.37/0.57 (step @p229 :rule eq-refl :args (@t113)) % 0.37/0.57 (step @p230 :rule cong :premises (@p229) :args ((forall @t22 (= @t113 @t113)))) % 0.37/0.57 (step @p231 :rule trans :premises (@p230 @p12)) % 0.37/0.57 (step @p232 :rule refl :args (@t113)) % 0.37/0.57 (step @p233 :rule ho_cong :premises (@p157 @p17)) % 0.37/0.57 (step @p234 :rule cong :premises (@p233 @p232) :args (@t114)) % 0.37/0.57 (step @p235 :rule cong :premises (@p234) :args (@t115)) % 0.37/0.57 (step @p236 :rule trans :premises (@p235 @p231)) % 0.37/0.57 (step @p237 :rule true_elim :premises (@p236)) % 0.37/0.57 (step @p238 :rule eq_resolve :premises (@p237 @p228)) % 0.37/0.57 (step @p239 :rule eq-symm :args (@t117 @t107)) % 0.37/0.57 (step @p240 :rule refl :args (@t118)) % 0.37/0.57 (step @p241 :rule cong :premises (@p240 @p239) :args ((=> @t118 @t119))) % 0.37/0.57 (assume-push @p304 @t118) % 0.37/0.57 (step @p243 :rule instantiate :premises (@p238) :args (@t39)) % 0.37/0.57 (step-pop @p305 :rule scope :premises (@p243)) % 0.37/0.57 (step @p244 :rule process_scope :premises (@p305) :args (@t119)) % 0.37/0.57 (step @p246 :rule eq_resolve :premises (@p244 @p241)) % 0.37/0.57 (step @p247 :rule implies_elim :premises (@p246)) % 0.37/0.57 (step @p248 :rule chain_m_resolution :premises (@p247 @p238) :args (@t120 @t41 (@list @t118))) % 0.37/0.57 (step @p249 :rule cnf_equiv_pos2 :args (@t120)) % 0.37/0.57 (step @p250 :rule reordering :premises (@p249) :args ((or @t107 @t122 @t121))) % 0.37/0.57 (step @p251 :rule cnf_and_pos :args (@t35 0)) % 0.37/0.57 (step @p252 :rule reordering :premises (@p251) :args ((or @t34 @t123))) % 0.37/0.57 (step @p253 :rule cnf_and_pos :args (@t35 1)) % 0.37/0.57 (step @p254 :rule reordering :premises (@p253) :args ((or @t32 @t123))) % 0.37/0.57 (step @p255 :rule cnf_or_neg :args (@t117 0)) % 0.37/0.57 (step @p256 :rule cnf_or_neg :args (@t117 1)) % 0.37/0.57 (step @p257 :rule cnf_or_pos :args (@t34)) % 0.37/0.57 (step @p258 :rule reordering :premises (@p257) :args ((or @t31 @t33 (not @t34)))) % 0.37/0.57 (step @p259 :rule cnf_or_pos :args (@t32)) % 0.37/0.57 (step @p260 :rule reordering :premises (@p259) :args ((or @t31 @t30 (not @t32)))) % 0.37/0.57 (step @p261 :rule cnf_and_neg :args (@t116)) % 0.37/0.57 (step @p262 :rule chain_m_resolution :premises (@p261 @p260 @p258 @p256 @p255 @p254 @p252 @p250 @p248 @p222 @p34 @p220 @p219) :args (@t111 (@list false false true true false false true false false false true true) (@list @t30 @t33 @t116 @t31 @t32 @t34 @t117 @t120 @t35 @t40 @t107 @t108))) % 0.37/0.57 (step @p263 :rule cnf_equiv_pos2 :args (@t40)) % 0.37/0.57 (step @p264 :rule reordering :premises (@p263) :args ((or @t36 @t123 @t110))) % 0.37/0.57 (step @p265 :rule chain_m_resolution :premises (@p264 @p262 @p34) :args (@t123 @t106 (@list @t36 @t40))) % 0.37/0.57 (step @p266 :rule cnf_equiv_neg1 :args (@t108)) % 0.37/0.57 (step @p267 :rule reordering :premises (@p266) :args ((or @t36 @t107 @t108))) % 0.37/0.57 (step @p268 :rule chain_m_resolution :premises (@p267 @p262 @p219) :args (@t107 (@list true true) (@list @t36 @t108))) % 0.37/0.57 (step @p269 :rule cnf_equiv_pos1 :args (@t120)) % 0.37/0.57 (step @p270 :rule reordering :premises (@p269) :args ((or (not @t107) @t117 @t121))) % 0.37/0.57 (step @p271 :rule chain_m_resolution :premises (@p270 @p268 @p248) :args (@t117 (@list false false) (@list @t107 @t120))) % 0.37/0.57 (step @p272 :rule cnf_and_pos :args (@t116 0)) % 0.37/0.57 (step @p273 :rule reordering :premises (@p272) :args ((or @t33 @t124))) % 0.37/0.57 (step @p274 :rule cnf_and_pos :args (@t116 1)) % 0.37/0.57 (step @p275 :rule reordering :premises (@p274) :args ((or @t30 @t124))) % 0.37/0.57 (step @p276 :rule cnf_or_neg :args (@t34 1)) % 0.37/0.58 (step @p277 :rule cnf_or_neg :args (@t32 1)) % 0.37/0.58 (step @p278 :rule cnf_and_neg :args (@t35)) % 0.37/0.58 (step @p279 :rule chain_m_resolution :premises (@p278 @p265 @p277 @p276 @p275 @p273) :args (@t124 (@list true false false false false) (@list @t35 @t32 @t34 @t30 @t33))) % 0.37/0.58 (step @p280 :rule cnf_or_pos :args (@t117)) % 0.37/0.58 (step @p281 :rule reordering :premises (@p280) :args ((or @t31 @t116 @t122))) % 0.37/0.58 (step @p282 :rule chain_m_resolution :premises (@p281 @p279 @p271) :args (@t31 @t106 (@list @t116 @t117))) % 0.37/0.58 (step @p283 :rule cnf_or_neg :args (@t34 0)) % 0.37/0.58 (step @p284 :rule chain_m_resolution :premises (@p283 @p282) :args (@t34 @t41 @t125)) % 0.37/0.58 (step @p285 :rule cnf_or_neg :args (@t32 0)) % 0.37/0.58 (step @p286 :rule chain_m_resolution :premises (@p285 @p282) :args (@t32 @t41 @t125)) % 0.37/0.58 (step @p287 false :rule chain_m_resolution :premises (@p278 @p286 @p284 @p265) :args (false (@list false false true) (@list @t32 @t34 @t35))) % 0.37/0.58 ) % 0.37/0.58 % SZS output end Proof % 0.37/0.58 % cvc5 exiting %------------------------------------------------------------------------------