%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO364^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n018.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 09:12:30 AM UTC 2026 % Result : Theorem 6.22s 6.41s % Output : Proof 6.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO364^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n018.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Wed Jun 3 00:05:35 EDT 2026 % 0.17/0.35 % CPUTime : % 0.32/0.50 %----Proving TH0 % 6.22/6.41 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 6.22/6.41 % SZS status Theorem % 6.22/6.41 % SZS output start Proof % 6.22/6.41 ( % 6.22/6.41 (declare-sort tptp.a 0) % 6.22/6.41 (declare-const tptp.f (-> (-> tptp.a tptp.a) tptp.a tptp.a)) % 6.22/6.41 (declare-const tptp.h (-> tptp.a tptp.a)) % 6.22/6.41 (declare-const tptp.g (-> (-> tptp.a tptp.a) tptp.a tptp.a)) % 6.22/6.41 (declare-const tptp.j (-> tptp.a tptp.a)) % 6.22/6.41 (define @t1 () (_ tptp.g tptp.j)) % 6.22/6.41 (define @t2 () (@var "Xq" (-> (-> tptp.a tptp.a) Bool))) % 6.22/6.41 (define @t3 () (_ @t2 @t1)) % 6.22/6.41 (define @t4 () (_ tptp.f tptp.h)) % 6.22/6.41 (define @t5 () (_ @t2 @t4)) % 6.22/6.41 (define @t6 () (@list @t2)) % 6.22/6.41 (define @t7 () (forall @t6 (=> @t5 @t3))) % 6.22/6.41 (define @t8 () (@var "Z" tptp.a)) % 6.22/6.41 (define @t9 () (_ tptp.j @t8)) % 6.22/6.41 (define @t10 () (@var "Xq" (-> tptp.a Bool))) % 6.22/6.41 (define @t11 () (_ @t10 @t9)) % 6.22/6.41 (define @t12 () (_ tptp.h @t8)) % 6.22/6.41 (define @t13 () (_ @t10 @t12)) % 6.22/6.41 (define @t14 () (@list @t8 @t10)) % 6.22/6.41 (define @t15 () (forall @t14 (=> @t13 @t11))) % 6.22/6.41 (define @t16 () (@var "Y" tptp.a)) % 6.22/6.41 (define @t17 () (@var "X" (-> tptp.a tptp.a))) % 6.22/6.41 (define @t18 () (_ (_ tptp.g @t17) @t16)) % 6.22/6.41 (define @t19 () (_ @t10 @t18)) % 6.22/6.41 (define @t20 () (_ (_ tptp.f @t17) @t16)) % 6.22/6.41 (define @t21 () (_ @t10 @t20)) % 6.22/6.41 (define @t22 () (@list @t17 @t16 @t10)) % 6.22/6.41 (define @t23 () (forall @t22 (=> @t21 @t19))) % 6.22/6.41 (define @t24 () (and @t23 @t15)) % 6.22/6.41 (define @t25 () (=> @t24 @t7)) % 6.22/6.41 (define @t26 () (not @t25)) % 6.22/6.41 (define @t27 () (_ @t2 @t1)) % 6.22/6.41 (define @t28 () (_ @t2 @t4)) % 6.22/6.41 (define @t29 () (not @t5)) % 6.22/6.41 (define @t30 () (or @t29 @t3)) % 6.22/6.41 (define @t31 () (tptp.j @t8)) % 6.22/6.41 (define @t32 () (_ @t10 @t31)) % 6.22/6.41 (define @t33 () (tptp.h @t8)) % 6.22/6.41 (define @t34 () (_ @t10 @t33)) % 6.22/6.41 (define @t35 () (not @t13)) % 6.22/6.41 (define @t36 () (or @t35 @t11)) % 6.22/6.41 (define @t37 () (tptp.g @t17 @t16)) % 6.22/6.41 (define @t38 () (_ @t10 @t37)) % 6.22/6.41 (define @t39 () (tptp.f @t17 @t16)) % 6.22/6.41 (define @t40 () (_ @t10 @t39)) % 6.22/6.41 (define @t41 () (not @t21)) % 6.22/6.41 (define @t42 () (or @t41 @t19)) % 6.22/6.41 (define @t43 () (@quantifiers_skolemize (forall @t6 (or (not @t28) @t27)) 0)) % 6.22/6.41 (define @t44 () (_ @t43 @t1)) % 6.22/6.41 (define @t45 () (_ @t43 @t4)) % 6.22/6.41 (define @t46 () (not @t45)) % 6.22/6.41 (define @t47 () (or @t46 @t44)) % 6.22/6.41 (define @t48 () (not @t44)) % 6.22/6.41 (define @t49 () (@list true)) % 6.22/6.41 (define @t50 () (@list @t47)) % 6.22/6.41 (define @t51 () (= @t4 @t1)) % 6.22/6.41 (define @t52 () (not @t51)) % 6.22/6.41 (define @t53 () (= false true)) % 6.22/6.41 (define @t54 () (and @t45 @t51 @t48)) % 6.22/6.41 (define @t55 () (@const 0 tptp.a)) % 6.22/6.41 (define @t56 () (tptp.f tptp.h @t55)) % 6.22/6.41 (define @t57 () (= @t56 (tptp.g tptp.j @t55))) % 6.22/6.41 (define @t58 () (not @t57)) % 6.22/6.41 (define @t59 () (@purify @t4)) % 6.22/6.41 (define @t60 () (_ @t59 @t55)) % 6.22/6.41 (define @t61 () (_ @t4 @t55)) % 6.22/6.41 (define @t62 () (= @t61 @t60)) % 6.22/6.41 (define @t63 () (= @t4 @t59)) % 6.22/6.41 (define @t64 () (and @t63 @t62)) % 6.22/6.41 (define @t65 () (_ @t4 @t55)) % 6.22/6.41 (define @t66 () (= @t61 @t65)) % 6.22/6.41 (define @t67 () (@const 1 tptp.a)) % 6.22/6.41 (define @t68 () (tptp.h @t67)) % 6.22/6.41 (define @t69 () (tptp.j @t67)) % 6.22/6.41 (define @t70 () (= @t69 @t68)) % 6.22/6.41 (define @t71 () (_ tptp.h @t67)) % 6.22/6.41 (define @t72 () (= @t71 @t68)) % 6.22/6.41 (define @t73 () (= @t69 @t71)) % 6.22/6.41 (define @t74 () (= @t68 @t71)) % 6.22/6.41 (define @t75 () (not @t74)) % 6.22/6.41 (define @t76 () (or @t75 @t73)) % 6.22/6.41 (define @t77 () (forall @t14 (or (not @t34) @t32))) % 6.22/6.41 (define @t78 () (@var "BOUND_VARIABLE_217558" tptp.a)) % 6.22/6.41 (define @t79 () (lambda (@list @t78) (= @t71 @t78))) % 6.22/6.41 (define @t80 () (_ @t79 @t69)) % 6.22/6.41 (define @t81 () (_ @t79 @t68)) % 6.22/6.41 (define @t82 () (not @t81)) % 6.22/6.41 (define @t83 () (or @t82 @t80)) % 6.22/6.41 (define @t84 () (@list false)) % 6.22/6.41 (define @t85 () (= tptp.j tptp.h)) % 6.22/6.41 (define @t86 () (tptp.g tptp.h @t55)) % 6.22/6.41 (define @t87 () (_ @t59 @t55)) % 6.22/6.41 (define @t88 () (= @t87 @t86)) % 6.22/6.41 (define @t89 () (= @t56 @t87)) % 6.22/6.41 (define @t90 () (not @t89)) % 6.22/6.41 (define @t91 () (or @t90 @t88)) % 6.22/6.41 (define @t92 () (forall @t22 (or (not @t40) @t38))) % 6.22/6.41 (define @t93 () (@var "BOUND_VARIABLE_172356" tptp.a)) % 6.22/6.41 (define @t94 () (lambda (@list @t93) (= @t87 @t93))) % 6.22/6.41 (define @t95 () (@var "BOUND_VARIABLE_1004947" tptp.a)) % 6.22/6.41 (define @t96 () (lambda (@list @t95) (tptp.h @t95))) % 6.22/6.41 (define @t97 () (tptp.g @t96 @t55)) % 6.22/6.41 (define @t98 () (_ @t94 @t97)) % 6.22/6.41 (define @t99 () (tptp.f @t96 @t55)) % 6.22/6.41 (define @t100 () (_ @t94 @t99)) % 6.22/6.41 (define @t101 () (not @t100)) % 6.22/6.41 (define @t102 () (or @t101 @t98)) % 6.22/6.41 (define @t103 () (= @t60 @t86)) % 6.22/6.41 (define @t104 () (= @t56 @t60)) % 6.22/6.41 (define @t105 () (not @t104)) % 6.22/6.41 (define @t106 () (or @t105 @t103)) % 6.22/6.41 (define @t107 () (not @t103)) % 6.22/6.41 (define @t108 () (not @t85)) % 6.22/6.41 (define @t109 () (and @t107 @t103)) % 6.22/6.41 (assume @p1 @t26) % 6.22/6.41 (assume @p2 true) % 6.22/6.41 (step @p3 :rule refl :args (@t27)) % 6.22/6.41 (step @p4 :rule refl :args (@t3)) % 6.22/6.41 (step @p5 :rule cong :premises (@p4 @p3) :args ((= @t3 @t27))) % 6.22/6.41 (step @p6 :rule symm :premises (@p5)) % 6.22/6.41 (step @p7 :rule eq_resolve :premises (@p4 @p6)) % 6.22/6.41 (step @p8 :rule refl :args (@t28)) % 6.22/6.41 (step @p9 :rule refl :args (@t5)) % 6.22/6.41 (step @p10 :rule cong :premises (@p9 @p8) :args ((= @t5 @t28))) % 6.22/6.41 (step @p11 :rule symm :premises (@p10)) % 6.22/6.41 (step @p12 :rule eq_resolve :premises (@p9 @p11)) % 6.22/6.41 (step @p13 :rule cong :premises (@p12) :args (@t29)) % 6.22/6.41 (step @p14 :rule nary_cong :premises (@p13 @p7) :args (@t30)) % 6.22/6.41 (step @p15 :rule cong :premises (@p14) :args ((forall @t6 @t30))) % 6.22/6.41 (step @p16 :rule bool-impl-elim :args (@t5 @t3)) % 6.22/6.41 (step @p17 :rule cong :premises (@p16) :args (@t7)) % 6.22/6.41 (step @p18 :rule trans :premises (@p17 @p15)) % 6.22/6.41 (step @p19 :rule refl :args ((_ @t10 @t9))) % 6.22/6.41 (step @p20 :rule refl :args (@t31)) % 6.22/6.41 (step @p21 :rule cong :premises (@p20) :args (@t32)) % 6.22/6.41 (step @p22 :rule trans :premises (@p21 @p19)) % 6.22/6.41 (step @p23 :rule refl :args (@t10)) % 6.22/6.41 (step @p24 :rule ho_cong :premises (@p23 @p20)) % 6.22/6.41 (step @p25 :rule cong :premises (@p24 @p22) :args ((= (_ @t10 @t31) @t32))) % 6.22/6.41 (step @p26 :rule symm :premises (@p25)) % 6.22/6.41 (step @p27 :rule refl :args (@t11)) % 6.22/6.41 (step @p28 :rule eq_resolve :premises (@p27 @p26)) % 6.22/6.41 (step @p29 :rule refl :args (@t9)) % 6.22/6.41 (step @p30 :rule cong :premises (@p29 @p20) :args ((= @t9 @t31))) % 6.22/6.41 (step @p31 :rule symm :premises (@p30)) % 6.22/6.41 (step @p32 :rule eq_resolve :premises (@p29 @p31)) % 6.22/6.41 (step @p33 :rule ho_cong :premises (@p23 @p32)) % 6.22/6.41 (step @p34 :rule trans :premises (@p33 @p28)) % 6.22/6.41 (step @p35 :rule refl :args ((_ @t10 @t12))) % 6.22/6.41 (step @p36 :rule refl :args (@t33)) % 6.22/6.41 (step @p37 :rule cong :premises (@p36) :args (@t34)) % 6.22/6.41 (step @p38 :rule trans :premises (@p37 @p35)) % 6.22/6.41 (step @p39 :rule ho_cong :premises (@p23 @p36)) % 6.22/6.41 (step @p40 :rule cong :premises (@p39 @p38) :args ((= (_ @t10 @t33) @t34))) % 6.22/6.41 (step @p41 :rule symm :premises (@p40)) % 6.22/6.41 (step @p42 :rule refl :args (@t13)) % 6.22/6.41 (step @p43 :rule eq_resolve :premises (@p42 @p41)) % 6.22/6.41 (step @p44 :rule refl :args (@t12)) % 6.22/6.41 (step @p45 :rule cong :premises (@p44 @p36) :args ((= @t12 @t33))) % 6.22/6.41 (step @p46 :rule symm :premises (@p45)) % 6.22/6.41 (step @p47 :rule eq_resolve :premises (@p44 @p46)) % 6.22/6.41 (step @p48 :rule ho_cong :premises (@p23 @p47)) % 6.22/6.41 (step @p49 :rule trans :premises (@p48 @p43)) % 6.22/6.41 (step @p50 :rule cong :premises (@p49) :args (@t35)) % 6.22/6.41 (step @p51 :rule nary_cong :premises (@p50 @p34) :args (@t36)) % 6.22/6.41 (step @p52 :rule cong :premises (@p51) :args ((forall @t14 @t36))) % 6.22/6.41 (step @p53 :rule bool-impl-elim :args (@t13 @t11)) % 6.22/6.41 (step @p54 :rule cong :premises (@p53) :args (@t15)) % 6.22/6.41 (step @p55 :rule trans :premises (@p54 @p52)) % 6.22/6.41 (step @p56 :rule refl :args ((_ @t10 @t18))) % 6.22/6.41 (step @p57 :rule refl :args (@t37)) % 6.22/6.41 (step @p58 :rule cong :premises (@p57) :args (@t38)) % 6.22/6.41 (step @p59 :rule trans :premises (@p58 @p56)) % 6.22/6.41 (step @p60 :rule ho_cong :premises (@p23 @p57)) % 6.22/6.41 (step @p61 :rule cong :premises (@p60 @p59) :args ((= (_ @t10 @t37) @t38))) % 6.22/6.41 (step @p62 :rule symm :premises (@p61)) % 6.22/6.41 (step @p63 :rule refl :args (@t19)) % 6.22/6.41 (step @p64 :rule eq_resolve :premises (@p63 @p62)) % 6.22/6.41 (step @p65 :rule refl :args (@t18)) % 6.22/6.41 (step @p66 :rule cong :premises (@p65 @p57) :args ((= @t18 @t37))) % 6.22/6.41 (step @p67 :rule symm :premises (@p66)) % 6.22/6.41 (step @p68 :rule eq_resolve :premises (@p65 @p67)) % 6.22/6.41 (step @p69 :rule ho_cong :premises (@p23 @p68)) % 6.22/6.41 (step @p70 :rule trans :premises (@p69 @p64)) % 6.22/6.41 (step @p71 :rule refl :args ((_ @t10 @t20))) % 6.22/6.41 (step @p72 :rule refl :args (@t39)) % 6.22/6.41 (step @p73 :rule cong :premises (@p72) :args (@t40)) % 6.22/6.41 (step @p74 :rule trans :premises (@p73 @p71)) % 6.22/6.41 (step @p75 :rule ho_cong :premises (@p23 @p72)) % 6.22/6.41 (step @p76 :rule cong :premises (@p75 @p74) :args ((= (_ @t10 @t39) @t40))) % 6.22/6.41 (step @p77 :rule symm :premises (@p76)) % 6.22/6.41 (step @p78 :rule refl :args (@t21)) % 6.22/6.41 (step @p79 :rule eq_resolve :premises (@p78 @p77)) % 6.22/6.41 (step @p80 :rule refl :args (@t20)) % 6.22/6.41 (step @p81 :rule cong :premises (@p80 @p72) :args ((= @t20 @t39))) % 6.22/6.41 (step @p82 :rule symm :premises (@p81)) % 6.22/6.41 (step @p83 :rule eq_resolve :premises (@p80 @p82)) % 6.22/6.41 (step @p84 :rule ho_cong :premises (@p23 @p83)) % 6.22/6.41 (step @p85 :rule trans :premises (@p84 @p79)) % 6.22/6.41 (step @p86 :rule cong :premises (@p85) :args (@t41)) % 6.22/6.41 (step @p87 :rule nary_cong :premises (@p86 @p70) :args (@t42)) % 6.22/6.41 (step @p88 :rule cong :premises (@p87) :args ((forall @t22 @t42))) % 6.22/6.41 (step @p89 :rule bool-impl-elim :args (@t21 @t19)) % 6.22/6.41 (step @p90 :rule cong :premises (@p89) :args (@t23)) % 6.22/6.41 (step @p91 :rule trans :premises (@p90 @p88)) % 6.22/6.41 (step @p92 :rule nary_cong :premises (@p91 @p55) :args (@t24)) % 6.22/6.41 (step @p93 :rule cong :premises (@p92 @p18) :args (@t25)) % 6.22/6.41 (step @p94 :rule cong :premises (@p93) :args (@t26)) % 6.22/6.41 (step @p95 :rule eq_resolve :premises (@p1 @p94)) % 6.22/6.41 (step @p96 :rule not_implies_elim2 :premises (@p95)) % 6.22/6.41 (step @p97 :rule skolemize :premises (@p96)) % 6.22/6.41 (step @p98 :rule cnf_or_neg :args (@t47 1)) % 6.22/6.41 (step @p99 :rule chain_m_resolution :premises (@p98 @p97) :args (@t48 @t49 @t50)) % 6.22/6.41 (step @p100 :rule bool-double-not-elim :args (@t45)) % 6.22/6.41 (step @p101 :rule refl :args (@t47)) % 6.22/6.41 (step @p102 :rule nary_cong :premises (@p101 @p100) :args ((or @t47 (not @t46)))) % 6.22/6.41 (step @p103 :rule cnf_or_neg :args (@t47 0)) % 6.22/6.41 (step @p104 :rule eq_resolve :premises (@p103 @p102)) % 6.22/6.41 (step @p105 :rule reordering :premises (@p104) :args ((or @t45 @t47))) % 6.22/6.41 (step @p106 :rule chain_m_resolution :premises (@p105 @p97) :args (@t45 @t49 @t50)) % 6.22/6.41 (step @p107 :rule refl :args (@t52)) % 6.22/6.41 (step @p108 :rule bool-double-not-elim :args (@t44)) % 6.22/6.41 (step @p109 :rule refl :args (@t46)) % 6.22/6.41 (step @p110 :rule nary_cong :premises (@p109 @p108 @p107) :args ((or @t46 (not @t48) @t52))) % 6.22/6.41 (assume-push @p301 @t45) % 6.22/6.41 (assume-push @p302 @t51) % 6.22/6.41 (assume-push @p303 @t48) % 6.22/6.41 (step @p114 :rule evaluate :args (@t53)) % 6.22/6.41 (step @p115 :rule true_intro :premises (@p106)) % 6.22/6.41 (step @p116 :rule symm :premises (@p302)) % 6.22/6.41 (step @p117 :rule cong :premises (@p116) :args (@t44)) % 6.22/6.41 (step @p118 :rule false_intro :premises (@p99)) % 6.22/6.41 (step @p119 :rule symm :premises (@p118)) % 6.22/6.41 (step @p120 :rule trans :premises (@p119 @p117 @p115)) % 6.22/6.41 (step @p121 false :rule eq_resolve :premises (@p120 @p114)) % 6.22/6.41 (step-pop @p304 :rule scope :premises (@p121)) % 6.22/6.41 (step-pop @p305 :rule scope :premises (@p304)) % 6.22/6.41 (step-pop @p306 :rule scope :premises (@p305)) % 6.22/6.41 (step @p122 :rule process_scope :premises (@p306) :args (false)) % 6.22/6.41 (assume-push @p307 @t45) % 6.22/6.41 (assume-push @p308 @t48) % 6.22/6.41 (assume-push @p309 @t51) % 6.22/6.41 (step @p129 :rule and_intro :premises (@p106 @p309 @p99)) % 6.22/6.41 (step-pop @p310 :rule scope :premises (@p129)) % 6.22/6.41 (step-pop @p311 :rule scope :premises (@p310)) % 6.22/6.41 (step-pop @p312 :rule scope :premises (@p311)) % 6.22/6.41 (step @p130 :rule process_scope :premises (@p312) :args (@t54)) % 6.22/6.41 (step @p134 :rule implies_elim :premises (@p130)) % 6.22/6.41 (step @p135 :rule resolution :premises (@p134 @p122) :args (true @t54)) % 6.22/6.41 (step @p136 :rule not_and :premises (@p135)) % 6.22/6.41 (step @p137 :rule eq_resolve :premises (@p136 @p110)) % 6.22/6.41 (step @p138 :rule chain_m_resolution :premises (@p137 @p106 @p99) :args (@t52 (@list false true) (@list @t45 @t44))) % 6.22/6.41 ; WARNING: add trust step for TRUST % 6.22/6.41 ; trust TRUST THEORY_LEMMA % 6.22/6.41 (step @p139 :rule trust :premises () :args ((or @t51 @t58))) % 6.22/6.41 (step @p140 :rule chain_m_resolution :premises (@p139 @p138) :args (@t58 @t49 (@list @t51))) % 6.22/6.41 (step @p141 :rule refl :args (@t60)) % 6.22/6.41 (step @p142 :rule refl :args (@t56)) % 6.22/6.41 (step @p143 :rule refl :args (@t61)) % 6.22/6.41 (step @p144 :rule cong :premises (@p143 @p142) :args ((= @t61 @t56))) % 6.22/6.41 (step @p145 :rule symm :premises (@p144)) % 6.22/6.41 (step @p146 :rule eq_resolve :premises (@p143 @p145)) % 6.22/6.41 (step @p147 :rule cong :premises (@p146 @p141) :args (@t62)) % 6.22/6.41 (step @p148 :rule refl :args (@t63)) % 6.22/6.41 (step @p149 :rule nary_cong :premises (@p148 @p147) :args (@t64)) % 6.22/6.41 (step @p150 :rule eq-symm :args (@t60 @t61)) % 6.22/6.41 (step @p151 :rule eq-symm :args (@t59 @t4)) % 6.22/6.41 (step @p152 :rule nary_cong :premises (@p151 @p150) :args ((and (= @t59 @t4) (= @t60 @t61)))) % 6.22/6.41 (step @p153 :rule trans :premises (@p152 @p149)) % 6.22/6.41 (step @p154 :rule evaluate :args ((and true true))) % 6.22/6.41 (step @p155 :rule eq-refl :args (@t61)) % 6.22/6.41 (step @p156 :rule refl :args (@t65)) % 6.22/6.41 (step @p157 :rule refl :args (@t61)) % 6.22/6.41 (step @p158 :rule cong :premises (@p157 @p156) :args (@t66)) % 6.22/6.41 (step @p159 :rule trans :premises (@p158 @p155)) % 6.22/6.41 (step @p160 :rule eq-refl :args (@t4)) % 6.22/6.41 (step @p161 :rule nary_cong :premises (@p160 @p159) :args ((and (= @t4 @t4) @t66))) % 6.22/6.41 (step @p162 :rule trans :premises (@p161 @p154)) % 6.22/6.41 (step @p163 :rule refl :args (@t55)) % 6.22/6.41 (step @p164 :rule skolem_intro :args (@t59)) % 6.22/6.41 (step @p165 :rule ho_cong :premises (@p164 @p163)) % 6.22/6.41 (step @p166 :rule cong :premises (@p157 @p165) :args (@t62)) % 6.22/6.41 (step @p167 :rule refl :args (@t4)) % 6.22/6.41 (step @p168 :rule cong :premises (@p167 @p164) :args (@t63)) % 6.22/6.41 (step @p169 :rule nary_cong :premises (@p168 @p166) :args (@t64)) % 6.22/6.41 (step @p170 :rule trans :premises (@p152 @p169 @p162)) % 6.22/6.41 (step @p171 :rule true_elim :premises (@p170)) % 6.22/6.41 (step @p172 :rule eq_resolve :premises (@p171 @p153)) % 6.22/6.41 (step @p173 :rule and_elim :premises (@p172) :args (1)) % 6.22/6.41 (step @p174 :rule not_implies_elim1 :premises (@p95)) % 6.22/6.41 (step @p175 :rule and_elim :premises (@p174) :args (1)) % 6.22/6.41 (step @p176 :rule aci_norm :args ((= (or false @t70) @t70))) % 6.22/6.41 (step @p177 :rule refl :args (@t68)) % 6.22/6.41 (step @p178 :rule refl :args (@t71)) % 6.22/6.41 (step @p179 :rule cong :premises (@p178 @p177) :args (@t72)) % 6.22/6.41 (step @p180 :rule symm :premises (@p179)) % 6.22/6.41 (step @p181 :rule eq_resolve :premises (@p178 @p180)) % 6.22/6.41 (step @p182 :rule refl :args (@t69)) % 6.22/6.41 (step @p183 :rule cong :premises (@p182 @p181) :args (@t73)) % 6.22/6.41 (step @p184 :rule evaluate :args ((not true))) % 6.22/6.41 (step @p185 :rule eq-refl :args (@t68)) % 6.22/6.41 (step @p186 :rule refl :args (@t68)) % 6.22/6.41 (step @p187 :rule cong :premises (@p186 @p181) :args (@t74)) % 6.22/6.41 (step @p188 :rule trans :premises (@p187 @p185)) % 6.22/6.41 (step @p189 :rule cong :premises (@p188) :args (@t75)) % 6.22/6.41 (step @p190 :rule trans :premises (@p189 @p184)) % 6.22/6.41 (step @p191 :rule nary_cong :premises (@p190 @p183) :args (@t76)) % 6.22/6.41 (step @p192 :rule trans :premises (@p191 @p176)) % 6.22/6.41 (step @p193 :rule refl :args (@t77)) % 6.22/6.41 (step @p194 :rule cong :premises (@p193 @p192) :args ((=> @t77 @t76))) % 6.22/6.41 (step @p195 :rule eq-symm :args (@t71 @t69)) % 6.22/6.41 (step @p196 :rule beta-reduce :args ((= @t80 (= @t71 @t69)))) % 6.22/6.41 (step @p197 :rule trans :premises (@p196 @p195)) % 6.22/6.41 (step @p198 :rule eq-symm :args (@t71 @t68)) % 6.22/6.41 (step @p199 :rule beta-reduce :args ((= @t81 @t72))) % 6.22/6.41 (step @p200 :rule trans :premises (@p199 @p198)) % 6.22/6.41 (step @p201 :rule cong :premises (@p200) :args (@t82)) % 6.22/6.41 (step @p202 :rule nary_cong :premises (@p201 @p197) :args (@t83)) % 6.22/6.41 (step @p203 :rule cong :premises (@p193 @p202) :args ((=> @t77 @t83))) % 6.22/6.41 (assume-push @p313 @t77) % 6.22/6.41 (step @p205 :rule instantiate :premises (@p175) :args ((@list @t67 @t79))) % 6.22/6.41 (step-pop @p314 :rule scope :premises (@p205)) % 6.22/6.41 (step @p206 :rule process_scope :premises (@p314) :args (@t83)) % 6.22/6.41 (step @p208 :rule eq_resolve :premises (@p206 @p203)) % 6.22/6.41 (step @p209 :rule eq_resolve :premises (@p208 @p194)) % 6.22/6.41 (step @p210 :rule implies_elim :premises (@p209)) % 6.22/6.41 (step @p211 :rule chain_m_resolution :premises (@p210 @p175) :args (@t70 @t84 (@list @t77))) % 6.22/6.41 ; trust TRUST THEORY_LEMMA % 6.22/6.41 (step @p212 :rule trust :premises () :args ((or @t85 (not @t70)))) % 6.22/6.41 (step @p213 :rule chain_m_resolution :premises (@p212 @p211) :args (@t85 @t84 (@list @t70))) % 6.22/6.41 (step @p214 :rule and_elim :premises (@p174) :args (0)) % 6.22/6.41 (step @p215 :rule refl :args (@t86)) % 6.22/6.41 (step @p216 :rule cong :premises (@p156 @p157) :args ((= @t65 @t61))) % 6.22/6.41 (step @p217 :rule trans :premises (@p216 @p155)) % 6.22/6.41 (step @p218 :rule ho_cong :premises (@p164 @p163)) % 6.22/6.41 (step @p219 :rule cong :premises (@p165 @p218) :args ((= @t60 @t87))) % 6.22/6.41 (step @p220 :rule eq-symm :args (@t87 @t60)) % 6.22/6.41 (step @p221 :rule trans :premises (@p220 @p219 @p217)) % 6.22/6.41 (step @p222 :rule true_elim :premises (@p221)) % 6.22/6.41 (step @p223 :rule cong :premises (@p222 @p215) :args (@t88)) % 6.22/6.41 (step @p224 :rule refl :args (@t56)) % 6.22/6.41 (step @p225 :rule cong :premises (@p224 @p222) :args (@t89)) % 6.22/6.41 (step @p226 :rule cong :premises (@p225) :args (@t90)) % 6.22/6.41 (step @p227 :rule nary_cong :premises (@p226 @p223) :args (@t91)) % 6.22/6.41 (step @p228 :rule refl :args (@t92)) % 6.22/6.41 (step @p229 :rule cong :premises (@p228 @p227) :args ((=> @t92 @t91))) % 6.22/6.41 (step @p230 :rule beta-reduce :args ((= (_ @t94 @t86) @t88))) % 6.22/6.41 (step @p231 :rule lambda-elim :args ((= @t96 tptp.h))) % 6.22/6.41 (step @p232 :rule cong :premises (@p231 @p163) :args (@t97)) % 6.22/6.41 (step @p233 :rule cong :premises (@p232) :args (@t98)) % 6.22/6.41 (step @p234 :rule trans :premises (@p233 @p230)) % 6.22/6.41 (step @p235 :rule eq-symm :args (@t87 @t56)) % 6.22/6.41 (step @p236 :rule beta-reduce :args ((= (_ @t94 @t56) (= @t87 @t56)))) % 6.22/6.41 (step @p237 :rule trans :premises (@p236 @p235)) % 6.22/6.41 (step @p238 :rule cong :premises (@p231 @p163) :args (@t99)) % 6.22/6.41 (step @p239 :rule cong :premises (@p238) :args (@t100)) % 6.22/6.41 (step @p240 :rule trans :premises (@p239 @p237)) % 6.22/6.41 (step @p241 :rule cong :premises (@p240) :args (@t101)) % 6.22/6.41 (step @p242 :rule nary_cong :premises (@p241 @p234) :args (@t102)) % 6.22/6.41 (step @p243 :rule cong :premises (@p228 @p242) :args ((=> @t92 @t102))) % 6.22/6.41 (assume-push @p315 @t92) % 6.22/6.41 (step @p245 :rule instantiate :premises (@p214) :args ((@list @t96 @t55 @t94))) % 6.22/6.41 (step-pop @p316 :rule scope :premises (@p245)) % 6.22/6.41 (step @p246 :rule process_scope :premises (@p316) :args (@t102)) % 6.22/6.41 (step @p248 :rule eq_resolve :premises (@p246 @p243)) % 6.22/6.41 (step @p249 :rule eq_resolve :premises (@p248 @p229)) % 6.22/6.41 (step @p250 :rule implies_elim :premises (@p249)) % 6.22/6.41 (step @p251 :rule chain_m_resolution :premises (@p250 @p214) :args (@t106 @t84 (@list @t92))) % 6.22/6.41 (step @p252 :rule cnf_or_pos :args (@t106)) % 6.22/6.41 (step @p253 :rule reordering :premises (@p252) :args ((or @t105 @t103 (not @t106)))) % 6.22/6.41 (step @p254 :rule chain_m_resolution :premises (@p253 @p173 @p251) :args (@t103 (@list false false) (@list @t104 @t106))) % 6.22/6.41 (step @p255 :rule refl :args (@t107)) % 6.22/6.41 (step @p256 :rule refl :args (@t105)) % 6.22/6.41 (step @p257 :rule bool-double-not-elim :args (@t57)) % 6.22/6.41 (step @p258 :rule refl :args (@t108)) % 6.22/6.41 (step @p259 :rule nary_cong :premises (@p258 @p257 @p256 @p255) :args ((or @t108 (not @t58) @t105 @t107))) % 6.22/6.41 (assume-push @p317 @t107) % 6.22/6.41 (assume-push @p318 @t103) % 6.22/6.41 (step @p114 :rule evaluate :args (@t53)) % 6.22/6.41 (step @p262 :rule true_intro :premises (@p254)) % 6.22/6.41 (step @p263 :rule false_intro :premises (@p317)) % 6.22/6.41 (step @p264 :rule symm :premises (@p263)) % 6.22/6.41 (step @p265 :rule trans :premises (@p264 @p262)) % 6.22/6.41 (step @p266 false :rule eq_resolve :premises (@p265 @p114)) % 6.22/6.41 (step-pop @p319 :rule scope :premises (@p266)) % 6.22/6.41 (step-pop @p320 :rule scope :premises (@p319)) % 6.22/6.41 (step @p267 :rule process_scope :premises (@p320) :args (false)) % 6.22/6.41 (assume-push @p321 @t85) % 6.22/6.41 (assume-push @p322 @t58) % 6.22/6.41 (assume-push @p323 @t104) % 6.22/6.41 (assume-push @p324 @t103) % 6.22/6.41 (assume-push @p325 @t104) % 6.22/6.41 (assume-push @p326 @t58) % 6.22/6.41 (assume-push @p327 @t85) % 6.22/6.41 (step @p277 :rule false_intro :premises (@p322)) % 6.22/6.41 (step @p278 :rule symm :premises (@p213)) % 6.22/6.41 (step @p279 :rule cong :premises (@p278 @p163) :args (@t86)) % 6.22/6.41 (step @p280 :rule symm :premises (@p173)) % 6.22/6.41 (step @p281 :rule cong :premises (@p280 @p279) :args (@t103)) % 6.22/6.41 (step @p282 :rule trans :premises (@p281 @p277)) % 6.22/6.41 (step @p283 :rule false_elim :premises (@p282)) % 6.22/6.41 (step-pop @p328 :rule scope :premises (@p283)) % 6.22/6.41 (step-pop @p329 :rule scope :premises (@p328)) % 6.22/6.41 (step-pop @p330 :rule scope :premises (@p329)) % 6.22/6.41 (step @p284 :rule process_scope :premises (@p330) :args (@t107)) % 6.22/6.41 (step @p288 :rule and_intro :premises (@p173 @p322 @p213)) % 6.22/6.41 (step @p289 :rule modus_ponens :premises (@p288 @p284)) % 6.22/6.41 (step @p290 :rule and_intro :premises (@p289 @p254)) % 6.22/6.41 (step-pop @p331 :rule scope :premises (@p290)) % 6.22/6.41 (step-pop @p332 :rule scope :premises (@p331)) % 6.22/6.41 (step-pop @p333 :rule scope :premises (@p332)) % 6.22/6.41 (step-pop @p334 :rule scope :premises (@p333)) % 6.22/6.41 (step @p291 :rule process_scope :premises (@p334) :args (@t109)) % 6.22/6.41 (step @p296 :rule implies_elim :premises (@p291)) % 6.22/6.41 (step @p297 :rule resolution :premises (@p296 @p267) :args (true @t109)) % 6.22/6.41 (step @p298 :rule not_and :premises (@p297)) % 6.22/6.41 (step @p299 :rule eq_resolve :premises (@p298 @p259)) % 6.22/6.41 (step @p300 false :rule chain_m_resolution :premises (@p299 @p254 @p213 @p173 @p140) :args (false (@list false false false true) (@list @t103 @t85 @t104 @t57))) % 6.22/6.41 ) % 6.22/6.41 % SZS output end Proof % 6.22/6.41 % cvc5 exiting %------------------------------------------------------------------------------