%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU896^5 : 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 : n021.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 08:53:29 AM UTC 2026 % Result : Theorem 0.38s 0.57s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU896^5 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n021.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 17:59:05 EDT 2026 % 0.18/0.35 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.38/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.57 % SZS status Theorem % 0.38/0.57 % SZS output start Proof % 0.38/0.57 ( % 0.38/0.57 (declare-sort tptp.b 0) % 0.38/0.57 (declare-sort tptp.a 0) % 0.38/0.57 (declare-const tptp.x tptp.b) % 0.38/0.57 (declare-const tptp.g (-> tptp.b tptp.a)) % 0.38/0.57 (declare-const tptp.y tptp.b) % 0.38/0.57 (define @t1 () (_ tptp.g tptp.y)) % 0.38/0.57 (define @t2 () (@var "Xv" tptp.a)) % 0.38/0.57 (define @t3 () (_ tptp.g tptp.x)) % 0.38/0.57 (define @t4 () (@list @t2)) % 0.38/0.57 (define @t5 () (lambda @t4 (or (= @t2 @t3) (= @t2 @t1)))) % 0.38/0.57 (define @t6 () (@var "Xt" tptp.b)) % 0.38/0.57 (define @t7 () (_ tptp.g @t6)) % 0.38/0.57 (define @t8 () (@var "Xz" tptp.a)) % 0.38/0.57 (define @t9 () (= @t8 @t7)) % 0.38/0.57 (define @t10 () (or (= @t6 tptp.x) (= @t6 tptp.y))) % 0.38/0.57 (define @t11 () (and @t10 @t9)) % 0.38/0.57 (define @t12 () (@list @t6)) % 0.38/0.57 (define @t13 () (exists @t12 @t11)) % 0.38/0.57 (define @t14 () (@list @t8)) % 0.38/0.57 (define @t15 () (lambda @t14 @t13)) % 0.38/0.57 (define @t16 () (= @t15 @t5)) % 0.38/0.57 (define @t17 () (not @t16)) % 0.38/0.57 (define @t18 () (tptp.g tptp.y)) % 0.38/0.57 (define @t19 () (@purify @t18)) % 0.38/0.57 (define @t20 () (@purify @t1)) % 0.38/0.57 (define @t21 () (@const 0 tptp.a)) % 0.38/0.57 (define @t22 () (= @t20 @t21)) % 0.38/0.57 (define @t23 () (@purify @t3)) % 0.38/0.57 (define @t24 () (= @t23 @t21)) % 0.38/0.57 (define @t25 () (or @t24 @t22)) % 0.38/0.57 (define @t26 () (= @t2 @t20)) % 0.38/0.57 (define @t27 () (= @t2 @t23)) % 0.38/0.57 (define @t28 () (or @t27 @t26)) % 0.38/0.57 (define @t29 () (lambda @t4 @t28)) % 0.38/0.57 (define @t30 () (@purify @t29)) % 0.38/0.57 (define @t31 () (= @t8 @t19)) % 0.38/0.57 (define @t32 () (not @t31)) % 0.38/0.57 (define @t33 () (tptp.g tptp.x)) % 0.38/0.57 (define @t34 () (@purify @t33)) % 0.38/0.57 (define @t35 () (= @t8 @t34)) % 0.38/0.57 (define @t36 () (not @t35)) % 0.38/0.57 (define @t37 () (and @t36 @t32)) % 0.38/0.57 (define @t38 () (not @t37)) % 0.38/0.57 (define @t39 () (lambda @t14 @t38)) % 0.38/0.57 (define @t40 () (@purify @t39)) % 0.38/0.57 (define @t41 () (not (= @t8 @t18))) % 0.38/0.57 (define @t42 () (not (= @t8 @t33))) % 0.38/0.57 (define @t43 () (lambda @t14 (not (and @t42 @t41)))) % 0.38/0.57 (define @t44 () (= @t5 @t43)) % 0.38/0.57 (define @t45 () (not (= tptp.y tptp.y))) % 0.38/0.57 (define @t46 () (or @t45 @t41)) % 0.38/0.57 (define @t47 () (@var "BOUND_VARIABLE_7469" tptp.b)) % 0.38/0.57 (define @t48 () (not (= @t8 (tptp.g @t47)))) % 0.38/0.57 (define @t49 () (not (= tptp.y @t47))) % 0.38/0.57 (define @t50 () (@list @t47)) % 0.38/0.57 (define @t51 () (or @t49 @t49 @t48)) % 0.38/0.57 (define @t52 () (or @t49 @t48)) % 0.38/0.57 (define @t53 () (forall @t50 @t52)) % 0.38/0.57 (define @t54 () (not (= tptp.x tptp.x))) % 0.38/0.57 (define @t55 () (or @t54 @t42)) % 0.38/0.57 (define @t56 () (@var "BOUND_VARIABLE_7459" tptp.b)) % 0.38/0.57 (define @t57 () (not (= @t8 (tptp.g @t56)))) % 0.38/0.57 (define @t58 () (not (= tptp.x @t56))) % 0.38/0.57 (define @t59 () (@list @t56)) % 0.38/0.57 (define @t60 () (or @t58 @t58 @t57)) % 0.38/0.57 (define @t61 () (or @t58 @t57)) % 0.38/0.57 (define @t62 () (forall @t59 @t61)) % 0.38/0.57 (define @t63 () (tptp.g @t6)) % 0.38/0.57 (define @t64 () (not (= @t8 @t63))) % 0.38/0.57 (define @t65 () (= tptp.y @t6)) % 0.38/0.57 (define @t66 () (not @t65)) % 0.38/0.57 (define @t67 () (or @t66 @t64)) % 0.38/0.57 (define @t68 () (forall @t12 @t67)) % 0.38/0.57 (define @t69 () (@list @t6)) % 0.38/0.57 (define @t70 () (= tptp.x @t6)) % 0.38/0.57 (define @t71 () (not @t70)) % 0.38/0.57 (define @t72 () (or @t71 @t64)) % 0.38/0.57 (define @t73 () (forall @t12 @t72)) % 0.38/0.57 (define @t74 () (and @t73 @t68)) % 0.38/0.57 (define @t75 () (and @t71 @t66)) % 0.38/0.57 (define @t76 () (not @t9)) % 0.38/0.57 (define @t77 () (or @t75 @t76)) % 0.38/0.57 (define @t78 () (or @t70 @t65)) % 0.38/0.57 (define @t79 () (and @t78 @t9)) % 0.38/0.57 (define @t80 () (forall @t12 (not @t79))) % 0.38/0.58 (define @t81 () (not @t80)) % 0.38/0.58 (define @t82 () (= @t19 @t21)) % 0.38/0.58 (define @t83 () (not @t82)) % 0.38/0.58 (define @t84 () (= @t34 @t21)) % 0.38/0.58 (define @t85 () (not @t84)) % 0.38/0.58 (define @t86 () (and @t85 @t83)) % 0.38/0.58 (define @t87 () (not @t86)) % 0.38/0.58 (define @t88 () (or (= @t3 @t21) (= @t1 @t21))) % 0.38/0.58 (define @t89 () (or (= @t21 @t3) (= @t21 @t1))) % 0.38/0.58 (define @t90 () (_ @t5 @t21)) % 0.38/0.58 (define @t91 () (_ @t30 @t21)) % 0.38/0.58 (define @t92 () (not (and (not (= @t33 @t21)) (not (= @t18 @t21))))) % 0.38/0.58 (define @t93 () (not (= @t21 @t18))) % 0.38/0.58 (define @t94 () (not (= @t21 @t33))) % 0.38/0.58 (define @t95 () (and @t94 @t93)) % 0.38/0.58 (define @t96 () (not @t95)) % 0.38/0.58 (define @t97 () (_ @t43 @t21)) % 0.38/0.58 (define @t98 () (_ @t40 @t21)) % 0.38/0.58 (define @t99 () (= @t98 @t91)) % 0.38/0.58 (define @t100 () (not @t99)) % 0.38/0.58 (define @t101 () (= @t40 @t30)) % 0.38/0.58 (define @t102 () (or @t101 @t100)) % 0.38/0.58 (define @t103 () (= @t25 @t87)) % 0.38/0.58 (define @t104 () (not @t25)) % 0.38/0.58 (define @t105 () (= @t18 @t19)) % 0.38/0.58 (define @t106 () (= @t18 @t20)) % 0.38/0.58 (define @t107 () (and @t105 @t106 @t22)) % 0.38/0.58 (define @t108 () (not @t22)) % 0.38/0.58 (define @t109 () (not @t106)) % 0.38/0.58 (define @t110 () (not @t105)) % 0.38/0.58 (define @t111 () (@list false false true false true false)) % 0.38/0.58 (define @t112 () (= @t33 @t34)) % 0.38/0.58 (define @t113 () (= @t33 @t23)) % 0.38/0.58 (define @t114 () (and @t112 @t113 @t24)) % 0.38/0.58 (define @t115 () (not @t24)) % 0.38/0.58 (define @t116 () (not @t113)) % 0.38/0.58 (define @t117 () (not @t112)) % 0.38/0.58 (define @t118 () (@list true true)) % 0.38/0.58 (define @t119 () (and @t112 @t113 @t115)) % 0.38/0.58 (define @t120 () (and @t105 @t106 @t108)) % 0.38/0.58 (assume @p1 @t17) % 0.38/0.58 (assume @p2 true) % 0.38/0.58 (step @p3 :rule skolem_intro :args (@t19)) % 0.38/0.58 (step @p4 :rule symm :premises (@p3)) % 0.38/0.58 (step @p5 :rule refl :args (@t20)) % 0.38/0.58 (step @p6 :rule refl :args (@t18)) % 0.38/0.58 (step @p7 :rule refl :args (@t1)) % 0.38/0.58 (step @p8 :rule cong :premises (@p7 @p6) :args ((= @t1 @t18))) % 0.38/0.58 (step @p9 :rule symm :premises (@p8)) % 0.38/0.58 (step @p10 :rule eq_resolve :premises (@p7 @p9)) % 0.38/0.58 (step @p11 :rule cong :premises (@p10 @p5) :args ((= @t1 @t20))) % 0.38/0.58 (step @p12 :rule eq-symm :args (@t20 @t1)) % 0.38/0.58 (step @p13 :rule trans :premises (@p12 @p11)) % 0.38/0.58 (step @p14 :rule skolem_intro :args (@t20)) % 0.38/0.58 (step @p15 :rule eq_resolve :premises (@p14 @p13)) % 0.38/0.58 (step @p16 :rule cnf_or_neg :args (@t25 1)) % 0.38/0.58 (step @p17 :rule eq-symm :args (@t30 @t40)) % 0.38/0.58 (step @p18 :rule eq-refl :args (@t43)) % 0.38/0.58 (step @p19 :rule refl :args (@t8)) % 0.38/0.58 (step @p20 :rule cong :premises (@p19 @p3) :args (@t31)) % 0.38/0.58 (step @p21 :rule cong :premises (@p20) :args (@t32)) % 0.38/0.58 (step @p22 :rule skolem_intro :args (@t34)) % 0.38/0.58 (step @p23 :rule cong :premises (@p19 @p22) :args (@t35)) % 0.38/0.58 (step @p24 :rule cong :premises (@p23) :args (@t36)) % 0.38/0.58 (step @p25 :rule nary_cong :premises (@p24 @p21) :args (@t37)) % 0.38/0.58 (step @p26 :rule cong :premises (@p25) :args (@t38)) % 0.38/0.58 (step @p27 :rule cong :premises (@p26) :args (@t39)) % 0.38/0.58 (step @p28 :rule skolem_intro :args (@t40)) % 0.38/0.58 (step @p29 :rule trans :premises (@p28 @p27)) % 0.38/0.58 (step @p30 :rule refl :args (@t43)) % 0.38/0.58 (step @p31 :rule cong :premises (@p30 @p29) :args ((= @t43 @t40))) % 0.38/0.58 (step @p32 :rule trans :premises (@p31 @p18)) % 0.38/0.58 (step @p33 :rule true_elim :premises (@p32)) % 0.38/0.58 (step @p34 :rule eq-refl :args (@t5)) % 0.38/0.58 (step @p35 :rule refl :args (@t2)) % 0.38/0.58 (step @p36 :rule cong :premises (@p35 @p14) :args (@t26)) % 0.38/0.58 (step @p37 :rule skolem_intro :args (@t23)) % 0.38/0.58 (step @p38 :rule cong :premises (@p35 @p37) :args (@t27)) % 0.38/0.58 (step @p39 :rule nary_cong :premises (@p38 @p36) :args (@t28)) % 0.38/0.58 (step @p40 :rule cong :premises (@p39) :args (@t29)) % 0.38/0.58 (step @p41 :rule skolem_intro :args (@t30)) % 0.38/0.58 (step @p42 :rule trans :premises (@p41 @p40)) % 0.38/0.58 (step @p43 :rule refl :args (@t5)) % 0.38/0.58 (step @p44 :rule cong :premises (@p43 @p42) :args ((= @t5 @t30))) % 0.38/0.58 (step @p45 :rule trans :premises (@p44 @p34)) % 0.38/0.58 (step @p46 :rule true_elim :premises (@p45)) % 0.38/0.58 (step @p47 :rule cong :premises (@p46 @p33) :args (@t44)) % 0.38/0.58 (step @p48 :rule trans :premises (@p47 @p17)) % 0.38/0.58 (step @p49 :rule cong :premises (@p48) :args ((not @t44))) % 0.38/0.58 (step @p50 :rule eq-symm :args (@t43 @t5)) % 0.38/0.58 (step @p51 :rule aci_norm :args ((= (or false @t41) @t41))) % 0.38/0.58 (step @p52 :rule refl :args (@t41)) % 0.38/0.58 (step @p53 :rule evaluate :args ((not true))) % 0.38/0.58 (step @p54 :rule eq-refl :args (tptp.y)) % 0.38/0.58 (step @p55 :rule cong :premises (@p54) :args (@t45)) % 0.38/0.58 (step @p56 :rule trans :premises (@p55 @p53)) % 0.38/0.58 (step @p57 :rule nary_cong :premises (@p56 @p52) :args (@t46)) % 0.38/0.58 (step @p58 :rule trans :premises (@p57 @p51)) % 0.38/0.58 (step @p59 :rule quant-var-elim-eq :args ((= (forall @t50 (or (not (= @t47 tptp.y)) @t49 @t48)) @t46))) % 0.38/0.58 (step @p60 :rule refl :args (@t48)) % 0.38/0.58 (step @p61 :rule refl :args (@t49)) % 0.38/0.58 (step @p62 :rule eq-symm :args (tptp.y @t47)) % 0.38/0.58 (step @p63 :rule cong :premises (@p62) :args (@t49)) % 0.38/0.58 (step @p64 :rule nary_cong :premises (@p63 @p61 @p60) :args (@t51)) % 0.38/0.58 (step @p65 :rule aci_norm :args ((= @t52 @t51))) % 0.38/0.58 (step @p66 :rule trans :premises (@p65 @p64)) % 0.38/0.58 (step @p67 :rule cong :premises (@p66) :args (@t53)) % 0.38/0.58 (step @p68 :rule trans :premises (@p67 @p59)) % 0.38/0.58 (step @p69 :rule trans :premises (@p68 @p58)) % 0.38/0.58 (step @p70 :rule aci_norm :args ((= (or false @t42) @t42))) % 0.38/0.58 (step @p71 :rule refl :args (@t42)) % 0.38/0.58 (step @p72 :rule eq-refl :args (tptp.x)) % 0.38/0.58 (step @p73 :rule cong :premises (@p72) :args (@t54)) % 0.38/0.58 (step @p74 :rule trans :premises (@p73 @p53)) % 0.38/0.58 (step @p75 :rule nary_cong :premises (@p74 @p71) :args (@t55)) % 0.38/0.58 (step @p76 :rule trans :premises (@p75 @p70)) % 0.38/0.58 (step @p77 :rule quant-var-elim-eq :args ((= (forall @t59 (or (not (= @t56 tptp.x)) @t58 @t57)) @t55))) % 0.38/0.58 (step @p78 :rule refl :args (@t57)) % 0.38/0.58 (step @p79 :rule refl :args (@t58)) % 0.38/0.58 (step @p80 :rule eq-symm :args (tptp.x @t56)) % 0.38/0.58 (step @p81 :rule cong :premises (@p80) :args (@t58)) % 0.38/0.58 (step @p82 :rule nary_cong :premises (@p81 @p79 @p78) :args (@t60)) % 0.38/0.58 (step @p83 :rule aci_norm :args ((= @t61 @t60))) % 0.38/0.58 (step @p84 :rule trans :premises (@p83 @p82)) % 0.38/0.58 (step @p85 :rule cong :premises (@p84) :args (@t62)) % 0.38/0.58 (step @p86 :rule trans :premises (@p85 @p77)) % 0.38/0.58 (step @p87 :rule trans :premises (@p86 @p76)) % 0.38/0.58 (step @p88 :rule nary_cong :premises (@p87 @p69) :args ((and @t62 @t53))) % 0.38/0.58 (step @p89 :rule alpha_equiv :args (@t68 @t69 (@list @t47))) % 0.38/0.58 (step @p90 :rule alpha_equiv :args (@t73 @t69 (@list @t56))) % 0.38/0.58 (step @p91 :rule nary_cong :premises (@p90 @p89) :args (@t74)) % 0.38/0.58 (step @p92 :rule quant-miniscope-and :args ((= (forall @t12 (and @t72 @t67)) @t74))) % 0.38/0.58 (step @p93 :rule trans :premises (@p92 @p91)) % 0.38/0.58 (step @p94 :rule trans :premises (@p93 @p88)) % 0.38/0.58 (step @p95 :rule bool-or-and-distrib :args (@t71 @t66 true @t64 false)) % 0.38/0.58 (step @p96 :rule cong :premises (@p95) :args ((forall @t12 (or @t75 @t64)))) % 0.38/0.58 (step @p97 :rule trans :premises (@p96 @p94)) % 0.38/0.58 (step @p98 :rule refl :args (@t63)) % 0.38/0.58 (step @p99 :rule refl :args (@t7)) % 0.38/0.58 (step @p100 :rule cong :premises (@p99 @p98) :args ((= @t7 @t63))) % 0.38/0.58 (step @p101 :rule symm :premises (@p100)) % 0.38/0.58 (step @p102 :rule eq_resolve :premises (@p99 @p101)) % 0.38/0.58 (step @p103 :rule refl :args (@t8)) % 0.38/0.58 (step @p104 :rule cong :premises (@p103 @p102) :args (@t9)) % 0.38/0.58 (step @p105 :rule cong :premises (@p104) :args (@t76)) % 0.38/0.58 (step @p106 :rule refl :args (@t75)) % 0.38/0.58 (step @p107 :rule nary_cong :premises (@p106 @p105) :args (@t77)) % 0.38/0.58 (step @p108 :rule cong :premises (@p107) :args ((forall @t12 @t77))) % 0.38/0.58 (step @p109 :rule trans :premises (@p108 @p97)) % 0.38/0.58 (step @p110 :rule refl :args (@t76)) % 0.38/0.58 (step @p111 :rule bool-or-de-morgan :args (@t70 @t65 false)) % 0.38/0.58 (step @p112 :rule nary_cong :premises (@p111 @p110) :args ((or (not @t78) @t76))) % 0.38/0.58 (step @p113 :rule bool-and-de-morgan :args (@t78 @t9 true)) % 0.38/0.58 (step @p114 :rule trans :premises (@p113 @p112)) % 0.38/0.58 (step @p115 :rule cong :premises (@p114) :args (@t80)) % 0.38/0.58 (step @p116 :rule trans :premises (@p115 @p109)) % 0.38/0.58 (step @p117 :rule cong :premises (@p116) :args (@t81)) % 0.38/0.58 (step @p118 :rule exists-elim :args ((= (exists @t12 @t79) @t81))) % 0.38/0.58 (step @p119 :rule trans :premises (@p118 @p117)) % 0.38/0.58 (step @p120 :rule refl :args (@t9)) % 0.38/0.58 (step @p121 :rule eq-symm :args (@t6 tptp.y)) % 0.38/0.58 (step @p122 :rule eq-symm :args (@t6 tptp.x)) % 0.38/0.58 (step @p123 :rule nary_cong :premises (@p122 @p121) :args (@t10)) % 0.38/0.58 (step @p124 :rule nary_cong :premises (@p123 @p120) :args (@t11)) % 0.38/0.58 (step @p125 :rule cong :premises (@p124) :args (@t13)) % 0.38/0.58 (step @p126 :rule trans :premises (@p125 @p119)) % 0.38/0.58 (step @p127 :rule cong :premises (@p126) :args (@t15)) % 0.38/0.58 (step @p128 :rule cong :premises (@p127 @p43) :args (@t16)) % 0.38/0.58 (step @p129 :rule trans :premises (@p128 @p50)) % 0.38/0.58 (step @p130 :rule cong :premises (@p129) :args (@t17)) % 0.38/0.58 (step @p131 :rule trans :premises (@p130 @p49)) % 0.38/0.58 (step @p132 :rule eq_resolve :premises (@p1 @p131)) % 0.38/0.58 (step @p133 :rule eq-symm :args (@t87 @t25)) % 0.38/0.58 (step @p134 :rule eq-refl :args (@t88)) % 0.38/0.58 (step @p135 :rule eq-symm :args (@t21 @t1)) % 0.38/0.58 (step @p136 :rule eq-symm :args (@t21 @t3)) % 0.38/0.58 (step @p137 :rule nary_cong :premises (@p136 @p135) :args (@t89)) % 0.38/0.58 (step @p138 :rule beta-reduce :args ((= @t90 @t89))) % 0.38/0.58 (step @p139 :rule trans :premises (@p138 @p137)) % 0.38/0.58 (step @p140 :rule refl :args (@t88)) % 0.38/0.58 (step @p141 :rule cong :premises (@p140 @p139) :args ((= @t88 @t90))) % 0.38/0.58 (step @p142 :rule trans :premises (@p141 @p134)) % 0.38/0.58 (step @p143 :rule eq-symm :args (@t90 @t88)) % 0.38/0.58 (step @p144 :rule trans :premises (@p143 @p142)) % 0.38/0.58 (step @p145 :rule refl :args (@t21)) % 0.38/0.58 (step @p146 :rule cong :premises (@p14 @p145) :args (@t22)) % 0.38/0.58 (step @p147 :rule cong :premises (@p37 @p145) :args (@t24)) % 0.38/0.58 (step @p148 :rule nary_cong :premises (@p147 @p146) :args (@t25)) % 0.38/0.58 (step @p149 :rule ho_cong :premises (@p42 @p145)) % 0.38/0.58 (step @p150 :rule cong :premises (@p149 @p148) :args ((= @t91 @t25))) % 0.38/0.58 (step @p151 :rule trans :premises (@p150 @p144)) % 0.38/0.58 (step @p152 :rule true_elim :premises (@p151)) % 0.38/0.58 (step @p153 :rule eq-refl :args (@t92)) % 0.38/0.58 (step @p154 :rule eq-symm :args (@t21 @t18)) % 0.38/0.58 (step @p155 :rule cong :premises (@p154) :args (@t93)) % 0.38/0.58 (step @p156 :rule eq-symm :args (@t21 @t33)) % 0.38/0.58 (step @p157 :rule cong :premises (@p156) :args (@t94)) % 0.38/0.58 (step @p158 :rule nary_cong :premises (@p157 @p155) :args (@t95)) % 0.38/0.58 (step @p159 :rule cong :premises (@p158) :args (@t96)) % 0.38/0.58 (step @p160 :rule beta-reduce :args ((= @t97 @t96))) % 0.38/0.58 (step @p161 :rule trans :premises (@p160 @p159)) % 0.38/0.58 (step @p162 :rule refl :args (@t92)) % 0.38/0.58 (step @p163 :rule cong :premises (@p162 @p161) :args ((= @t92 @t97))) % 0.38/0.58 (step @p164 :rule trans :premises (@p163 @p153)) % 0.38/0.58 (step @p165 :rule eq-symm :args (@t97 @t92)) % 0.38/0.58 (step @p166 :rule trans :premises (@p165 @p164)) % 0.38/0.58 (step @p167 :rule cong :premises (@p3 @p145) :args (@t82)) % 0.38/0.58 (step @p168 :rule cong :premises (@p167) :args (@t83)) % 0.38/0.58 (step @p169 :rule cong :premises (@p22 @p145) :args (@t84)) % 0.38/0.58 (step @p170 :rule cong :premises (@p169) :args (@t85)) % 0.38/0.58 (step @p171 :rule nary_cong :premises (@p170 @p168) :args (@t86)) % 0.38/0.58 (step @p172 :rule cong :premises (@p171) :args (@t87)) % 0.38/0.58 (step @p173 :rule ho_cong :premises (@p29 @p145)) % 0.38/0.58 (step @p174 :rule cong :premises (@p173 @p172) :args ((= @t98 @t87))) % 0.38/0.58 (step @p175 :rule trans :premises (@p174 @p166)) % 0.38/0.58 (step @p176 :rule true_elim :premises (@p175)) % 0.38/0.58 (step @p177 :rule cong :premises (@p176 @p152) :args (@t99)) % 0.38/0.58 (step @p178 :rule trans :premises (@p177 @p133)) % 0.38/0.58 (step @p179 :rule cong :premises (@p178) :args (@t100)) % 0.38/0.58 (step @p180 :rule refl :args (@t101)) % 0.38/0.58 (step @p181 :rule nary_cong :premises (@p180 @p179) :args (@t102)) % 0.38/0.58 ; WARNING: add trust step for TRUST % 0.38/0.58 ; trust TRUST THEORY_LEMMA % 0.38/0.58 (step @p182 :rule trust :premises () :args (@t102)) % 0.38/0.58 (step @p183 :rule eq_resolve :premises (@p182 @p181)) % 0.38/0.58 (step @p184 :rule chain_m_resolution :premises (@p183 @p132) :args ((not @t103) (@list true) (@list @t101))) % 0.38/0.58 (step @p185 :rule bool-double-not-elim :args (@t86)) % 0.38/0.58 (step @p186 :rule refl :args (@t104)) % 0.38/0.58 (step @p187 :rule refl :args (@t103)) % 0.38/0.58 (step @p188 :rule nary_cong :premises (@p187 @p186 @p185) :args ((or @t103 @t104 (not @t87)))) % 0.38/0.58 (step @p189 :rule cnf_equiv_neg2 :args (@t103)) % 0.38/0.58 (step @p190 :rule eq_resolve :premises (@p189 @p188)) % 0.38/0.58 (step @p191 :rule reordering :premises (@p190) :args ((or @t86 @t103 @t104))) % 0.38/0.58 (step @p192 :rule cnf_and_pos :args (@t86 1)) % 0.38/0.58 (step @p193 :rule reordering :premises (@p192) :args ((or @t83 @t87))) % 0.38/0.58 (assume-push @p328 @t105) % 0.38/0.58 (assume-push @p329 @t106) % 0.38/0.58 (assume-push @p330 @t22) % 0.38/0.58 (assume-push @p331 @t22) % 0.38/0.58 (assume-push @p332 @t106) % 0.38/0.58 (assume-push @p333 @t105) % 0.38/0.58 (step @p200 :rule trans :premises (@p3 @p15 @p330)) % 0.38/0.58 (step-pop @p334 :rule scope :premises (@p200)) % 0.38/0.58 (step-pop @p335 :rule scope :premises (@p334)) % 0.38/0.58 (step-pop @p336 :rule scope :premises (@p335)) % 0.38/0.58 (step @p201 :rule process_scope :premises (@p336) :args (@t82)) % 0.38/0.58 (step @p205 :rule and_intro :premises (@p330 @p15 @p4)) % 0.38/0.58 (step @p206 :rule modus_ponens :premises (@p205 @p201)) % 0.38/0.58 (step-pop @p337 :rule scope :premises (@p206)) % 0.38/0.58 (step-pop @p338 :rule scope :premises (@p337)) % 0.38/0.58 (step-pop @p339 :rule scope :premises (@p338)) % 0.38/0.58 (step @p207 :rule process_scope :premises (@p339) :args (@t82)) % 0.38/0.58 (step @p211 :rule implies_elim :premises (@p207)) % 0.38/0.58 (step @p212 :rule cnf_and_neg :args (@t107)) % 0.38/0.58 (step @p213 :rule resolution :premises (@p212 @p211) :args (true @t107)) % 0.38/0.58 (step @p214 :rule reordering :premises (@p213) :args ((or @t110 @t109 @t82 @t108))) % 0.38/0.58 (step @p215 :rule chain_m_resolution :premises (@p214 @p15 @p4 @p193 @p191 @p184 @p16) :args (@t108 @t111 (@list @t106 @t105 @t82 @t86 @t103 @t25))) % 0.38/0.58 (step @p216 :rule cnf_or_neg :args (@t25 0)) % 0.38/0.58 (step @p217 :rule cnf_and_pos :args (@t86 0)) % 0.38/0.58 (step @p218 :rule reordering :premises (@p217) :args ((or @t85 @t87))) % 0.38/0.58 (step @p219 :rule symm :premises (@p22)) % 0.38/0.58 (step @p220 :rule refl :args (@t23)) % 0.38/0.58 (step @p221 :rule refl :args (@t33)) % 0.38/0.58 (step @p222 :rule refl :args (@t3)) % 0.38/0.58 (step @p223 :rule cong :premises (@p222 @p221) :args ((= @t3 @t33))) % 0.38/0.58 (step @p224 :rule symm :premises (@p223)) % 0.38/0.58 (step @p225 :rule eq_resolve :premises (@p222 @p224)) % 0.38/0.58 (step @p226 :rule cong :premises (@p225 @p220) :args ((= @t3 @t23))) % 0.38/0.58 (step @p227 :rule eq-symm :args (@t23 @t3)) % 0.38/0.58 (step @p228 :rule trans :premises (@p227 @p226)) % 0.38/0.58 (step @p229 :rule eq_resolve :premises (@p37 @p228)) % 0.38/0.58 (assume-push @p340 @t112) % 0.38/0.58 (assume-push @p341 @t113) % 0.38/0.58 (assume-push @p342 @t24) % 0.38/0.58 (assume-push @p343 @t24) % 0.38/0.58 (assume-push @p344 @t113) % 0.38/0.58 (assume-push @p345 @t112) % 0.38/0.58 (step @p236 :rule trans :premises (@p22 @p229 @p342)) % 0.38/0.58 (step-pop @p346 :rule scope :premises (@p236)) % 0.38/0.58 (step-pop @p347 :rule scope :premises (@p346)) % 0.38/0.58 (step-pop @p348 :rule scope :premises (@p347)) % 0.38/0.58 (step @p237 :rule process_scope :premises (@p348) :args (@t84)) % 0.38/0.58 (step @p241 :rule and_intro :premises (@p342 @p229 @p219)) % 0.38/0.58 (step @p242 :rule modus_ponens :premises (@p241 @p237)) % 0.38/0.58 (step-pop @p349 :rule scope :premises (@p242)) % 0.38/0.58 (step-pop @p350 :rule scope :premises (@p349)) % 0.38/0.58 (step-pop @p351 :rule scope :premises (@p350)) % 0.38/0.58 (step @p243 :rule process_scope :premises (@p351) :args (@t84)) % 0.38/0.58 (step @p247 :rule implies_elim :premises (@p243)) % 0.38/0.58 (step @p248 :rule cnf_and_neg :args (@t114)) % 0.38/0.58 (step @p249 :rule resolution :premises (@p248 @p247) :args (true @t114)) % 0.38/0.58 (step @p250 :rule reordering :premises (@p249) :args ((or @t117 @t116 @t84 @t115))) % 0.38/0.58 (step @p251 :rule chain_m_resolution :premises (@p250 @p229 @p219 @p218 @p191 @p184 @p216) :args (@t115 @t111 (@list @t113 @t112 @t84 @t86 @t103 @t25))) % 0.38/0.58 (step @p252 :rule cnf_or_pos :args (@t25)) % 0.38/0.58 (step @p253 :rule reordering :premises (@p252) :args ((or @t24 @t22 @t104))) % 0.38/0.58 (step @p254 :rule chain_m_resolution :premises (@p253 @p251 @p215) :args (@t104 @t118 (@list @t24 @t22))) % 0.38/0.58 (step @p255 :rule cnf_equiv_neg1 :args (@t103)) % 0.38/0.58 (step @p256 :rule reordering :premises (@p255) :args ((or @t25 @t87 @t103))) % 0.38/0.58 (step @p257 :rule chain_m_resolution :premises (@p256 @p254 @p184) :args (@t87 @t118 (@list @t25 @t103))) % 0.38/0.58 (step @p258 :rule refl :args (@t85)) % 0.38/0.58 (step @p259 :rule bool-double-not-elim :args (@t24)) % 0.38/0.58 (step @p260 :rule refl :args (@t116)) % 0.38/0.58 (step @p261 :rule refl :args (@t117)) % 0.38/0.58 (step @p262 :rule nary_cong :premises (@p261 @p260 @p259 @p258) :args ((or @t117 @t116 (not @t115) @t85))) % 0.38/0.58 (assume-push @p352 @t112) % 0.38/0.58 (assume-push @p353 @t113) % 0.38/0.58 (assume-push @p354 @t115) % 0.38/0.58 (assume-push @p355 @t115) % 0.38/0.58 (assume-push @p356 @t113) % 0.38/0.58 (assume-push @p357 @t112) % 0.38/0.58 (step @p269 :rule false_intro :premises (@p354)) % 0.38/0.58 (step @p270 :rule trans :premises (@p22 @p229)) % 0.38/0.58 (step @p271 :rule cong :premises (@p270 @p145) :args (@t84)) % 0.38/0.58 (step @p272 :rule trans :premises (@p271 @p269)) % 0.38/0.58 (step @p273 :rule false_elim :premises (@p272)) % 0.38/0.58 (step-pop @p358 :rule scope :premises (@p273)) % 0.38/0.58 (step-pop @p359 :rule scope :premises (@p358)) % 0.38/0.58 (step-pop @p360 :rule scope :premises (@p359)) % 0.38/0.58 (step @p274 :rule process_scope :premises (@p360) :args (@t85)) % 0.38/0.58 (step @p278 :rule and_intro :premises (@p354 @p229 @p219)) % 0.38/0.58 (step @p279 :rule modus_ponens :premises (@p278 @p274)) % 0.38/0.58 (step-pop @p361 :rule scope :premises (@p279)) % 0.38/0.58 (step-pop @p362 :rule scope :premises (@p361)) % 0.38/0.58 (step-pop @p363 :rule scope :premises (@p362)) % 0.38/0.58 (step @p280 :rule process_scope :premises (@p363) :args (@t85)) % 0.38/0.58 (step @p284 :rule implies_elim :premises (@p280)) % 0.38/0.58 (step @p285 :rule cnf_and_neg :args (@t119)) % 0.38/0.58 (step @p286 :rule resolution :premises (@p285 @p284) :args (true @t119)) % 0.38/0.58 (step @p287 :rule eq_resolve :premises (@p286 @p262)) % 0.38/0.58 (step @p288 :rule chain_m_resolution :premises (@p287 @p219 @p229 @p251) :args (@t85 (@list false false true) (@list @t112 @t113 @t24))) % 0.38/0.58 (step @p289 :rule bool-double-not-elim :args (@t82)) % 0.38/0.58 (step @p290 :rule bool-double-not-elim :args (@t84)) % 0.38/0.58 (step @p291 :rule refl :args (@t86)) % 0.38/0.58 (step @p292 :rule nary_cong :premises (@p291 @p290 @p289) :args ((or @t86 (not @t85) (not @t83)))) % 0.38/0.58 (step @p293 :rule cnf_and_neg :args (@t86)) % 0.38/0.58 (step @p294 :rule eq_resolve :premises (@p293 @p292)) % 0.38/0.58 (step @p295 :rule reordering :premises (@p294) :args ((or @t84 @t82 @t86))) % 0.38/0.58 (step @p296 :rule chain_m_resolution :premises (@p295 @p288 @p257) :args (@t82 @t118 (@list @t84 @t86))) % 0.38/0.58 (step @p297 :rule refl :args (@t83)) % 0.38/0.58 (step @p298 :rule bool-double-not-elim :args (@t22)) % 0.38/0.58 (step @p299 :rule refl :args (@t109)) % 0.38/0.58 (step @p300 :rule refl :args (@t110)) % 0.38/0.58 (step @p301 :rule nary_cong :premises (@p300 @p299 @p298 @p297) :args ((or @t110 @t109 (not @t108) @t83))) % 0.38/0.58 (assume-push @p364 @t105) % 0.38/0.58 (assume-push @p365 @t106) % 0.38/0.58 (assume-push @p366 @t108) % 0.38/0.58 (assume-push @p367 @t108) % 0.38/0.58 (assume-push @p368 @t106) % 0.38/0.58 (assume-push @p369 @t105) % 0.38/0.58 (step @p308 :rule false_intro :premises (@p366)) % 0.38/0.58 (step @p309 :rule trans :premises (@p3 @p15)) % 0.38/0.58 (step @p310 :rule cong :premises (@p309 @p145) :args (@t82)) % 0.38/0.58 (step @p311 :rule trans :premises (@p310 @p308)) % 0.38/0.58 (step @p312 :rule false_elim :premises (@p311)) % 0.38/0.58 (step-pop @p370 :rule scope :premises (@p312)) % 0.38/0.58 (step-pop @p371 :rule scope :premises (@p370)) % 0.38/0.58 (step-pop @p372 :rule scope :premises (@p371)) % 0.38/0.58 (step @p313 :rule process_scope :premises (@p372) :args (@t83)) % 0.38/0.58 (step @p317 :rule and_intro :premises (@p366 @p15 @p4)) % 0.38/0.58 (step @p318 :rule modus_ponens :premises (@p317 @p313)) % 0.38/0.58 (step-pop @p373 :rule scope :premises (@p318)) % 0.38/0.58 (step-pop @p374 :rule scope :premises (@p373)) % 0.38/0.58 (step-pop @p375 :rule scope :premises (@p374)) % 0.38/0.58 (step @p319 :rule process_scope :premises (@p375) :args (@t83)) % 0.38/0.58 (step @p323 :rule implies_elim :premises (@p319)) % 0.38/0.58 (step @p324 :rule cnf_and_neg :args (@t120)) % 0.38/0.58 (step @p325 :rule resolution :premises (@p324 @p323) :args (true @t120)) % 0.38/0.58 (step @p326 :rule eq_resolve :premises (@p325 @p301)) % 0.38/0.58 (step @p327 false :rule chain_m_resolution :premises (@p326 @p296 @p215 @p15 @p4) :args (false (@list false true false false) (@list @t82 @t22 @t106 @t105))) % 0.38/0.58 ) % 0.38/0.58 % SZS output end Proof % 0.38/0.58 % cvc5 exiting %------------------------------------------------------------------------------