%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET557^6 : TPTP v9.2.1. Released v5.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n026.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 08:48:03 AM UTC 2026 % Result : Theorem 25.48s 25.79s % Output : Proof 25.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET557^6 : TPTP v9.2.1. Released v5.1.0. % 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 : n026.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 16:01:25 EDT 2026 % 0.16/0.35 % CPUTime : % 0.26/0.49 %----Proving TH0 % 25.48/25.79 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 25.48/25.79 % SZS status Theorem % 25.48/25.79 % SZS output start Proof % 25.48/25.79 ( % 25.48/25.79 (declare-sort $$unsorted 0) % 25.48/25.79 (define @t1 () (@var "F" (-> $$unsorted Bool))) % 25.48/25.79 (define @t2 () (@var "J" $$unsorted)) % 25.48/25.79 (define @t3 () (@var "G" (-> $$unsorted $$unsorted Bool))) % 25.48/25.79 (define @t4 () (_ @t3 @t2)) % 25.48/25.79 (define @t5 () (@var "S" (-> $$unsorted Bool))) % 25.48/25.79 (define @t6 () (_ @t5 @t2)) % 25.48/25.79 (define @t7 () (and @t6 (= @t4 @t1))) % 25.48/25.79 (define @t8 () (@list @t2)) % 25.48/25.79 (define @t9 () (exists @t8 @t7)) % 25.48/25.79 (define @t10 () (@var "Xx" $$unsorted)) % 25.48/25.79 (define @t11 () (_ @t5 @t10)) % 25.48/25.79 (define @t12 () (_ @t1 @t10)) % 25.48/25.79 (define @t13 () (@list @t10)) % 25.48/25.79 (define @t14 () (forall @t13 (=> @t12 @t11))) % 25.48/25.79 (define @t15 () (=> @t14 @t9)) % 25.48/25.79 (define @t16 () (@list @t1)) % 25.48/25.79 (define @t17 () (forall @t16 @t15)) % 25.48/25.79 (define @t18 () (@list @t3)) % 25.48/25.79 (define @t19 () (exists @t18 @t17)) % 25.48/25.79 (define @t20 () (not @t19)) % 25.48/25.79 (define @t21 () (@list @t5)) % 25.48/25.79 (define @t22 () (forall @t21 @t20)) % 25.48/25.79 (define @t23 () (not @t22)) % 25.48/25.79 (define @t24 () (= @t1 @t4)) % 25.48/25.79 (define @t25 () (not @t24)) % 25.48/25.79 (define @t26 () (_ @t5 @t2)) % 25.48/25.79 (define @t27 () (not (forall @t8 (or (not @t26) @t25)))) % 25.48/25.79 (define @t28 () (_ @t5 @t10)) % 25.48/25.79 (define @t29 () (_ @t1 @t10)) % 25.48/25.79 (define @t30 () (not @t29)) % 25.48/25.79 (define @t31 () (forall @t13 (or @t30 @t28))) % 25.48/25.79 (define @t32 () (forall @t16 (or (not @t31) @t27))) % 25.48/25.79 (define @t33 () (not @t32)) % 25.48/25.79 (define @t34 () (forall (@list @t5 @t3) @t33)) % 25.48/25.79 (define @t35 () (forall @t18 @t33)) % 25.48/25.79 (define @t36 () (not @t6)) % 25.48/25.79 (define @t37 () (or @t36 @t25)) % 25.48/25.79 (define @t38 () (and @t6 @t24)) % 25.48/25.79 (define @t39 () (forall @t8 (not @t38))) % 25.48/25.79 (define @t40 () (not @t39)) % 25.48/25.79 (define @t41 () (not @t12)) % 25.48/25.79 (define @t42 () (or @t41 @t11)) % 25.48/25.79 (define @t43 () (@quantifiers_skolemize @t34 1)) % 25.48/25.79 (define @t44 () (_ @t43 @t2)) % 25.48/25.79 (define @t45 () (@quantifiers_skolemize @t34 0)) % 25.48/25.79 (define @t46 () (not (_ @t45 @t2))) % 25.48/25.79 (define @t47 () (_ @t45 @t10)) % 25.48/25.79 (define @t48 () (forall @t16 (or (not (forall @t13 (or @t30 @t47))) (not (forall @t8 (or @t46 (not (= @t1 @t44)))))))) % 25.48/25.79 (define @t49 () (not @t34)) % 25.48/25.79 (define @t50 () (not (not @t48))) % 25.48/25.79 (define @t51 () (@list true)) % 25.48/25.79 (define @t52 () (@var "BOUND_VARIABLE_14609" $$unsorted)) % 25.48/25.79 (define @t53 () (and (_ @t45 @t52) (not (_ @t43 @t52 @t52)))) % 25.48/25.79 (define @t54 () (@list @t52)) % 25.48/25.79 (define @t55 () (lambda @t54 @t53)) % 25.48/25.79 (define @t56 () (forall @t8 (or @t46 (not (= @t44 @t55))))) % 25.48/25.79 (define @t57 () (not @t56)) % 25.48/25.79 (define @t58 () (not (= @t55 @t44))) % 25.48/25.79 (define @t59 () (or @t46 @t58)) % 25.48/25.79 (define @t60 () (forall @t8 @t59)) % 25.48/25.79 (define @t61 () (not @t60)) % 25.48/25.79 (define @t62 () (_ @t43 @t10 @t10)) % 25.48/25.79 (define @t63 () (not @t47)) % 25.48/25.79 (define @t64 () (not @t62)) % 25.48/25.79 (define @t65 () (and @t47 @t64)) % 25.48/25.79 (define @t66 () (or (not @t65) @t47)) % 25.48/25.79 (define @t67 () (_ @t55 @t10)) % 25.48/25.79 (define @t68 () (not @t67)) % 25.48/25.79 (define @t69 () (or @t68 @t47)) % 25.48/25.79 (define @t70 () (forall @t13 @t69)) % 25.48/25.79 (define @t71 () (not @t70)) % 25.48/25.79 (define @t72 () (or @t71 @t61)) % 25.48/25.79 (define @t73 () (@purify @t55)) % 25.48/25.79 (define @t74 () (@quantifiers_skolemize @t56 0)) % 25.48/25.79 (define @t75 () (_ @t43 @t74)) % 25.48/25.79 (define @t76 () (= @t75 @t73)) % 25.48/25.79 (define @t77 () (not @t76)) % 25.48/25.79 (define @t78 () (_ @t45 @t74)) % 25.48/25.79 (define @t79 () (not @t78)) % 25.48/25.79 (define @t80 () (or @t79 @t77)) % 25.48/25.79 (define @t81 () (not @t80)) % 25.48/25.79 (define @t82 () (= @t55 @t75)) % 25.48/25.79 (define @t83 () (not @t82)) % 25.48/25.79 (define @t84 () (or @t79 @t83)) % 25.48/25.79 (define @t85 () (not @t84)) % 25.48/25.79 (define @t86 () (not (= @t75 @t55))) % 25.48/25.79 (define @t87 () (or @t79 @t86)) % 25.48/25.79 (define @t88 () (not @t87)) % 25.48/25.79 (define @t89 () (@list @t80)) % 25.48/25.79 (define @t90 () (@purify @t75)) % 25.48/25.79 (define @t91 () (_ @t90 @t74)) % 25.48/25.79 (define @t92 () (_ @t43 @t74 @t74)) % 25.48/25.79 (define @t93 () (_ @t75 @t74)) % 25.48/25.79 (define @t94 () (= @t93 @t91)) % 25.48/25.79 (define @t95 () (= @t75 @t90)) % 25.48/25.79 (define @t96 () (and @t95 @t94)) % 25.48/25.79 (define @t97 () (_ @t75 @t74)) % 25.48/25.79 (define @t98 () (= @t93 @t97)) % 25.48/25.79 (define @t99 () (not @t92)) % 25.48/25.79 (define @t100 () (and @t78 @t99)) % 25.48/25.79 (define @t101 () (not @t100)) % 25.48/25.79 (define @t102 () (_ @t73 @t52)) % 25.48/25.79 (define @t103 () (_ @t55 @t52)) % 25.48/25.79 (define @t104 () (= @t102 @t103)) % 25.48/25.79 (define @t105 () (forall @t54 @t104)) % 25.48/25.79 (define @t106 () (_ @t73 @t74)) % 25.48/25.79 (define @t107 () (= @t100 @t106)) % 25.48/25.79 (define @t108 () (not @t107)) % 25.48/25.79 (define @t109 () (not @t106)) % 25.48/25.79 (define @t110 () (and @t76 @t91 @t95)) % 25.48/25.79 (define @t111 () (not @t91)) % 25.48/25.79 (define @t112 () (not @t95)) % 25.48/25.79 (define @t113 () (and @t76 @t95 @t111)) % 25.48/25.79 (assume @p1 @t23) % 25.48/25.79 (assume @p2 true) % 25.48/25.79 (step @p3 :rule quant-merge-prenex :args ((= (forall @t21 @t35) @t34))) % 25.48/25.79 (step @p4 :rule bool-double-not-elim :args (@t35)) % 25.48/25.79 (step @p5 :rule exists-elim :args ((= (exists @t18 @t32) (not @t35)))) % 25.48/25.79 (step @p6 :rule bool-impl-elim :args (@t31 @t27)) % 25.48/25.79 (step @p7 :rule cong :premises (@p6) :args ((forall @t16 (=> @t31 @t27)))) % 25.48/25.79 (step @p8 :rule refl :args (@t25)) % 25.48/25.79 (step @p9 :rule refl :args (@t26)) % 25.48/25.79 (step @p10 :rule refl :args (@t6)) % 25.48/25.79 (step @p11 :rule cong :premises (@p10 @p9) :args ((= @t6 @t26))) % 25.48/25.79 (step @p12 :rule symm :premises (@p11)) % 25.48/25.79 (step @p13 :rule eq_resolve :premises (@p10 @p12)) % 25.48/25.79 (step @p14 :rule cong :premises (@p13) :args (@t36)) % 25.48/25.79 (step @p15 :rule nary_cong :premises (@p14 @p8) :args (@t37)) % 25.48/25.79 (step @p16 :rule cong :premises (@p15) :args ((forall @t8 @t37))) % 25.48/25.79 (step @p17 :rule bool-and-de-morgan :args (@t6 @t24 true)) % 25.48/25.79 (step @p18 :rule cong :premises (@p17) :args (@t39)) % 25.48/25.79 (step @p19 :rule trans :premises (@p18 @p16)) % 25.48/25.79 (step @p20 :rule cong :premises (@p19) :args (@t40)) % 25.48/25.79 (step @p21 :rule exists-elim :args ((= (exists @t8 @t38) @t40))) % 25.48/25.79 (step @p22 :rule trans :premises (@p21 @p20)) % 25.48/25.79 (step @p23 :rule eq-symm :args (@t4 @t1)) % 25.48/25.79 (step @p24 :rule refl :args (@t6)) % 25.48/25.79 (step @p25 :rule nary_cong :premises (@p24 @p23) :args (@t7)) % 25.48/25.79 (step @p26 :rule cong :premises (@p25) :args (@t9)) % 25.48/25.79 (step @p27 :rule trans :premises (@p26 @p22)) % 25.48/25.79 (step @p28 :rule refl :args (@t28)) % 25.48/25.79 (step @p29 :rule refl :args (@t11)) % 25.48/25.79 (step @p30 :rule cong :premises (@p29 @p28) :args ((= @t11 @t28))) % 25.48/25.79 (step @p31 :rule symm :premises (@p30)) % 25.48/25.79 (step @p32 :rule eq_resolve :premises (@p29 @p31)) % 25.48/25.79 (step @p33 :rule refl :args (@t29)) % 25.48/25.79 (step @p34 :rule refl :args (@t12)) % 25.48/25.79 (step @p35 :rule cong :premises (@p34 @p33) :args ((= @t12 @t29))) % 25.48/25.79 (step @p36 :rule symm :premises (@p35)) % 25.48/25.79 (step @p37 :rule eq_resolve :premises (@p34 @p36)) % 25.48/25.79 (step @p38 :rule cong :premises (@p37) :args (@t41)) % 25.48/25.79 (step @p39 :rule nary_cong :premises (@p38 @p32) :args (@t42)) % 25.48/25.79 (step @p40 :rule cong :premises (@p39) :args ((forall @t13 @t42))) % 25.48/25.79 (step @p41 :rule bool-impl-elim :args (@t12 @t11)) % 25.48/25.79 (step @p42 :rule cong :premises (@p41) :args (@t14)) % 25.48/25.79 (step @p43 :rule trans :premises (@p42 @p40)) % 25.48/25.79 (step @p44 :rule cong :premises (@p43 @p27) :args (@t15)) % 25.48/25.79 (step @p45 :rule cong :premises (@p44) :args (@t17)) % 25.48/25.79 (step @p46 :rule trans :premises (@p45 @p7)) % 25.48/25.79 (step @p47 :rule cong :premises (@p46) :args (@t19)) % 25.48/25.79 (step @p48 :rule trans :premises (@p47 @p5)) % 25.48/25.79 (step @p49 :rule cong :premises (@p48) :args (@t20)) % 25.48/25.79 (step @p50 :rule trans :premises (@p49 @p4)) % 25.48/25.79 (step @p51 :rule cong :premises (@p50) :args (@t22)) % 25.48/25.79 (step @p52 :rule trans :premises (@p51 @p3)) % 25.48/25.79 (step @p53 :rule cong :premises (@p52) :args (@t23)) % 25.48/25.79 (step @p54 :rule eq_resolve :premises (@p1 @p53)) % 25.48/25.79 (step @p55 :rule refl :args (@t48)) % 25.48/25.79 (step @p56 :rule bool-double-not-elim :args (@t34)) % 25.48/25.79 (step @p57 :rule nary_cong :premises (@p56 @p55) :args ((or (not @t49) @t48))) % 25.48/25.79 (step @p58 :rule bool-double-not-elim :args (@t48)) % 25.48/25.79 (step @p59 :rule refl :args (@t49)) % 25.48/25.79 (step @p60 :rule cong :premises (@p59 @p58) :args ((=> @t49 @t50))) % 25.48/25.79 (assume-push @p281 @t49) % 25.48/25.79 (step @p62 :rule skolemize :premises (@p54)) % 25.48/25.79 (step-pop @p282 :rule scope :premises (@p62)) % 25.48/25.79 (step @p63 :rule process_scope :premises (@p282) :args (@t50)) % 25.48/25.79 (step @p65 :rule eq_resolve :premises (@p63 @p60)) % 25.48/25.79 (step @p66 :rule implies_elim :premises (@p65)) % 25.48/25.79 (step @p67 :rule eq_resolve :premises (@p66 @p57)) % 25.48/25.79 (step @p68 :rule chain_m_resolution :premises (@p67 @p54) :args (@t48 @t51 (@list @t34))) % 25.48/25.79 (step @p69 :rule aci_norm :args ((= (or false @t57) @t57))) % 25.48/25.79 (step @p70 :rule eq-symm :args (@t55 @t44)) % 25.48/25.79 (step @p71 :rule cong :premises (@p70) :args (@t58)) % 25.48/25.79 (step @p72 :rule refl :args (@t46)) % 25.48/25.79 (step @p73 :rule nary_cong :premises (@p72 @p71) :args (@t59)) % 25.48/25.79 (step @p74 :rule cong :premises (@p73) :args (@t60)) % 25.48/25.79 (step @p75 :rule cong :premises (@p74) :args (@t61)) % 25.48/25.79 (step @p76 :rule evaluate :args ((not true))) % 25.48/25.79 (step @p77 :rule quant-unused-vars :args ((= (forall @t13 true) true))) % 25.48/25.79 (step @p78 :rule bool-or-taut2 :args (false @t47 (or @t62) false)) % 25.48/25.79 (step @p79 :rule aci_norm :args ((= (or (or @t63 @t62) @t47) (or @t63 @t62 @t47)))) % 25.48/25.79 (step @p80 :rule trans :premises (@p79 @p78)) % 25.48/25.79 (step @p81 :rule refl :args (@t47)) % 25.48/25.79 (step @p82 :rule bool-double-not-elim :args (@t62)) % 25.48/25.79 (step @p83 :rule refl :args (@t63)) % 25.48/25.79 (step @p84 :rule nary_cong :premises (@p83 @p82) :args ((or @t63 (not @t64)))) % 25.48/25.79 (step @p85 :rule bool-and-de-morgan :args (@t47 @t64 true)) % 25.48/25.79 (step @p86 :rule trans :premises (@p85 @p84)) % 25.48/25.79 (step @p87 :rule nary_cong :premises (@p86 @p81) :args (@t66)) % 25.48/25.79 (step @p88 :rule trans :premises (@p87 @p80)) % 25.48/25.79 (step @p89 :rule cong :premises (@p88) :args ((forall @t13 @t66))) % 25.48/25.79 (step @p90 :rule trans :premises (@p89 @p77)) % 25.48/25.79 (step @p91 :rule refl :args (@t47)) % 25.48/25.79 (step @p92 :rule beta-reduce :args ((= @t67 @t65))) % 25.48/25.79 (step @p93 :rule cong :premises (@p92) :args (@t68)) % 25.48/25.79 (step @p94 :rule nary_cong :premises (@p93 @p91) :args (@t69)) % 25.48/25.79 (step @p95 :rule cong :premises (@p94) :args (@t70)) % 25.48/25.79 (step @p96 :rule trans :premises (@p95 @p90)) % 25.48/25.79 (step @p97 :rule cong :premises (@p96) :args (@t71)) % 25.48/25.79 (step @p98 :rule trans :premises (@p97 @p76)) % 25.48/25.79 (step @p99 :rule nary_cong :premises (@p98 @p75) :args (@t72)) % 25.48/25.79 (step @p100 :rule trans :premises (@p99 @p69)) % 25.48/25.79 (step @p101 :rule cong :premises (@p55 @p100) :args ((=> @t48 @t72))) % 25.48/25.79 (assume-push @p283 @t48) % 25.48/25.79 (step @p103 :rule instantiate :premises (@p68) :args ((@list @t55))) % 25.48/25.79 (step-pop @p284 :rule scope :premises (@p103)) % 25.48/25.79 (step @p104 :rule process_scope :premises (@p284) :args (@t72)) % 25.48/25.79 (step @p106 :rule eq_resolve :premises (@p104 @p101)) % 25.48/25.79 (step @p107 :rule implies_elim :premises (@p106)) % 25.48/25.79 (step @p108 :rule chain_m_resolution :premises (@p107 @p68) :args (@t57 (@list false) (@list @t48))) % 25.48/25.79 (step @p109 :rule refl :args (@t81)) % 25.48/25.79 (step @p110 :rule bool-double-not-elim :args (@t56)) % 25.48/25.79 (step @p111 :rule nary_cong :premises (@p110 @p109) :args ((or (not @t57) @t81))) % 25.48/25.79 (step @p112 :rule eq-symm :args (@t73 @t75)) % 25.48/25.79 (step @p113 :rule refl :args (@t75)) % 25.48/25.79 (step @p114 :rule eq-refl :args (@t55)) % 25.48/25.79 (step @p115 :rule skolem_intro :args (@t73)) % 25.48/25.79 (step @p116 :rule refl :args (@t55)) % 25.48/25.79 (step @p117 :rule cong :premises (@p116 @p115) :args ((= @t55 @t73))) % 25.48/25.79 (step @p118 :rule trans :premises (@p117 @p114)) % 25.48/25.79 (step @p119 :rule true_elim :premises (@p118)) % 25.48/25.79 (step @p120 :rule cong :premises (@p119 @p113) :args (@t82)) % 25.48/25.79 (step @p121 :rule trans :premises (@p120 @p112)) % 25.48/25.79 (step @p122 :rule cong :premises (@p121) :args (@t83)) % 25.48/25.79 (step @p123 :rule refl :args (@t79)) % 25.48/25.79 (step @p124 :rule nary_cong :premises (@p123 @p122) :args (@t84)) % 25.48/25.79 (step @p125 :rule cong :premises (@p124) :args (@t85)) % 25.48/25.79 (step @p126 :rule refl :args (@t57)) % 25.48/25.79 (step @p127 :rule cong :premises (@p126 @p125) :args ((=> @t57 @t85))) % 25.48/25.79 (step @p128 :rule eq-symm :args (@t75 @t55)) % 25.48/25.79 (step @p129 :rule cong :premises (@p128) :args (@t86)) % 25.48/25.79 (step @p130 :rule nary_cong :premises (@p123 @p129) :args (@t87)) % 25.48/25.79 (step @p131 :rule cong :premises (@p130) :args (@t88)) % 25.48/25.79 (step @p132 :rule cong :premises (@p126 @p131) :args ((=> @t57 @t88))) % 25.48/25.79 (step @p133 :rule trans :premises (@p132 @p127)) % 25.48/25.79 (assume-push @p285 @t57) % 25.48/25.79 (step @p135 :rule skolemize :premises (@p108)) % 25.48/25.79 (step-pop @p286 :rule scope :premises (@p135)) % 25.48/25.79 (step @p136 :rule process_scope :premises (@p286) :args (@t88)) % 25.48/25.79 (step @p138 :rule eq_resolve :premises (@p136 @p133)) % 25.48/25.79 (step @p139 :rule implies_elim :premises (@p138)) % 25.48/25.79 (step @p140 :rule eq_resolve :premises (@p139 @p111)) % 25.48/25.79 (step @p141 :rule chain_m_resolution :premises (@p140 @p108) :args (@t81 @t51 (@list @t56))) % 25.48/25.79 (step @p142 :rule bool-double-not-elim :args (@t76)) % 25.48/25.79 (step @p143 :rule refl :args (@t80)) % 25.48/25.79 (step @p144 :rule nary_cong :premises (@p143 @p142) :args ((or @t80 (not @t77)))) % 25.48/25.79 (step @p145 :rule cnf_or_neg :args (@t80 1)) % 25.48/25.79 (step @p146 :rule eq_resolve :premises (@p145 @p144)) % 25.48/25.79 (step @p147 :rule reordering :premises (@p146) :args ((or @t76 @t80))) % 25.48/25.79 (step @p148 :rule chain_m_resolution :premises (@p147 @p141) :args (@t76 @t51 @t89)) % 25.48/25.79 (step @p149 :rule refl :args (@t91)) % 25.48/25.79 (step @p150 :rule refl :args (@t92)) % 25.48/25.79 (step @p151 :rule refl :args (@t93)) % 25.48/25.79 (step @p152 :rule cong :premises (@p151 @p150) :args ((= @t93 @t92))) % 25.48/25.79 (step @p153 :rule symm :premises (@p152)) % 25.48/25.79 (step @p154 :rule eq_resolve :premises (@p151 @p153)) % 25.48/25.79 (step @p155 :rule cong :premises (@p154 @p149) :args (@t94)) % 25.48/25.79 (step @p156 :rule refl :args (@t95)) % 25.48/25.79 (step @p157 :rule nary_cong :premises (@p156 @p155) :args (@t96)) % 25.48/25.79 (step @p158 :rule eq-symm :args (@t91 @t93)) % 25.48/25.79 (step @p159 :rule eq-symm :args (@t90 @t75)) % 25.48/25.79 (step @p160 :rule nary_cong :premises (@p159 @p158) :args ((and (= @t90 @t75) (= @t91 @t93)))) % 25.48/25.79 (step @p161 :rule trans :premises (@p160 @p157)) % 25.48/25.79 (step @p162 :rule evaluate :args ((and true true))) % 25.48/25.79 (step @p163 :rule eq-refl :args (@t93)) % 25.48/25.79 (step @p164 :rule refl :args (@t97)) % 25.48/25.79 (step @p165 :rule refl :args (@t93)) % 25.48/25.79 (step @p166 :rule cong :premises (@p165 @p164) :args (@t98)) % 25.48/25.79 (step @p167 :rule trans :premises (@p166 @p163)) % 25.48/25.79 (step @p168 :rule eq-refl :args (@t75)) % 25.48/25.79 (step @p169 :rule nary_cong :premises (@p168 @p167) :args ((and (= @t75 @t75) @t98))) % 25.48/25.79 (step @p170 :rule trans :premises (@p169 @p162)) % 25.48/25.79 (step @p171 :rule refl :args (@t74)) % 25.48/25.79 (step @p172 :rule skolem_intro :args (@t90)) % 25.48/25.79 (step @p173 :rule ho_cong :premises (@p172 @p171)) % 25.48/25.79 (step @p174 :rule cong :premises (@p165 @p173) :args (@t94)) % 25.48/25.79 (step @p175 :rule cong :premises (@p113 @p172) :args (@t95)) % 25.48/25.79 (step @p176 :rule nary_cong :premises (@p175 @p174) :args (@t96)) % 25.48/25.79 (step @p177 :rule trans :premises (@p160 @p176 @p170)) % 25.48/25.79 (step @p178 :rule true_elim :premises (@p177)) % 25.48/25.79 (step @p179 :rule eq_resolve :premises (@p178 @p161)) % 25.48/25.79 (step @p180 :rule and_elim :premises (@p179) :args (0)) % 25.48/25.79 (step @p181 :rule and_elim :premises (@p179) :args (1)) % 25.48/25.79 (step @p182 :rule equiv_elim1 :premises (@p181)) % 25.48/25.79 (step @p183 :rule cnf_and_pos :args (@t100 1)) % 25.48/25.79 (step @p184 :rule reordering :premises (@p183) :args ((or @t99 @t101))) % 25.48/25.79 (step @p185 :rule eq-symm :args (@t102 @t53)) % 25.48/25.79 (step @p186 :rule beta-reduce :args ((= @t103 @t53))) % 25.48/25.79 (step @p187 :rule refl :args (@t102)) % 25.48/25.79 (step @p188 :rule cong :premises (@p187 @p186) :args (@t104)) % 25.48/25.79 (step @p189 :rule trans :premises (@p188 @p185)) % 25.48/25.79 (step @p190 :rule cong :premises (@p189) :args (@t105)) % 25.48/25.79 (step @p191 :rule quant-unused-vars :args ((= (forall @t54 true) true))) % 25.48/25.79 (step @p192 :rule eq-refl :args (@t103)) % 25.48/25.79 (step @p193 :rule cong :premises (@p192) :args ((forall @t54 (= @t103 @t103)))) % 25.48/25.79 (step @p194 :rule trans :premises (@p193 @p191)) % 25.48/25.79 (step @p195 :rule refl :args (@t103)) % 25.48/25.79 (step @p196 :rule refl :args (@t52)) % 25.48/25.79 (step @p197 :rule ho_cong :premises (@p115 @p196)) % 25.48/25.79 (step @p198 :rule cong :premises (@p197 @p195) :args (@t104)) % 25.48/25.79 (step @p199 :rule cong :premises (@p198) :args (@t105)) % 25.48/25.79 (step @p200 :rule trans :premises (@p199 @p194)) % 25.48/25.79 (step @p201 :rule true_elim :premises (@p200)) % 25.48/25.79 (step @p202 :rule eq_resolve :premises (@p201 @p190)) % 25.48/25.79 (step @p203 :rule instantiate :premises (@p202) :args ((@list @t74))) % 25.48/25.79 (step @p204 :rule cnf_equiv_pos2 :args (@t107)) % 25.48/25.79 (step @p205 :rule reordering :premises (@p204) :args ((or @t100 @t109 @t108))) % 25.48/25.79 (assume-push @p287 @t76) % 25.48/25.79 (assume-push @p288 @t91) % 25.48/25.79 (assume-push @p289 @t95) % 25.48/25.79 (assume-push @p290 @t91) % 25.48/25.79 (assume-push @p291 @t95) % 25.48/25.79 (assume-push @p292 @t76) % 25.48/25.79 (step @p212 :rule true_intro :premises (@p288)) % 25.48/25.79 (step @p213 :rule symm :premises (@p148)) % 25.48/25.79 (step @p214 :rule trans :premises (@p213 @p180)) % 25.48/25.79 (step @p215 :rule ho_cong :premises (@p214 @p171)) % 25.48/25.79 (step @p216 :rule trans :premises (@p215 @p212)) % 25.48/25.79 (step @p217 :rule true_elim :premises (@p216)) % 25.48/25.79 (step-pop @p293 :rule scope :premises (@p217)) % 25.48/25.79 (step-pop @p294 :rule scope :premises (@p293)) % 25.48/25.79 (step-pop @p295 :rule scope :premises (@p294)) % 25.48/25.79 (step @p218 :rule process_scope :premises (@p295) :args (@t106)) % 25.48/25.79 (step @p222 :rule and_intro :premises (@p288 @p180 @p148)) % 25.48/25.79 (step @p223 :rule modus_ponens :premises (@p222 @p218)) % 25.48/25.79 (step-pop @p296 :rule scope :premises (@p223)) % 25.48/25.79 (step-pop @p297 :rule scope :premises (@p296)) % 25.48/25.79 (step-pop @p298 :rule scope :premises (@p297)) % 25.48/25.79 (step @p224 :rule process_scope :premises (@p298) :args (@t106)) % 25.48/25.79 (step @p228 :rule implies_elim :premises (@p224)) % 25.48/25.79 (step @p229 :rule cnf_and_neg :args (@t110)) % 25.48/25.79 (step @p230 :rule resolution :premises (@p229 @p228) :args (true @t110)) % 25.48/25.79 (step @p231 :rule reordering :premises (@p230) :args ((or @t77 @t112 @t111 @t106))) % 25.48/25.79 (step @p232 :rule chain_m_resolution :premises (@p231 @p180 @p148 @p205 @p203 @p184 @p182) :args (@t99 (@list false false true false true false) (@list @t95 @t76 @t106 @t107 @t100 @t91))) % 25.48/25.80 (step @p233 :rule equiv_elim2 :premises (@p181)) % 25.48/25.80 (step @p234 :rule chain_m_resolution :premises (@p233 @p232) :args (@t111 @t51 (@list @t92))) % 25.48/25.80 (step @p235 :rule bool-double-not-elim :args (@t78)) % 25.48/25.80 (step @p236 :rule nary_cong :premises (@p143 @p235) :args ((or @t80 (not @t79)))) % 25.48/25.80 (step @p237 :rule cnf_or_neg :args (@t80 0)) % 25.48/25.80 (step @p238 :rule eq_resolve :premises (@p237 @p236)) % 25.48/25.80 (step @p239 :rule reordering :premises (@p238) :args ((or @t78 @t80))) % 25.48/25.80 (step @p240 :rule chain_m_resolution :premises (@p239 @p141) :args (@t78 @t51 @t89)) % 25.48/25.80 (step @p241 :rule bool-double-not-elim :args (@t92)) % 25.48/25.80 (step @p242 :rule refl :args (@t100)) % 25.48/25.80 (step @p243 :rule nary_cong :premises (@p242 @p123 @p241) :args ((or @t100 @t79 (not @t99)))) % 25.48/25.80 (step @p244 :rule cnf_and_neg :args (@t100)) % 25.48/25.80 (step @p245 :rule eq_resolve :premises (@p244 @p243)) % 25.48/25.80 (step @p246 :rule reordering :premises (@p245) :args ((or @t79 @t92 @t100))) % 25.48/25.80 (step @p247 :rule chain_m_resolution :premises (@p246 @p240 @p232) :args (@t100 (@list false true) (@list @t78 @t92))) % 25.48/25.80 (step @p248 :rule cnf_equiv_pos1 :args (@t107)) % 25.48/25.80 (step @p249 :rule reordering :premises (@p248) :args ((or @t106 @t101 @t108))) % 25.48/25.80 (step @p250 :rule chain_m_resolution :premises (@p249 @p247 @p203) :args (@t106 (@list false false) (@list @t100 @t107))) % 25.48/25.80 (step @p251 :rule refl :args (@t109)) % 25.48/25.80 (step @p252 :rule bool-double-not-elim :args (@t91)) % 25.48/25.80 (step @p253 :rule refl :args (@t112)) % 25.48/25.80 (step @p254 :rule refl :args (@t77)) % 25.48/25.80 (step @p255 :rule nary_cong :premises (@p254 @p253 @p252 @p251) :args ((or @t77 @t112 (not @t111) @t109))) % 25.48/25.80 (assume-push @p299 @t76) % 25.48/25.80 (assume-push @p300 @t95) % 25.48/25.80 (assume-push @p301 @t111) % 25.48/25.80 (assume-push @p302 @t111) % 25.48/25.80 (assume-push @p303 @t95) % 25.48/25.80 (assume-push @p304 @t76) % 25.48/25.80 (step @p262 :rule false_intro :premises (@p301)) % 25.48/25.80 (step @p213 :rule symm :premises (@p148)) % 25.48/25.80 (step @p214 :rule trans :premises (@p213 @p180)) % 25.48/25.80 (step @p215 :rule ho_cong :premises (@p214 @p171)) % 25.48/25.80 (step @p263 :rule trans :premises (@p215 @p262)) % 25.48/25.80 (step @p264 :rule false_elim :premises (@p263)) % 25.48/25.80 (step-pop @p305 :rule scope :premises (@p264)) % 25.48/25.80 (step-pop @p306 :rule scope :premises (@p305)) % 25.48/25.80 (step-pop @p307 :rule scope :premises (@p306)) % 25.48/25.80 (step @p265 :rule process_scope :premises (@p307) :args (@t109)) % 25.48/25.80 (step @p269 :rule and_intro :premises (@p301 @p180 @p148)) % 25.48/25.80 (step @p270 :rule modus_ponens :premises (@p269 @p265)) % 25.48/25.80 (step-pop @p308 :rule scope :premises (@p270)) % 25.48/25.80 (step-pop @p309 :rule scope :premises (@p308)) % 25.48/25.80 (step-pop @p310 :rule scope :premises (@p309)) % 25.48/25.80 (step @p271 :rule process_scope :premises (@p310) :args (@t109)) % 25.48/25.80 (step @p275 :rule implies_elim :premises (@p271)) % 25.48/25.80 (step @p276 :rule cnf_and_neg :args (@t113)) % 25.48/25.80 (step @p277 :rule resolution :premises (@p276 @p275) :args (true @t113)) % 25.48/25.80 (step @p278 :rule eq_resolve :premises (@p277 @p255)) % 25.48/25.80 (step @p279 :rule reordering :premises (@p278) :args ((or @t77 @t91 @t112 @t109))) % 25.48/25.80 (step @p280 false :rule chain_m_resolution :premises (@p279 @p250 @p234 @p180 @p148) :args (false (@list false true false false) (@list @t106 @t91 @t95 @t76))) % 25.48/25.80 ) % 25.48/25.80 % SZS output end Proof % 25.48/25.80 % cvc5 exiting %------------------------------------------------------------------------------