%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYN417+1 : TPTP v9.2.1. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n012.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 09:08:50 AM UTC 2026 % Result : Theorem 0.17s 0.37s % Output : Proof 0.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SYN417+1 : TPTP v9.2.1. Released v2.0.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n012.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 23:27:33 EDT 2026 % 0.07/0.25 % CPUTime : % 0.17/0.33 %----Proving TF0_NAR, FOF, or CNF % 0.17/0.37 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.17/0.37 % SZS status Theorem % 0.17/0.37 % SZS output start Proof % 0.17/0.37 ( % 0.17/0.37 (declare-sort $$unsorted 0) % 0.17/0.37 (declare-const tptp.g (-> $$unsorted $$unsorted)) % 0.17/0.37 (declare-const tptp.f (-> $$unsorted $$unsorted)) % 0.17/0.37 (define @t1 () (@var "Y" $$unsorted)) % 0.17/0.37 (define @t2 () (@var "X" $$unsorted)) % 0.17/0.37 (define @t3 () (= @t2 @t1)) % 0.17/0.37 (define @t4 () (= @t1 (tptp.g (tptp.f @t1)))) % 0.17/0.37 (define @t5 () (@list @t1)) % 0.17/0.37 (define @t6 () (forall @t5 (=> @t4 @t3))) % 0.17/0.37 (define @t7 () (= @t2 (tptp.g (tptp.f @t2)))) % 0.17/0.37 (define @t8 () (and @t7 @t6)) % 0.17/0.37 (define @t9 () (@list @t2)) % 0.17/0.37 (define @t10 () (exists @t9 @t8)) % 0.17/0.37 (define @t11 () (= @t1 (tptp.f (tptp.g @t1)))) % 0.17/0.37 (define @t12 () (forall @t5 (=> @t11 @t3))) % 0.17/0.37 (define @t13 () (= @t2 (tptp.f (tptp.g @t2)))) % 0.17/0.37 (define @t14 () (and @t13 @t12)) % 0.17/0.37 (define @t15 () (exists @t9 @t14)) % 0.17/0.37 (define @t16 () (= @t15 @t10)) % 0.17/0.37 (define @t17 () (not @t16)) % 0.17/0.37 (define @t18 () (not @t4)) % 0.17/0.37 (define @t19 () (forall @t5 (or @t18 @t3))) % 0.17/0.37 (define @t20 () (forall @t9 (or (not @t7) (not @t19)))) % 0.17/0.37 (define @t21 () (not @t11)) % 0.17/0.37 (define @t22 () (forall @t5 (or @t21 @t3))) % 0.17/0.37 (define @t23 () (forall @t9 (or (not @t13) (not @t22)))) % 0.17/0.37 (define @t24 () (not @t20)) % 0.17/0.37 (define @t25 () (not @t24)) % 0.17/0.37 (define @t26 () (not @t23)) % 0.17/0.37 (define @t27 () (not @t26)) % 0.17/0.37 (define @t28 () (and @t7 @t19)) % 0.17/0.37 (define @t29 () (forall @t9 (not @t28))) % 0.17/0.37 (define @t30 () (not @t29)) % 0.17/0.37 (define @t31 () (and @t13 @t22)) % 0.17/0.37 (define @t32 () (forall @t9 (not @t31))) % 0.17/0.37 (define @t33 () (not @t32)) % 0.17/0.37 (define @t34 () (@quantifiers_skolemize @t23 0)) % 0.17/0.37 (define @t35 () (forall @t5 (or @t21 (= @t1 @t34)))) % 0.17/0.37 (define @t36 () (not @t35)) % 0.17/0.37 (define @t37 () (tptp.g @t34)) % 0.17/0.37 (define @t38 () (tptp.f @t37)) % 0.17/0.37 (define @t39 () (= @t34 @t38)) % 0.17/0.37 (define @t40 () (not @t39)) % 0.17/0.37 (define @t41 () (or @t40 @t36)) % 0.17/0.37 (define @t42 () (not @t41)) % 0.17/0.37 (define @t43 () (or @t21 (= @t34 @t1))) % 0.17/0.37 (define @t44 () (forall @t5 @t43)) % 0.17/0.37 (define @t45 () (not @t44)) % 0.17/0.37 (define @t46 () (or @t40 @t45)) % 0.17/0.37 (define @t47 () (not @t46)) % 0.17/0.37 (define @t48 () (= @t37 (tptp.g @t38))) % 0.17/0.37 (define @t49 () (or @t18 (= @t37 @t1))) % 0.17/0.37 (define @t50 () (forall @t5 @t49)) % 0.17/0.37 (define @t51 () (not @t50)) % 0.17/0.37 (define @t52 () (not @t48)) % 0.17/0.37 (define @t53 () (or @t52 @t51)) % 0.17/0.37 (define @t54 () (forall @t5 (or @t18 (= @t1 @t37)))) % 0.17/0.37 (define @t55 () (not @t54)) % 0.17/0.37 (define @t56 () (or @t52 @t55)) % 0.17/0.37 (define @t57 () (@quantifiers_skolemize @t54 0)) % 0.17/0.37 (define @t58 () (= @t37 @t57)) % 0.17/0.37 (define @t59 () (tptp.f @t57)) % 0.17/0.37 (define @t60 () (tptp.g @t59)) % 0.17/0.37 (define @t61 () (= @t57 @t60)) % 0.17/0.37 (define @t62 () (not @t61)) % 0.17/0.37 (define @t63 () (or @t62 @t58)) % 0.17/0.37 (define @t64 () (not @t63)) % 0.17/0.37 (define @t65 () (or @t62 (= @t57 @t37))) % 0.17/0.37 (define @t66 () (not @t65)) % 0.17/0.37 (define @t67 () (= @t59 (tptp.f @t60))) % 0.17/0.37 (define @t68 () (not @t67)) % 0.17/0.37 (define @t69 () (or @t68 (= @t59 @t34))) % 0.17/0.37 (define @t70 () (= @t34 @t59)) % 0.17/0.37 (define @t71 () (or @t68 @t70)) % 0.17/0.37 (define @t72 () (and @t61 @t70)) % 0.17/0.37 (define @t73 () (@quantifiers_skolemize @t20 0)) % 0.17/0.37 (define @t74 () (tptp.f @t73)) % 0.17/0.37 (define @t75 () (or @t21 (= @t74 @t1))) % 0.17/0.37 (define @t76 () (forall @t5 @t75)) % 0.17/0.37 (define @t77 () (not @t76)) % 0.17/0.37 (define @t78 () (tptp.g @t74)) % 0.17/0.37 (define @t79 () (= @t74 (tptp.f @t78))) % 0.17/0.37 (define @t80 () (not @t79)) % 0.17/0.37 (define @t81 () (or @t80 @t77)) % 0.17/0.37 (define @t82 () (forall @t5 (or @t21 (= @t1 @t74)))) % 0.17/0.37 (define @t83 () (not @t82)) % 0.17/0.37 (define @t84 () (or @t80 @t83)) % 0.17/0.37 (define @t85 () (@list false)) % 0.17/0.37 (define @t86 () (@list @t23)) % 0.17/0.37 (define @t87 () (forall @t5 (or @t18 (= @t1 @t73)))) % 0.17/0.37 (define @t88 () (not @t87)) % 0.17/0.37 (define @t89 () (= @t73 @t78)) % 0.17/0.37 (define @t90 () (not @t89)) % 0.17/0.37 (define @t91 () (or @t90 @t88)) % 0.17/0.37 (define @t92 () (not @t91)) % 0.17/0.37 (define @t93 () (or @t18 (= @t73 @t1))) % 0.17/0.37 (define @t94 () (forall @t5 @t93)) % 0.17/0.37 (define @t95 () (not @t94)) % 0.17/0.37 (define @t96 () (or @t90 @t95)) % 0.17/0.37 (define @t97 () (not @t96)) % 0.17/0.37 (define @t98 () (@list true)) % 0.17/0.37 (define @t99 () (@list @t91)) % 0.17/0.37 (define @t100 () (@list false false)) % 0.17/0.37 (define @t101 () (@quantifiers_skolemize @t82 0)) % 0.17/0.37 (define @t102 () (= @t74 @t101)) % 0.17/0.37 (define @t103 () (tptp.g @t101)) % 0.17/0.37 (define @t104 () (tptp.f @t103)) % 0.17/0.37 (define @t105 () (= @t101 @t104)) % 0.17/0.37 (define @t106 () (not @t105)) % 0.17/0.37 (define @t107 () (or @t106 @t102)) % 0.17/0.37 (define @t108 () (not @t107)) % 0.17/0.37 (define @t109 () (or @t106 (= @t101 @t74))) % 0.17/0.37 (define @t110 () (not @t109)) % 0.17/0.37 (define @t111 () (@list @t107)) % 0.17/0.37 (define @t112 () (= @t103 (tptp.g @t104))) % 0.17/0.37 (define @t113 () (not @t112)) % 0.17/0.37 (define @t114 () (or @t113 (= @t103 @t73))) % 0.17/0.37 (define @t115 () (= @t73 @t103)) % 0.17/0.37 (define @t116 () (or @t113 @t115)) % 0.17/0.37 (define @t117 () (and @t105 @t115)) % 0.17/0.37 (assume @p1 @t17) % 0.17/0.37 (assume @p2 true) % 0.17/0.37 (step @p3 :rule bool-double-not-elim :args (@t20)) % 0.17/0.37 (step @p4 :rule bool-double-not-elim :args (@t23)) % 0.17/0.37 (step @p5 :rule nary_cong :premises (@p4 @p3) :args ((or @t27 @t25))) % 0.17/0.37 (step @p6 :rule bool-and-de-morgan :args (@t7 @t19 true)) % 0.17/0.37 (step @p7 :rule cong :premises (@p6) :args (@t29)) % 0.17/0.37 (step @p8 :rule cong :premises (@p7) :args (@t30)) % 0.17/0.37 (step @p9 :rule exists-elim :args ((= (exists @t9 @t28) @t30))) % 0.17/0.37 (step @p10 :rule trans :premises (@p9 @p8)) % 0.17/0.37 (step @p11 :rule bool-impl-elim :args (@t4 @t3)) % 0.17/0.37 (step @p12 :rule cong :premises (@p11) :args (@t6)) % 0.17/0.37 (step @p13 :rule refl :args (@t7)) % 0.17/0.37 (step @p14 :rule nary_cong :premises (@p13 @p12) :args (@t8)) % 0.17/0.37 (step @p15 :rule cong :premises (@p14) :args (@t10)) % 0.17/0.37 (step @p16 :rule trans :premises (@p15 @p10)) % 0.17/0.37 (step @p17 :rule bool-and-de-morgan :args (@t13 @t22 true)) % 0.17/0.37 (step @p18 :rule cong :premises (@p17) :args (@t32)) % 0.17/0.37 (step @p19 :rule cong :premises (@p18) :args (@t33)) % 0.17/0.37 (step @p20 :rule exists-elim :args ((= (exists @t9 @t31) @t33))) % 0.17/0.37 (step @p21 :rule trans :premises (@p20 @p19)) % 0.17/0.37 (step @p22 :rule bool-impl-elim :args (@t11 @t3)) % 0.17/0.37 (step @p23 :rule cong :premises (@p22) :args (@t12)) % 0.17/0.37 (step @p24 :rule refl :args (@t13)) % 0.17/0.37 (step @p25 :rule nary_cong :premises (@p24 @p23) :args (@t14)) % 0.17/0.37 (step @p26 :rule cong :premises (@p25) :args (@t15)) % 0.17/0.37 (step @p27 :rule trans :premises (@p26 @p21)) % 0.17/0.37 (step @p28 :rule cong :premises (@p27 @p16) :args (@t16)) % 0.17/0.37 (step @p29 :rule cong :premises (@p28) :args (@t17)) % 0.17/0.37 (step @p30 :rule eq_resolve :premises (@p1 @p29)) % 0.17/0.37 (step @p31 :rule not_equiv_elim2 :premises (@p30)) % 0.17/0.37 (step @p32 :rule eq_resolve :premises (@p31 @p5)) % 0.17/0.37 (step @p33 :rule refl :args (@t42)) % 0.17/0.37 (step @p34 :rule nary_cong :premises (@p4 @p33) :args ((or @t27 @t42))) % 0.17/0.37 (step @p35 :rule eq-symm :args (@t34 @t1)) % 0.17/0.37 (step @p36 :rule refl :args (@t21)) % 0.17/0.37 (step @p37 :rule nary_cong :premises (@p36 @p35) :args (@t43)) % 0.17/0.37 (step @p38 :rule cong :premises (@p37) :args (@t44)) % 0.17/0.37 (step @p39 :rule cong :premises (@p38) :args (@t45)) % 0.17/0.37 (step @p40 :rule refl :args (@t40)) % 0.17/0.37 (step @p41 :rule nary_cong :premises (@p40 @p39) :args (@t46)) % 0.17/0.37 (step @p42 :rule cong :premises (@p41) :args (@t47)) % 0.17/0.37 (step @p43 :rule refl :args (@t26)) % 0.17/0.37 (step @p44 :rule cong :premises (@p43 @p42) :args ((=> @t26 @t47))) % 0.17/0.37 (assume-push @p287 @t26) % 0.17/0.37 (step @p46 :rule skolemize :premises (@p287)) % 0.17/0.37 (step-pop @p288 :rule scope :premises (@p46)) % 0.17/0.37 (step @p47 :rule process_scope :premises (@p288) :args (@t47)) % 0.17/0.37 (step @p49 :rule eq_resolve :premises (@p47 @p44)) % 0.17/0.37 (step @p50 :rule implies_elim :premises (@p49)) % 0.17/0.37 (step @p51 :rule eq_resolve :premises (@p50 @p34)) % 0.17/0.37 (step @p52 :rule bool-double-not-elim :args (@t39)) % 0.17/0.37 (step @p53 :rule refl :args (@t41)) % 0.17/0.37 (step @p54 :rule nary_cong :premises (@p53 @p52) :args ((or @t41 (not @t40)))) % 0.17/0.37 (step @p55 :rule cnf_or_neg :args (@t41 0)) % 0.17/0.37 (step @p56 :rule eq_resolve :premises (@p55 @p54)) % 0.17/0.37 (step @p57 :rule reordering :premises (@p56) :args ((or @t39 @t41))) % 0.17/0.37 (step @p58 :rule bool-double-not-elim :args (@t35)) % 0.17/0.37 (step @p59 :rule nary_cong :premises (@p53 @p58) :args ((or @t41 (not @t36)))) % 0.17/0.37 (step @p60 :rule cnf_or_neg :args (@t41 1)) % 0.17/0.37 (step @p61 :rule eq_resolve :premises (@p60 @p59)) % 0.17/0.37 (step @p62 :rule reordering :premises (@p61) :args ((or @t35 @t41))) % 0.17/0.37 (assume-push @p289 @t39) % 0.17/0.37 (assume-push @p290 @t39) % 0.17/0.37 (step @p65 :rule cong :premises (@p289) :args (@t37)) % 0.17/0.37 (step-pop @p291 :rule scope :premises (@p65)) % 0.17/0.37 (step @p66 :rule process_scope :premises (@p291) :args (@t48)) % 0.17/0.37 (step @p68 :rule modus_ponens :premises (@p289 @p66)) % 0.17/0.37 (step-pop @p292 :rule scope :premises (@p68)) % 0.17/0.37 (step @p69 :rule process_scope :premises (@p292) :args (@t48)) % 0.17/0.37 (step @p71 :rule implies_elim :premises (@p69)) % 0.17/0.37 (step @p72 :rule eq-symm :args (@t37 @t1)) % 0.17/0.37 (step @p73 :rule refl :args (@t18)) % 0.17/0.37 (step @p74 :rule nary_cong :premises (@p73 @p72) :args (@t49)) % 0.17/0.37 (step @p75 :rule cong :premises (@p74) :args (@t50)) % 0.17/0.37 (step @p76 :rule cong :premises (@p75) :args (@t51)) % 0.17/0.37 (step @p77 :rule refl :args (@t52)) % 0.17/0.37 (step @p78 :rule nary_cong :premises (@p77 @p76) :args (@t53)) % 0.17/0.37 (step @p79 :rule refl :args (@t20)) % 0.17/0.37 (step @p80 :rule cong :premises (@p79 @p78) :args ((=> @t20 @t53))) % 0.17/0.37 (assume-push @p293 @t20) % 0.17/0.37 (step @p82 :rule instantiate :premises (@p293) :args ((@list @t37))) % 0.17/0.37 (step-pop @p294 :rule scope :premises (@p82)) % 0.17/0.37 (step @p83 :rule process_scope :premises (@p294) :args (@t53)) % 0.17/0.37 (step @p85 :rule eq_resolve :premises (@p83 @p80)) % 0.17/0.37 (step @p86 :rule implies_elim :premises (@p85)) % 0.17/0.37 (step @p87 :rule cnf_or_pos :args (@t56)) % 0.17/0.37 (step @p88 :rule reordering :premises (@p87) :args ((or @t52 @t55 (not @t56)))) % 0.17/0.37 (step @p89 :rule refl :args (@t64)) % 0.17/0.37 (step @p90 :rule bool-double-not-elim :args (@t54)) % 0.17/0.37 (step @p91 :rule nary_cong :premises (@p90 @p89) :args ((or (not @t55) @t64))) % 0.17/0.37 (step @p92 :rule eq-symm :args (@t57 @t37)) % 0.17/0.37 (step @p93 :rule refl :args (@t62)) % 0.17/0.37 (step @p94 :rule nary_cong :premises (@p93 @p92) :args (@t65)) % 0.17/0.37 (step @p95 :rule cong :premises (@p94) :args (@t66)) % 0.17/0.37 (step @p96 :rule refl :args (@t55)) % 0.17/0.37 (step @p97 :rule cong :premises (@p96 @p95) :args ((=> @t55 @t66))) % 0.17/0.37 (assume-push @p295 @t55) % 0.17/0.37 (step @p99 :rule skolemize :premises (@p295)) % 0.17/0.37 (step-pop @p296 :rule scope :premises (@p99)) % 0.17/0.37 (step @p100 :rule process_scope :premises (@p296) :args (@t66)) % 0.17/0.37 (step @p102 :rule eq_resolve :premises (@p100 @p97)) % 0.17/0.37 (step @p103 :rule implies_elim :premises (@p102)) % 0.17/0.37 (step @p104 :rule eq_resolve :premises (@p103 @p91)) % 0.17/0.37 (step @p105 :rule bool-double-not-elim :args (@t61)) % 0.17/0.37 (step @p106 :rule refl :args (@t63)) % 0.17/0.37 (step @p107 :rule nary_cong :premises (@p106 @p105) :args ((or @t63 (not @t62)))) % 0.17/0.37 (step @p108 :rule cnf_or_neg :args (@t63 0)) % 0.17/0.37 (step @p109 :rule eq_resolve :premises (@p108 @p107)) % 0.17/0.37 (step @p110 :rule reordering :premises (@p109) :args ((or @t61 @t63))) % 0.17/0.37 (step @p111 :rule cnf_or_neg :args (@t63 1)) % 0.17/0.37 (assume-push @p297 @t61) % 0.17/0.37 (assume-push @p298 @t61) % 0.17/0.37 (step @p114 :rule cong :premises (@p297) :args (@t59)) % 0.17/0.37 (step-pop @p299 :rule scope :premises (@p114)) % 0.17/0.37 (step @p115 :rule process_scope :premises (@p299) :args (@t67)) % 0.17/0.37 (step @p117 :rule modus_ponens :premises (@p297 @p115)) % 0.17/0.37 (step-pop @p300 :rule scope :premises (@p117)) % 0.17/0.37 (step @p118 :rule process_scope :premises (@p300) :args (@t67)) % 0.17/0.37 (step @p120 :rule implies_elim :premises (@p118)) % 0.17/0.37 (step @p121 :rule eq-symm :args (@t59 @t34)) % 0.17/0.37 (step @p122 :rule refl :args (@t68)) % 0.17/0.37 (step @p123 :rule nary_cong :premises (@p122 @p121) :args (@t69)) % 0.17/0.37 (step @p124 :rule refl :args (@t35)) % 0.17/0.37 (step @p125 :rule cong :premises (@p124 @p123) :args ((=> @t35 @t69))) % 0.17/0.37 (assume-push @p301 @t35) % 0.17/0.37 (step @p127 :rule instantiate :premises (@p301) :args ((@list @t59))) % 0.17/0.37 (step-pop @p302 :rule scope :premises (@p127)) % 0.17/0.37 (step @p128 :rule process_scope :premises (@p302) :args (@t69)) % 0.17/0.37 (step @p130 :rule eq_resolve :premises (@p128 @p125)) % 0.17/0.37 (step @p131 :rule implies_elim :premises (@p130)) % 0.17/0.37 (step @p132 :rule cnf_or_pos :args (@t71)) % 0.17/0.37 (step @p133 :rule reordering :premises (@p132) :args ((or @t68 @t70 (not @t71)))) % 0.17/0.37 (assume-push @p303 @t61) % 0.17/0.37 (assume-push @p304 @t70) % 0.17/0.37 (assume-push @p305 @t61) % 0.17/0.37 (assume-push @p306 @t70) % 0.17/0.37 (step @p138 :rule symm :premises (@p303)) % 0.17/0.37 (step @p139 :rule cong :premises (@p304) :args (@t37)) % 0.17/0.37 (step @p140 :rule trans :premises (@p139 @p138)) % 0.17/0.37 (step-pop @p307 :rule scope :premises (@p140)) % 0.17/0.37 (step-pop @p308 :rule scope :premises (@p307)) % 0.17/0.37 (step @p141 :rule process_scope :premises (@p308) :args (@t58)) % 0.17/0.37 (step @p144 :rule and_intro :premises (@p303 @p304)) % 0.17/0.37 (step @p145 :rule modus_ponens :premises (@p144 @p141)) % 0.17/0.37 (step-pop @p309 :rule scope :premises (@p145)) % 0.17/0.37 (step-pop @p310 :rule scope :premises (@p309)) % 0.17/0.37 (step @p146 :rule process_scope :premises (@p310) :args (@t58)) % 0.17/0.37 (step @p149 :rule implies_elim :premises (@p146)) % 0.17/0.37 (step @p150 :rule cnf_and_neg :args (@t72)) % 0.17/0.37 (step @p151 :rule resolution :premises (@p150 @p149) :args (true @t72)) % 0.17/0.37 (step @p152 :rule reordering :premises (@p151) :args ((or @t62 @t58 (not @t70)))) % 0.17/0.37 (step @p153 :rule chain_m_resolution :premises (@p152 @p133 @p131 @p120 @p111 @p110 @p104 @p88 @p86 @p71 @p62 @p57 @p51 @p32) :args (@t23 (@list false false false true false true true false false false false true false) (@list @t70 @t71 @t67 @t58 @t61 @t63 @t54 @t56 @t48 @t35 @t39 @t41 @t20))) % 0.17/0.37 (step @p154 :rule eq-symm :args (@t74 @t1)) % 0.17/0.37 (step @p155 :rule nary_cong :premises (@p36 @p154) :args (@t75)) % 0.17/0.37 (step @p156 :rule cong :premises (@p155) :args (@t76)) % 0.17/0.37 (step @p157 :rule cong :premises (@p156) :args (@t77)) % 0.17/0.37 (step @p158 :rule refl :args (@t80)) % 0.17/0.37 (step @p159 :rule nary_cong :premises (@p158 @p157) :args (@t81)) % 0.17/0.37 (step @p160 :rule refl :args (@t23)) % 0.17/0.37 (step @p161 :rule cong :premises (@p160 @p159) :args ((=> @t23 @t81))) % 0.17/0.37 (assume-push @p311 @t23) % 0.17/0.37 (step @p163 :rule instantiate :premises (@p311) :args ((@list @t74))) % 0.17/0.37 (step-pop @p312 :rule scope :premises (@p163)) % 0.17/0.37 (step @p164 :rule process_scope :premises (@p312) :args (@t81)) % 0.17/0.37 (step @p166 :rule eq_resolve :premises (@p164 @p161)) % 0.17/0.37 (step @p167 :rule implies_elim :premises (@p166)) % 0.17/0.37 (step @p168 :rule chain_m_resolution :premises (@p167 @p153) :args (@t84 @t85 @t86)) % 0.17/0.37 (step @p169 :rule not_equiv_elim1 :premises (@p30)) % 0.17/0.37 (step @p170 :rule chain_m_resolution :premises (@p169 @p153) :args (@t24 @t85 @t86)) % 0.17/0.37 (step @p171 :rule refl :args (@t92)) % 0.17/0.37 (step @p172 :rule nary_cong :premises (@p3 @p171) :args ((or @t25 @t92))) % 0.17/0.37 (step @p173 :rule eq-symm :args (@t73 @t1)) % 0.17/0.37 (step @p174 :rule nary_cong :premises (@p73 @p173) :args (@t93)) % 0.17/0.37 (step @p175 :rule cong :premises (@p174) :args (@t94)) % 0.17/0.37 (step @p176 :rule cong :premises (@p175) :args (@t95)) % 0.17/0.37 (step @p177 :rule refl :args (@t90)) % 0.17/0.37 (step @p178 :rule nary_cong :premises (@p177 @p176) :args (@t96)) % 0.17/0.37 (step @p179 :rule cong :premises (@p178) :args (@t97)) % 0.17/0.37 (step @p180 :rule refl :args (@t24)) % 0.17/0.37 (step @p181 :rule cong :premises (@p180 @p179) :args ((=> @t24 @t97))) % 0.17/0.37 (assume-push @p313 @t24) % 0.17/0.37 (step @p183 :rule skolemize :premises (@p313)) % 0.17/0.37 (step-pop @p314 :rule scope :premises (@p183)) % 0.17/0.37 (step @p184 :rule process_scope :premises (@p314) :args (@t97)) % 0.17/0.37 (step @p186 :rule eq_resolve :premises (@p184 @p181)) % 0.17/0.37 (step @p187 :rule implies_elim :premises (@p186)) % 0.17/0.37 (step @p188 :rule eq_resolve :premises (@p187 @p172)) % 0.17/0.37 (step @p189 :rule chain_m_resolution :premises (@p188 @p170) :args (@t92 @t98 (@list @t20))) % 0.17/0.37 (step @p190 :rule bool-double-not-elim :args (@t89)) % 0.17/0.37 (step @p191 :rule refl :args (@t91)) % 0.17/0.37 (step @p192 :rule nary_cong :premises (@p191 @p190) :args ((or @t91 (not @t90)))) % 0.17/0.37 (step @p193 :rule cnf_or_neg :args (@t91 0)) % 0.17/0.37 (step @p194 :rule eq_resolve :premises (@p193 @p192)) % 0.17/0.37 (step @p195 :rule reordering :premises (@p194) :args ((or @t89 @t91))) % 0.17/0.37 (step @p196 :rule chain_m_resolution :premises (@p195 @p189) :args (@t89 @t98 @t99)) % 0.17/0.37 (assume-push @p315 @t89) % 0.17/0.37 (assume-push @p316 @t89) % 0.17/0.37 (step @p199 :rule cong :premises (@p315) :args (@t74)) % 0.17/0.37 (step-pop @p317 :rule scope :premises (@p199)) % 0.17/0.37 (step @p200 :rule process_scope :premises (@p317) :args (@t79)) % 0.17/0.37 (step @p202 :rule modus_ponens :premises (@p315 @p200)) % 0.17/0.37 (step-pop @p318 :rule scope :premises (@p202)) % 0.17/0.37 (step @p203 :rule process_scope :premises (@p318) :args (@t79)) % 0.17/0.37 (step @p205 :rule implies_elim :premises (@p203)) % 0.17/0.37 (step @p206 :rule chain_m_resolution :premises (@p205 @p196) :args (@t79 @t85 (@list @t89))) % 0.17/0.37 (step @p207 :rule cnf_or_pos :args (@t84)) % 0.17/0.37 (step @p208 :rule reordering :premises (@p207) :args ((or @t80 @t83 (not @t84)))) % 0.17/0.37 (step @p209 :rule chain_m_resolution :premises (@p208 @p206 @p168) :args (@t83 @t100 (@list @t79 @t84))) % 0.17/0.37 (step @p210 :rule refl :args (@t108)) % 0.17/0.37 (step @p211 :rule bool-double-not-elim :args (@t82)) % 0.17/0.37 (step @p212 :rule nary_cong :premises (@p211 @p210) :args ((or (not @t83) @t108))) % 0.17/0.37 (step @p213 :rule eq-symm :args (@t101 @t74)) % 0.17/0.37 (step @p214 :rule refl :args (@t106)) % 0.17/0.37 (step @p215 :rule nary_cong :premises (@p214 @p213) :args (@t109)) % 0.17/0.37 (step @p216 :rule cong :premises (@p215) :args (@t110)) % 0.17/0.37 (step @p217 :rule refl :args (@t83)) % 0.17/0.37 (step @p218 :rule cong :premises (@p217 @p216) :args ((=> @t83 @t110))) % 0.17/0.37 (assume-push @p319 @t83) % 0.17/0.37 (step @p220 :rule skolemize :premises (@p319)) % 0.17/0.37 (step-pop @p320 :rule scope :premises (@p220)) % 0.17/0.37 (step @p221 :rule process_scope :premises (@p320) :args (@t110)) % 0.17/0.37 (step @p223 :rule eq_resolve :premises (@p221 @p218)) % 0.17/0.37 (step @p224 :rule implies_elim :premises (@p223)) % 0.17/0.37 (step @p225 :rule eq_resolve :premises (@p224 @p212)) % 0.17/0.37 (step @p226 :rule chain_m_resolution :premises (@p225 @p209) :args (@t108 @t98 (@list @t82))) % 0.17/0.37 (step @p227 :rule bool-double-not-elim :args (@t105)) % 0.17/0.37 (step @p228 :rule refl :args (@t107)) % 0.17/0.37 (step @p229 :rule nary_cong :premises (@p228 @p227) :args ((or @t107 (not @t106)))) % 0.17/0.37 (step @p230 :rule cnf_or_neg :args (@t107 0)) % 0.17/0.37 (step @p231 :rule eq_resolve :premises (@p230 @p229)) % 0.17/0.37 (step @p232 :rule reordering :premises (@p231) :args ((or @t105 @t107))) % 0.17/0.37 (step @p233 :rule chain_m_resolution :premises (@p232 @p226) :args (@t105 @t98 @t111)) % 0.17/0.37 (step @p234 :rule cnf_or_neg :args (@t107 1)) % 0.17/0.37 (step @p235 :rule chain_m_resolution :premises (@p234 @p226) :args ((not @t102) @t98 @t111)) % 0.17/0.37 (step @p236 :rule bool-double-not-elim :args (@t87)) % 0.17/0.37 (step @p237 :rule nary_cong :premises (@p191 @p236) :args ((or @t91 (not @t88)))) % 0.17/0.37 (step @p238 :rule cnf_or_neg :args (@t91 1)) % 0.17/0.37 (step @p239 :rule eq_resolve :premises (@p238 @p237)) % 0.17/0.37 (step @p240 :rule reordering :premises (@p239) :args ((or @t87 @t91))) % 0.17/0.37 (step @p241 :rule chain_m_resolution :premises (@p240 @p189) :args (@t87 @t98 @t99)) % 0.17/0.37 (step @p242 :rule eq-symm :args (@t103 @t73)) % 0.17/0.37 (step @p243 :rule refl :args (@t113)) % 0.17/0.37 (step @p244 :rule nary_cong :premises (@p243 @p242) :args (@t114)) % 0.17/0.37 (step @p245 :rule refl :args (@t87)) % 0.17/0.37 (step @p246 :rule cong :premises (@p245 @p244) :args ((=> @t87 @t114))) % 0.17/0.37 (assume-push @p321 @t87) % 0.17/0.37 (step @p248 :rule instantiate :premises (@p321) :args ((@list @t103))) % 0.17/0.37 (step-pop @p322 :rule scope :premises (@p248)) % 0.17/0.37 (step @p249 :rule process_scope :premises (@p322) :args (@t114)) % 0.17/0.37 (step @p251 :rule eq_resolve :premises (@p249 @p246)) % 0.17/0.37 (step @p252 :rule implies_elim :premises (@p251)) % 0.17/0.37 (step @p253 :rule chain_m_resolution :premises (@p252 @p241) :args (@t116 @t85 (@list @t87))) % 0.17/0.37 (assume-push @p323 @t105) % 0.17/0.37 (assume-push @p324 @t105) % 0.17/0.37 (step @p256 :rule cong :premises (@p323) :args (@t103)) % 0.17/0.37 (step-pop @p325 :rule scope :premises (@p256)) % 0.17/0.37 (step @p257 :rule process_scope :premises (@p325) :args (@t112)) % 0.17/0.37 (step @p259 :rule modus_ponens :premises (@p323 @p257)) % 0.17/0.37 (step-pop @p326 :rule scope :premises (@p259)) % 0.17/0.37 (step @p260 :rule process_scope :premises (@p326) :args (@t112)) % 0.17/0.37 (step @p262 :rule implies_elim :premises (@p260)) % 0.17/0.37 (step @p263 :rule chain_m_resolution :premises (@p262 @p233) :args (@t112 @t85 (@list @t105))) % 0.17/0.37 (step @p264 :rule cnf_or_pos :args (@t116)) % 0.17/0.37 (step @p265 :rule reordering :premises (@p264) :args ((or @t113 @t115 (not @t116)))) % 0.17/0.37 (step @p266 :rule chain_m_resolution :premises (@p265 @p263 @p253) :args (@t115 @t100 (@list @t112 @t116))) % 0.17/0.37 (assume-push @p327 @t105) % 0.17/0.37 (assume-push @p328 @t115) % 0.17/0.37 (assume-push @p329 @t105) % 0.17/0.37 (assume-push @p330 @t115) % 0.17/0.37 (step @p271 :rule symm :premises (@p327)) % 0.17/0.37 (step @p272 :rule cong :premises (@p328) :args (@t74)) % 0.17/0.37 (step @p273 :rule trans :premises (@p272 @p271)) % 0.17/0.37 (step-pop @p331 :rule scope :premises (@p273)) % 0.17/0.37 (step-pop @p332 :rule scope :premises (@p331)) % 0.17/0.37 (step @p274 :rule process_scope :premises (@p332) :args (@t102)) % 0.17/0.37 (step @p277 :rule and_intro :premises (@p327 @p328)) % 0.17/0.37 (step @p278 :rule modus_ponens :premises (@p277 @p274)) % 0.17/0.37 (step-pop @p333 :rule scope :premises (@p278)) % 0.17/0.37 (step-pop @p334 :rule scope :premises (@p333)) % 0.17/0.37 (step @p279 :rule process_scope :premises (@p334) :args (@t102)) % 0.17/0.37 (step @p282 :rule implies_elim :premises (@p279)) % 0.17/0.37 (step @p283 :rule cnf_and_neg :args (@t117)) % 0.17/0.37 (step @p284 :rule resolution :premises (@p283 @p282) :args (true @t117)) % 0.17/0.37 (step @p285 :rule reordering :premises (@p284) :args ((or @t106 @t102 (not @t115)))) % 0.17/0.37 (step @p286 false :rule chain_m_resolution :premises (@p285 @p266 @p235 @p233) :args (false (@list false true false) (@list @t115 @t102 @t105))) % 0.17/0.37 ) % 0.17/0.37 % SZS output end Proof % 0.17/0.37 % cvc5 exiting %------------------------------------------------------------------------------