%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU187+1 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n004.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 08:50:53 AM UTC 2026 % Result : Theorem 0.38s 0.59s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU187+1 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n004.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 16:35:07 EDT 2026 % 0.16/0.34 % CPUTime : % 0.32/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.59 % SZS status Theorem % 0.38/0.59 % SZS output start Proof % 0.38/0.59 ( % 0.38/0.59 (declare-sort $$unsorted 0) % 0.38/0.59 (declare-const tptp.empty_set $$unsorted) % 0.38/0.59 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.38/0.59 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.38/0.59 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.38/0.59 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.38/0.59 (define @t1 () (@var "A" $$unsorted)) % 0.38/0.59 (define @t2 () (@var "B" $$unsorted)) % 0.38/0.59 (define @t3 () (tptp.in @t1 @t2)) % 0.38/0.59 (define @t4 () (@list @t1 @t2)) % 0.38/0.59 (define @t5 () (tptp.relation @t1)) % 0.38/0.59 (define @t6 () (tptp.empty @t1)) % 0.38/0.59 (define @t7 () (@list @t1)) % 0.38/0.59 (define @t8 () (tptp.unordered_pair @t1 @t2)) % 0.38/0.59 (define @t9 () (@var "D" $$unsorted)) % 0.38/0.59 (define @t10 () (@var "C" $$unsorted)) % 0.38/0.59 (define @t11 () (tptp.ordered_pair @t10 @t9)) % 0.38/0.59 (define @t12 () (tptp.in @t11 @t1)) % 0.38/0.59 (define @t13 () (@list @t9)) % 0.38/0.59 (define @t14 () (exists @t13 @t12)) % 0.38/0.59 (define @t15 () (tptp.in @t10 @t2)) % 0.38/0.59 (define @t16 () (= @t15 @t14)) % 0.38/0.59 (define @t17 () (@list @t10)) % 0.38/0.59 (define @t18 () (forall @t17 @t16)) % 0.38/0.59 (define @t19 () (tptp.relation_dom @t1)) % 0.38/0.59 (define @t20 () (= @t2 @t19)) % 0.38/0.59 (define @t21 () (= @t20 @t18)) % 0.38/0.59 (define @t22 () (@list @t2)) % 0.38/0.59 (define @t23 () (forall @t22 @t21)) % 0.38/0.59 (define @t24 () (=> @t5 @t23)) % 0.38/0.59 (define @t25 () (forall @t7 @t24)) % 0.38/0.59 (define @t26 () (tptp.ordered_pair @t9 @t10)) % 0.38/0.59 (define @t27 () (tptp.in @t26 @t1)) % 0.38/0.59 (define @t28 () (exists @t13 @t27)) % 0.38/0.59 (define @t29 () (= @t15 @t28)) % 0.38/0.59 (define @t30 () (forall @t17 @t29)) % 0.38/0.59 (define @t31 () (tptp.relation_rng @t1)) % 0.38/0.59 (define @t32 () (= @t2 @t31)) % 0.38/0.59 (define @t33 () (= @t32 @t30)) % 0.38/0.59 (define @t34 () (forall @t22 @t33)) % 0.38/0.59 (define @t35 () (=> @t5 @t34)) % 0.38/0.59 (define @t36 () (forall @t7 @t35)) % 0.38/0.59 (define @t37 () (tptp.singleton @t1)) % 0.38/0.59 (define @t38 () (tptp.ordered_pair @t1 @t2)) % 0.38/0.59 (define @t39 () (tptp.empty tptp.empty_set)) % 0.38/0.59 (define @t40 () (tptp.relation tptp.empty_set)) % 0.38/0.59 (define @t41 () (not @t6)) % 0.38/0.59 (define @t42 () (and @t41 @t5)) % 0.38/0.59 (define @t43 () (tptp.element @t1 @t2)) % 0.38/0.59 (define @t44 () (tptp.empty @t2)) % 0.38/0.59 (define @t45 () (= @t1 @t2)) % 0.38/0.59 (define @t46 () (tptp.relation_rng tptp.empty_set)) % 0.38/0.59 (define @t47 () (= @t46 tptp.empty_set)) % 0.38/0.59 (define @t48 () (tptp.relation_dom tptp.empty_set)) % 0.38/0.59 (define @t49 () (= @t48 tptp.empty_set)) % 0.38/0.59 (define @t50 () (and @t49 @t47)) % 0.38/0.59 (define @t51 () (not @t50)) % 0.38/0.59 (define @t52 () (forall @t4 (not (and @t3 @t44)))) % 0.38/0.59 (define @t53 () (@var "BOUND_VARIABLE_7549" $$unsorted)) % 0.38/0.59 (define @t54 () (tptp.in @t10 @t53)) % 0.38/0.59 (define @t55 () (not (forall @t13 (not @t12)))) % 0.38/0.59 (define @t56 () (forall @t17 (= @t54 @t55))) % 0.38/0.59 (define @t57 () (= (= @t53 @t19) @t56)) % 0.38/0.59 (define @t58 () (not @t5)) % 0.38/0.59 (define @t59 () (or @t58 @t57)) % 0.38/0.59 (define @t60 () (@list @t1 @t53)) % 0.38/0.59 (define @t61 () (forall @t60 @t59)) % 0.38/0.59 (define @t62 () (@list @t53)) % 0.38/0.59 (define @t63 () (forall @t62 @t59)) % 0.38/0.59 (define @t64 () (forall @t62 @t57)) % 0.38/0.59 (define @t65 () (@list @t2)) % 0.38/0.59 (define @t66 () (or @t58 @t64)) % 0.38/0.59 (define @t67 () (forall @t22 (= @t20 (forall @t17 (= @t15 @t55))))) % 0.38/0.59 (define @t68 () (tptp.in @t10 tptp.empty_set)) % 0.38/0.59 (define @t69 () (forall @t17 (= (not (forall @t13 (not (tptp.in @t11 tptp.empty_set)))) @t68))) % 0.38/0.59 (define @t70 () (= @t49 @t69)) % 0.38/0.59 (define @t71 () (not @t40)) % 0.38/0.59 (define @t72 () (or @t71 @t70)) % 0.38/0.59 (define @t73 () (forall @t60 (or @t58 (= (= @t19 @t53) (forall @t17 (= @t55 @t54)))))) % 0.38/0.59 (define @t74 () (@list tptp.empty_set tptp.empty_set)) % 0.38/0.59 (define @t75 () (= tptp.empty_set @t48)) % 0.38/0.59 (define @t76 () (= @t75 @t69)) % 0.38/0.59 (define @t77 () (or @t71 @t76)) % 0.38/0.59 (define @t78 () (@list false)) % 0.38/0.59 (define @t79 () (@list false false)) % 0.38/0.59 (define @t80 () (@quantifiers_skolemize @t69 0)) % 0.38/0.59 (define @t81 () (not @t39)) % 0.38/0.59 (define @t82 () (tptp.in @t80 tptp.empty_set)) % 0.38/0.59 (define @t83 () (not @t82)) % 0.38/0.59 (define @t84 () (or @t83 @t81)) % 0.38/0.59 (define @t85 () (forall @t13 (not (tptp.in (tptp.ordered_pair @t80 @t9) tptp.empty_set)))) % 0.38/0.59 (define @t86 () (tptp.ordered_pair @t80 (@quantifiers_skolemize @t85 0))) % 0.38/0.59 (define @t87 () (tptp.in @t86 tptp.empty_set)) % 0.38/0.59 (define @t88 () (not @t87)) % 0.38/0.59 (define @t89 () (or @t88 @t81)) % 0.38/0.59 (define @t90 () (not @t85)) % 0.38/0.59 (define @t91 () (not @t88)) % 0.38/0.59 (define @t92 () (@list true)) % 0.38/0.59 (define @t93 () (= @t90 @t82)) % 0.38/0.59 (define @t94 () (not @t93)) % 0.38/0.59 (define @t95 () (not @t69)) % 0.38/0.59 (define @t96 () (@var "BOUND_VARIABLE_7577" $$unsorted)) % 0.38/0.59 (define @t97 () (tptp.in @t10 @t96)) % 0.38/0.59 (define @t98 () (not (forall @t13 (not @t27)))) % 0.38/0.59 (define @t99 () (forall @t17 (= @t97 @t98))) % 0.38/0.59 (define @t100 () (= (= @t96 @t31) @t99)) % 0.38/0.59 (define @t101 () (or @t58 @t100)) % 0.38/0.59 (define @t102 () (@list @t1 @t96)) % 0.38/0.59 (define @t103 () (forall @t102 @t101)) % 0.38/0.59 (define @t104 () (@list @t96)) % 0.38/0.59 (define @t105 () (forall @t104 @t101)) % 0.38/0.59 (define @t106 () (forall @t104 @t100)) % 0.38/0.59 (define @t107 () (or @t58 @t106)) % 0.38/0.59 (define @t108 () (forall @t22 (= @t32 (forall @t17 (= @t15 @t98))))) % 0.38/0.59 (define @t109 () (not (forall @t13 (not (tptp.in @t26 tptp.empty_set))))) % 0.38/0.59 (define @t110 () (forall @t17 (= @t109 @t68))) % 0.38/0.59 (define @t111 () (= @t47 @t110)) % 0.38/0.59 (define @t112 () (or @t71 @t111)) % 0.38/0.59 (define @t113 () (forall @t102 (or @t58 (= (= @t31 @t96) (forall @t17 (= @t98 @t97)))))) % 0.38/0.59 (define @t114 () (forall @t17 (= @t68 @t109))) % 0.38/0.59 (define @t115 () (= tptp.empty_set @t46)) % 0.38/0.59 (define @t116 () (= @t115 @t114)) % 0.38/0.59 (define @t117 () (or @t71 @t116)) % 0.38/0.59 (define @t118 () (@quantifiers_skolemize @t114 0)) % 0.38/0.59 (define @t119 () (forall @t13 (not (tptp.in (tptp.ordered_pair @t9 @t118) tptp.empty_set)))) % 0.38/0.59 (define @t120 () (tptp.ordered_pair (@quantifiers_skolemize @t119 0) @t118)) % 0.38/0.59 (define @t121 () (tptp.in @t120 tptp.empty_set)) % 0.38/0.59 (define @t122 () (not @t121)) % 0.38/0.59 (define @t123 () (or @t122 @t81)) % 0.38/0.59 (define @t124 () (not @t119)) % 0.38/0.59 (define @t125 () (not @t122)) % 0.38/0.59 (define @t126 () (tptp.in @t118 tptp.empty_set)) % 0.38/0.59 (define @t127 () (not @t126)) % 0.38/0.59 (define @t128 () (or @t127 @t81)) % 0.38/0.59 (define @t129 () (= @t126 @t124)) % 0.38/0.59 (define @t130 () (not @t129)) % 0.38/0.59 (define @t131 () (not @t114)) % 0.38/0.59 (assume @p1 (forall @t4 (=> @t3 (not (tptp.in @t2 @t1))))) % 0.38/0.59 (assume @p2 (forall @t7 (=> @t6 @t5))) % 0.38/0.59 (assume @p3 (forall @t4 (= @t8 (tptp.unordered_pair @t2 @t1)))) % 0.38/0.59 (assume @p4 @t25) % 0.38/0.59 (assume @p5 @t36) % 0.38/0.59 (assume @p6 (forall @t4 (= @t38 (tptp.unordered_pair @t8 @t37)))) % 0.38/0.59 (assume @p7 true) % 0.38/0.59 (assume @p8 (forall @t7 (exists @t22 (tptp.element @t2 @t1)))) % 0.38/0.59 (assume @p9 @t39) % 0.38/0.59 (assume @p10 (forall @t4 (not (tptp.empty @t38)))) % 0.38/0.59 (assume @p11 (forall @t7 (not (tptp.empty @t37)))) % 0.38/0.59 (assume @p12 (forall @t4 (not (tptp.empty @t8)))) % 0.38/0.59 (assume @p13 (and @t39 @t40)) % 0.38/0.59 (assume @p14 (forall @t7 (=> @t42 (not (tptp.empty @t19))))) % 0.38/0.59 (assume @p15 (forall @t7 (=> @t42 (not (tptp.empty @t31))))) % 0.38/0.59 (assume @p16 (exists @t7 (and @t6 @t5))) % 0.38/0.59 (assume @p17 (exists @t7 @t6)) % 0.38/0.59 (assume @p18 (exists @t7 @t42)) % 0.38/0.59 (assume @p19 (exists @t7 @t41)) % 0.38/0.59 (assume @p20 (forall @t4 (=> @t3 @t43))) % 0.38/0.59 (assume @p21 (forall @t4 (=> @t43 (or @t44 @t3)))) % 0.38/0.59 (assume @p22 (forall @t4 (=> (forall @t17 (= (tptp.in @t10 @t1) @t15)) @t45))) % 0.38/0.59 (assume @p23 @t51) % 0.38/0.59 (assume @p24 (forall @t7 (=> @t6 (= @t1 tptp.empty_set)))) % 0.38/0.59 (assume @p25 @t52) % 0.38/0.59 (assume @p26 (forall @t4 (not (and @t6 (not @t45) @t44)))) % 0.38/0.59 (step @p27 :rule eq-symm :args (@t54 @t55)) % 0.38/0.59 (step @p28 :rule cong :premises (@p27) :args (@t56)) % 0.38/0.59 (step @p29 :rule eq-symm :args (@t53 @t19)) % 0.38/0.59 (step @p30 :rule cong :premises (@p29 @p28) :args (@t57)) % 0.38/0.59 (step @p31 :rule refl :args (@t58)) % 0.38/0.59 (step @p32 :rule nary_cong :premises (@p31 @p30) :args (@t59)) % 0.38/0.59 (step @p33 :rule cong :premises (@p32) :args (@t61)) % 0.38/0.59 (step @p34 :rule quant-merge-prenex :args ((= (forall @t7 @t63) @t61))) % 0.38/0.59 (step @p35 :rule alpha_equiv :args (@t64 (@list @t53) @t65)) % 0.38/0.59 (step @p36 :rule refl :args (@t58)) % 0.38/0.59 (step @p37 :rule nary_cong :premises (@p36 @p35) :args (@t66)) % 0.38/0.59 (step @p38 :rule quant-miniscope-or :args ((= @t63 @t66))) % 0.38/0.59 (step @p39 :rule trans :premises (@p38 @p37)) % 0.38/0.59 (step @p40 :rule symm :premises (@p39)) % 0.38/0.59 (step @p41 :rule cong :premises (@p40) :args ((forall @t7 (or @t58 @t67)))) % 0.38/0.59 (step @p42 :rule trans :premises (@p41 @p34)) % 0.38/0.59 (step @p43 :rule trans :premises (@p42 @p33)) % 0.38/0.59 (step @p44 :rule bool-impl-elim :args (@t5 @t67)) % 0.38/0.59 (step @p45 :rule cong :premises (@p44) :args ((forall @t7 (=> @t5 @t67)))) % 0.38/0.59 (step @p46 :rule trans :premises (@p45 @p43)) % 0.38/0.59 (step @p47 :rule exists-elim :args ((= @t14 @t55))) % 0.38/0.59 (step @p48 :rule refl :args (@t15)) % 0.38/0.59 (step @p49 :rule cong :premises (@p48 @p47) :args (@t16)) % 0.38/0.59 (step @p50 :rule cong :premises (@p49) :args (@t18)) % 0.38/0.59 (step @p51 :rule refl :args (@t20)) % 0.38/0.59 (step @p52 :rule cong :premises (@p51 @p50) :args (@t21)) % 0.38/0.59 (step @p53 :rule cong :premises (@p52) :args (@t23)) % 0.38/0.59 (step @p54 :rule refl :args (@t5)) % 0.38/0.59 (step @p55 :rule cong :premises (@p54 @p53) :args (@t24)) % 0.38/0.59 (step @p56 :rule cong :premises (@p55) :args (@t25)) % 0.38/0.59 (step @p57 :rule trans :premises (@p56 @p46)) % 0.38/0.59 (step @p58 :rule eq_resolve :premises (@p4 @p57)) % 0.38/0.59 (step @p59 :rule refl :args (@t69)) % 0.38/0.59 (step @p60 :rule eq-symm :args (@t48 tptp.empty_set)) % 0.38/0.59 (step @p61 :rule cong :premises (@p60 @p59) :args (@t70)) % 0.38/0.59 (step @p62 :rule refl :args (@t71)) % 0.38/0.59 (step @p63 :rule nary_cong :premises (@p62 @p61) :args (@t72)) % 0.38/0.59 (step @p64 :rule refl :args (@t73)) % 0.38/0.59 (step @p65 :rule cong :premises (@p64 @p63) :args ((=> @t73 @t72))) % 0.38/0.59 (assume-push @p206 @t73) % 0.38/0.59 (step @p67 :rule instantiate :premises (@p58) :args (@t74)) % 0.38/0.59 (step-pop @p207 :rule scope :premises (@p67)) % 0.38/0.59 (step @p68 :rule process_scope :premises (@p207) :args (@t72)) % 0.38/0.59 (step @p70 :rule eq_resolve :premises (@p68 @p65)) % 0.38/0.59 (step @p71 :rule implies_elim :premises (@p70)) % 0.38/0.59 (step @p72 :rule chain_m_resolution :premises (@p71 @p58) :args (@t77 @t78 (@list @t73))) % 0.38/0.59 (step @p73 :rule and_elim :premises (@p13) :args (1)) % 0.38/0.59 (step @p74 :rule cnf_or_pos :args (@t77)) % 0.38/0.59 (step @p75 :rule reordering :premises (@p74) :args ((or @t71 @t76 (not @t77)))) % 0.38/0.59 (step @p76 :rule chain_m_resolution :premises (@p75 @p73 @p72) :args (@t76 @t79 (@list @t40 @t77))) % 0.38/0.59 (step @p77 :rule bool-and-de-morgan :args (@t3 @t44 true)) % 0.38/0.59 (step @p78 :rule cong :premises (@p77) :args (@t52)) % 0.38/0.59 (step @p79 :rule eq_resolve :premises (@p25 @p78)) % 0.38/0.59 (step @p80 :rule instantiate :premises (@p79) :args ((@list @t80 tptp.empty_set))) % 0.38/0.59 (step @p81 :rule cnf_or_pos :args (@t84)) % 0.38/0.59 (step @p82 :rule reordering :premises (@p81) :args ((or @t81 @t83 (not @t84)))) % 0.38/0.59 (step @p83 :rule chain_m_resolution :premises (@p82 @p9 @p80) :args (@t83 @t79 (@list @t39 @t84))) % 0.38/0.59 (step @p84 :rule instantiate :premises (@p79) :args ((@list @t86 tptp.empty_set))) % 0.38/0.59 (step @p85 :rule cnf_or_pos :args (@t89)) % 0.38/0.59 (step @p86 :rule reordering :premises (@p85) :args ((or @t81 @t88 (not @t89)))) % 0.38/0.59 (step @p87 :rule chain_m_resolution :premises (@p86 @p9 @p84) :args (@t88 @t79 (@list @t39 @t89))) % 0.38/0.59 (step @p88 :rule refl :args (@t87)) % 0.38/0.59 (step @p89 :rule bool-double-not-elim :args (@t85)) % 0.38/0.59 (step @p90 :rule nary_cong :premises (@p89 @p88) :args ((or (not @t90) @t87))) % 0.38/0.59 (step @p91 :rule bool-double-not-elim :args (@t87)) % 0.38/0.59 (step @p92 :rule refl :args (@t90)) % 0.38/0.59 (step @p93 :rule cong :premises (@p92 @p91) :args ((=> @t90 @t91))) % 0.38/0.59 (assume-push @p208 @t90) % 0.38/0.59 (step @p95 :rule skolemize :premises (@p208)) % 0.38/0.59 (step-pop @p209 :rule scope :premises (@p95)) % 0.38/0.59 (step @p96 :rule process_scope :premises (@p209) :args (@t91)) % 0.38/0.59 (step @p98 :rule eq_resolve :premises (@p96 @p93)) % 0.38/0.59 (step @p99 :rule implies_elim :premises (@p98)) % 0.38/0.59 (step @p100 :rule eq_resolve :premises (@p99 @p90)) % 0.38/0.59 (step @p101 :rule chain_m_resolution :premises (@p100 @p87) :args (@t85 @t92 (@list @t87))) % 0.38/0.59 (step @p102 :rule cnf_equiv_neg1 :args (@t93)) % 0.38/0.59 (step @p103 :rule reordering :premises (@p102) :args ((or @t90 @t82 @t93))) % 0.38/0.59 (step @p104 :rule chain_m_resolution :premises (@p103 @p101 @p83) :args (@t93 (@list false true) (@list @t85 @t82))) % 0.38/0.59 (step @p105 :rule refl :args (@t94)) % 0.38/0.59 (step @p106 :rule bool-double-not-elim :args (@t69)) % 0.38/0.59 (step @p107 :rule nary_cong :premises (@p106 @p105) :args ((or (not @t95) @t94))) % 0.38/0.59 (assume-push @p210 @t95) % 0.38/0.59 (step @p109 :rule skolemize :premises (@p210)) % 0.38/0.59 (step-pop @p211 :rule scope :premises (@p109)) % 0.38/0.59 (step @p110 :rule process_scope :premises (@p211) :args (@t94)) % 0.38/0.59 (step @p112 :rule implies_elim :premises (@p110)) % 0.38/0.59 (step @p113 :rule eq_resolve :premises (@p112 @p107)) % 0.38/0.59 (step @p114 :rule chain_m_resolution :premises (@p113 @p104) :args (@t69 @t78 (@list @t93))) % 0.38/0.59 (step @p115 :rule cnf_equiv_pos2 :args (@t76)) % 0.38/0.59 (step @p116 :rule reordering :premises (@p115) :args ((or @t75 @t95 (not @t76)))) % 0.38/0.59 (step @p117 :rule chain_m_resolution :premises (@p116 @p114 @p76) :args (@t75 @t79 (@list @t69 @t76))) % 0.38/0.59 (step @p118 :rule eq-symm :args (@t97 @t98)) % 0.38/0.59 (step @p119 :rule cong :premises (@p118) :args (@t99)) % 0.38/0.59 (step @p120 :rule eq-symm :args (@t96 @t31)) % 0.38/0.59 (step @p121 :rule cong :premises (@p120 @p119) :args (@t100)) % 0.38/0.59 (step @p122 :rule nary_cong :premises (@p31 @p121) :args (@t101)) % 0.38/0.59 (step @p123 :rule cong :premises (@p122) :args (@t103)) % 0.38/0.59 (step @p124 :rule quant-merge-prenex :args ((= (forall @t7 @t105) @t103))) % 0.38/0.59 (step @p125 :rule alpha_equiv :args (@t106 (@list @t96) @t65)) % 0.38/0.59 (step @p126 :rule nary_cong :premises (@p36 @p125) :args (@t107)) % 0.38/0.59 (step @p127 :rule quant-miniscope-or :args ((= @t105 @t107))) % 0.38/0.59 (step @p128 :rule trans :premises (@p127 @p126)) % 0.38/0.59 (step @p129 :rule symm :premises (@p128)) % 0.38/0.59 (step @p130 :rule cong :premises (@p129) :args ((forall @t7 (or @t58 @t108)))) % 0.38/0.59 (step @p131 :rule trans :premises (@p130 @p124)) % 0.38/0.59 (step @p132 :rule trans :premises (@p131 @p123)) % 0.38/0.59 (step @p133 :rule bool-impl-elim :args (@t5 @t108)) % 0.38/0.59 (step @p134 :rule cong :premises (@p133) :args ((forall @t7 (=> @t5 @t108)))) % 0.38/0.59 (step @p135 :rule trans :premises (@p134 @p132)) % 0.38/0.59 (step @p136 :rule exists-elim :args ((= @t28 @t98))) % 0.38/0.59 (step @p137 :rule cong :premises (@p48 @p136) :args (@t29)) % 0.38/0.59 (step @p138 :rule cong :premises (@p137) :args (@t30)) % 0.38/0.59 (step @p139 :rule refl :args (@t32)) % 0.38/0.59 (step @p140 :rule cong :premises (@p139 @p138) :args (@t33)) % 0.38/0.59 (step @p141 :rule cong :premises (@p140) :args (@t34)) % 0.38/0.59 (step @p142 :rule cong :premises (@p54 @p141) :args (@t35)) % 0.38/0.59 (step @p143 :rule cong :premises (@p142) :args (@t36)) % 0.38/0.59 (step @p144 :rule trans :premises (@p143 @p135)) % 0.38/0.59 (step @p145 :rule eq_resolve :premises (@p5 @p144)) % 0.38/0.59 (step @p146 :rule eq-symm :args (@t109 @t68)) % 0.38/0.59 (step @p147 :rule cong :premises (@p146) :args (@t110)) % 0.38/0.59 (step @p148 :rule eq-symm :args (@t46 tptp.empty_set)) % 0.38/0.59 (step @p149 :rule cong :premises (@p148 @p147) :args (@t111)) % 0.38/0.59 (step @p150 :rule nary_cong :premises (@p62 @p149) :args (@t112)) % 0.38/0.59 (step @p151 :rule refl :args (@t113)) % 0.38/0.59 (step @p152 :rule cong :premises (@p151 @p150) :args ((=> @t113 @t112))) % 0.38/0.59 (assume-push @p212 @t113) % 0.38/0.59 (step @p154 :rule instantiate :premises (@p145) :args (@t74)) % 0.38/0.59 (step-pop @p213 :rule scope :premises (@p154)) % 0.38/0.59 (step @p155 :rule process_scope :premises (@p213) :args (@t112)) % 0.38/0.59 (step @p157 :rule eq_resolve :premises (@p155 @p152)) % 0.38/0.59 (step @p158 :rule implies_elim :premises (@p157)) % 0.38/0.59 (step @p159 :rule chain_m_resolution :premises (@p158 @p145) :args (@t117 @t78 (@list @t113))) % 0.38/0.59 (step @p160 :rule cnf_or_pos :args (@t117)) % 0.38/0.59 (step @p161 :rule reordering :premises (@p160) :args ((or @t71 @t116 (not @t117)))) % 0.38/0.59 (step @p162 :rule chain_m_resolution :premises (@p161 @p73 @p159) :args (@t116 @t79 (@list @t40 @t117))) % 0.38/0.59 (step @p163 :rule instantiate :premises (@p79) :args ((@list @t120 tptp.empty_set))) % 0.38/0.59 (step @p164 :rule cnf_or_pos :args (@t123)) % 0.38/0.59 (step @p165 :rule reordering :premises (@p164) :args ((or @t81 @t122 (not @t123)))) % 0.38/0.59 (step @p166 :rule chain_m_resolution :premises (@p165 @p9 @p163) :args (@t122 @t79 (@list @t39 @t123))) % 0.38/0.59 (step @p167 :rule refl :args (@t121)) % 0.38/0.59 (step @p168 :rule bool-double-not-elim :args (@t119)) % 0.38/0.59 (step @p169 :rule nary_cong :premises (@p168 @p167) :args ((or (not @t124) @t121))) % 0.38/0.59 (step @p170 :rule bool-double-not-elim :args (@t121)) % 0.38/0.59 (step @p171 :rule refl :args (@t124)) % 0.38/0.59 (step @p172 :rule cong :premises (@p171 @p170) :args ((=> @t124 @t125))) % 0.38/0.59 (assume-push @p214 @t124) % 0.38/0.59 (step @p174 :rule skolemize :premises (@p214)) % 0.38/0.59 (step-pop @p215 :rule scope :premises (@p174)) % 0.38/0.59 (step @p175 :rule process_scope :premises (@p215) :args (@t125)) % 0.38/0.59 (step @p177 :rule eq_resolve :premises (@p175 @p172)) % 0.38/0.59 (step @p178 :rule implies_elim :premises (@p177)) % 0.38/0.59 (step @p179 :rule eq_resolve :premises (@p178 @p169)) % 0.38/0.59 (step @p180 :rule chain_m_resolution :premises (@p179 @p166) :args (@t119 @t92 (@list @t121))) % 0.38/0.59 (step @p181 :rule instantiate :premises (@p79) :args ((@list @t118 tptp.empty_set))) % 0.38/0.59 (step @p182 :rule cnf_or_pos :args (@t128)) % 0.38/0.59 (step @p183 :rule reordering :premises (@p182) :args ((or @t81 @t127 (not @t128)))) % 0.38/0.59 (step @p184 :rule chain_m_resolution :premises (@p183 @p9 @p181) :args (@t127 @t79 (@list @t39 @t128))) % 0.38/0.59 (step @p185 :rule cnf_equiv_neg1 :args (@t129)) % 0.38/0.60 (step @p186 :rule reordering :premises (@p185) :args ((or @t126 @t124 @t129))) % 0.38/0.60 (step @p187 :rule chain_m_resolution :premises (@p186 @p184 @p180) :args (@t129 (@list true false) (@list @t126 @t119))) % 0.38/0.60 (step @p188 :rule refl :args (@t130)) % 0.38/0.60 (step @p189 :rule bool-double-not-elim :args (@t114)) % 0.38/0.60 (step @p190 :rule nary_cong :premises (@p189 @p188) :args ((or (not @t131) @t130))) % 0.38/0.60 (assume-push @p216 @t131) % 0.38/0.60 (step @p192 :rule skolemize :premises (@p216)) % 0.38/0.60 (step-pop @p217 :rule scope :premises (@p192)) % 0.38/0.60 (step @p193 :rule process_scope :premises (@p217) :args (@t130)) % 0.38/0.60 (step @p195 :rule implies_elim :premises (@p193)) % 0.38/0.60 (step @p196 :rule eq_resolve :premises (@p195 @p190)) % 0.38/0.60 (step @p197 :rule chain_m_resolution :premises (@p196 @p187) :args (@t114 @t78 (@list @t129))) % 0.38/0.60 (step @p198 :rule cnf_equiv_pos2 :args (@t116)) % 0.38/0.60 (step @p199 :rule reordering :premises (@p198) :args ((or @t115 @t131 (not @t116)))) % 0.38/0.60 (step @p200 :rule chain_m_resolution :premises (@p199 @p197 @p162) :args (@t115 @t79 (@list @t114 @t116))) % 0.38/0.60 (step @p201 :rule nary_cong :premises (@p60 @p148) :args (@t50)) % 0.38/0.60 (step @p202 :rule cong :premises (@p201) :args (@t51)) % 0.38/0.60 (step @p203 :rule eq_resolve :premises (@p23 @p202)) % 0.38/0.60 (step @p204 :rule not_and :premises (@p203)) % 0.38/0.60 (step @p205 false :rule chain_m_resolution :premises (@p204 @p200 @p117) :args (false @t79 (@list @t115 @t75))) % 0.38/0.60 ) % 0.38/0.60 % SZS output end Proof % 0.38/0.60 % cvc5 exiting %------------------------------------------------------------------------------