%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET352+4 : TPTP v9.2.1. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n006.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 08:47:49 AM UTC 2026 % Result : Theorem 0.40s 0.58s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET352+4 : TPTP v9.2.1. Released v2.2.0. % 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 : n006.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 15:29:49 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.40/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.40/0.58 % SZS status Theorem % 0.40/0.58 % SZS output start Proof % 0.40/0.58 ( % 0.40/0.58 (declare-sort $$unsorted 0) % 0.40/0.58 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.empty_set $$unsorted) % 0.40/0.58 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.40/0.58 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.40/0.58 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.40/0.58 (define @t1 () (@var "B" $$unsorted)) % 0.40/0.58 (define @t2 () (@var "X" $$unsorted)) % 0.40/0.58 (define @t3 () (tptp.member @t2 @t1)) % 0.40/0.58 (define @t4 () (@var "A" $$unsorted)) % 0.40/0.58 (define @t5 () (tptp.member @t2 @t4)) % 0.40/0.58 (define @t6 () (@list @t2)) % 0.40/0.58 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.40/0.58 (define @t8 () (tptp.subset @t4 @t1)) % 0.40/0.58 (define @t9 () (= @t8 @t7)) % 0.40/0.58 (define @t10 () (@list @t4 @t1)) % 0.40/0.58 (define @t11 () (forall @t10 @t9)) % 0.40/0.58 (define @t12 () (@list @t2 @t4)) % 0.40/0.58 (define @t13 () (@list @t2 @t4 @t1)) % 0.40/0.58 (define @t14 () (tptp.union @t4 @t1)) % 0.40/0.58 (define @t15 () (@var "E" $$unsorted)) % 0.40/0.58 (define @t16 () (= @t2 @t4)) % 0.40/0.58 (define @t17 () (or @t16 (= @t2 @t1))) % 0.40/0.58 (define @t18 () (tptp.unordered_pair @t4 @t1)) % 0.40/0.58 (define @t19 () (tptp.member @t2 @t18)) % 0.40/0.58 (define @t20 () (= @t19 @t17)) % 0.40/0.58 (define @t21 () (forall @t13 @t20)) % 0.40/0.58 (define @t22 () (@var "Y" $$unsorted)) % 0.40/0.58 (define @t23 () (tptp.member @t2 @t22)) % 0.40/0.58 (define @t24 () (tptp.member @t22 @t4)) % 0.40/0.58 (define @t25 () (and @t24 @t23)) % 0.40/0.58 (define @t26 () (@list @t22)) % 0.40/0.58 (define @t27 () (exists @t26 @t25)) % 0.40/0.58 (define @t28 () (tptp.member @t2 (tptp.sum @t4))) % 0.40/0.58 (define @t29 () (= @t28 @t27)) % 0.40/0.58 (define @t30 () (forall @t12 @t29)) % 0.40/0.58 (define @t31 () (forall @t10 (tptp.equal_set (tptp.sum @t18) @t14))) % 0.40/0.58 (define @t32 () (@quantifiers_skolemize @t31 1)) % 0.40/0.58 (define @t33 () (@quantifiers_skolemize @t31 0)) % 0.40/0.58 (define @t34 () (tptp.union @t33 @t32)) % 0.40/0.58 (define @t35 () (tptp.unordered_pair @t33 @t32)) % 0.40/0.58 (define @t36 () (tptp.sum @t35)) % 0.40/0.58 (define @t37 () (@list @t36 @t34)) % 0.40/0.58 (define @t38 () (tptp.member @t2 @t36)) % 0.40/0.58 (define @t39 () (tptp.member @t2 @t34)) % 0.40/0.58 (define @t40 () (forall @t6 (or (not @t39) @t38))) % 0.40/0.58 (define @t41 () (@quantifiers_skolemize @t40 0)) % 0.40/0.58 (define @t42 () (tptp.member @t41 @t34)) % 0.40/0.58 (define @t43 () (tptp.member @t41 @t36)) % 0.40/0.58 (define @t44 () (not @t42)) % 0.40/0.58 (define @t45 () (or @t44 @t43)) % 0.40/0.58 (define @t46 () (tptp.member @t41 @t32)) % 0.40/0.58 (define @t47 () (tptp.member @t41 @t33)) % 0.40/0.58 (define @t48 () (or @t47 @t46)) % 0.40/0.58 (define @t49 () (= @t42 @t48)) % 0.40/0.58 (define @t50 () (forall @t26 (not @t25))) % 0.40/0.58 (define @t51 () (not @t50)) % 0.40/0.58 (define @t52 () (not (tptp.member @t22 @t35))) % 0.40/0.58 (define @t53 () (forall @t26 (or @t52 (not (tptp.member @t41 @t22))))) % 0.40/0.58 (define @t54 () (not @t53)) % 0.40/0.58 (define @t55 () (= @t43 @t54)) % 0.40/0.58 (define @t56 () (not @t55)) % 0.40/0.58 (define @t57 () (not @t46)) % 0.40/0.58 (define @t58 () (tptp.member @t32 @t35)) % 0.40/0.58 (define @t59 () (not @t58)) % 0.40/0.58 (define @t60 () (or @t59 @t57)) % 0.40/0.58 (define @t61 () (not @t47)) % 0.40/0.58 (define @t62 () (tptp.member @t33 @t35)) % 0.40/0.58 (define @t63 () (not @t62)) % 0.40/0.58 (define @t64 () (or @t63 @t61)) % 0.40/0.58 (define @t65 () (= @t33 @t32)) % 0.40/0.58 (define @t66 () (or @t65 (= @t32 @t32))) % 0.40/0.58 (define @t67 () (= @t58 @t66)) % 0.40/0.58 (define @t68 () (forall @t13 (= @t19 (or (= @t4 @t2) (= @t1 @t2))))) % 0.40/0.58 (define @t69 () (@list false)) % 0.40/0.58 (define @t70 () (@list @t68)) % 0.40/0.58 (define @t71 () (or (= @t33 @t33) (= @t32 @t33))) % 0.40/0.58 (define @t72 () (= @t62 @t71)) % 0.40/0.58 (define @t73 () (not @t45)) % 0.40/0.58 (define @t74 () (not @t40)) % 0.40/0.58 (define @t75 () (tptp.subset @t34 @t36)) % 0.40/0.58 (define @t76 () (= @t75 @t40)) % 0.40/0.58 (define @t77 () (@list false false)) % 0.40/0.58 (define @t78 () (tptp.subset @t36 @t34)) % 0.40/0.58 (define @t79 () (and @t78 @t75)) % 0.40/0.58 (define @t80 () (tptp.equal_set @t36 @t34)) % 0.40/0.58 (define @t81 () (= @t80 @t79)) % 0.40/0.58 (define @t82 () (not @t79)) % 0.40/0.58 (define @t83 () (@list true false)) % 0.40/0.58 (define @t84 () (forall @t6 (or (not @t38) @t39))) % 0.40/0.58 (define @t85 () (= @t78 @t84)) % 0.40/0.58 (define @t86 () (not @t84)) % 0.40/0.58 (define @t87 () (@quantifiers_skolemize @t84 0)) % 0.40/0.58 (define @t88 () (tptp.member @t87 @t34)) % 0.40/0.58 (define @t89 () (tptp.member @t87 @t36)) % 0.40/0.58 (define @t90 () (not @t89)) % 0.40/0.58 (define @t91 () (or @t90 @t88)) % 0.40/0.58 (define @t92 () (not @t91)) % 0.40/0.58 (define @t93 () (@list true)) % 0.40/0.58 (define @t94 () (forall @t26 (or @t52 (not (tptp.member @t87 @t22))))) % 0.40/0.58 (define @t95 () (not @t94)) % 0.40/0.58 (define @t96 () (= @t89 @t95)) % 0.40/0.58 (define @t97 () (tptp.member @t87 @t32)) % 0.40/0.58 (define @t98 () (tptp.member @t87 @t33)) % 0.40/0.58 (define @t99 () (or @t98 @t97)) % 0.40/0.58 (define @t100 () (= @t88 @t99)) % 0.40/0.58 (define @t101 () (not @t99)) % 0.40/0.58 (define @t102 () (@quantifiers_skolemize @t94 0)) % 0.40/0.58 (define @t103 () (tptp.member @t87 @t102)) % 0.40/0.58 (define @t104 () (not @t103)) % 0.40/0.58 (define @t105 () (tptp.member @t102 @t35)) % 0.40/0.58 (define @t106 () (not @t105)) % 0.40/0.58 (define @t107 () (or @t106 @t104)) % 0.40/0.58 (define @t108 () (not @t107)) % 0.40/0.58 (define @t109 () (= @t32 @t102)) % 0.40/0.58 (define @t110 () (= @t33 @t102)) % 0.40/0.58 (define @t111 () (or @t110 @t109)) % 0.40/0.58 (define @t112 () (= @t105 @t111)) % 0.40/0.58 (define @t113 () (not @t109)) % 0.40/0.58 (define @t114 () (not @t97)) % 0.40/0.58 (define @t115 () (and @t114 @t109 @t103)) % 0.40/0.58 (define @t116 () (@list @t91)) % 0.40/0.58 (define @t117 () (not @t98)) % 0.40/0.58 (define @t118 () (not @t110)) % 0.40/0.58 (define @t119 () (and @t117 @t110)) % 0.40/0.58 (assume @p1 @t11) % 0.40/0.58 (assume @p2 (forall @t10 (= (tptp.equal_set @t4 @t1) (and @t8 (tptp.subset @t1 @t4))))) % 0.40/0.58 (assume @p3 (forall @t12 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.40/0.58 (assume @p4 (forall @t13 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.40/0.58 (assume @p5 (forall @t13 (= (tptp.member @t2 @t14) (or @t5 @t3)))) % 0.40/0.58 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.40/0.58 (assume @p7 (forall (@list @t1 @t4 @t15) (= (tptp.member @t1 (tptp.difference @t15 @t4)) (and (tptp.member @t1 @t15) (not (tptp.member @t1 @t4)))))) % 0.40/0.58 (assume @p8 (forall @t12 (= (tptp.member @t2 (tptp.singleton @t4)) @t16))) % 0.40/0.58 (assume @p9 @t21) % 0.40/0.58 (assume @p10 @t30) % 0.40/0.58 (assume @p11 (forall @t12 (= (tptp.member @t2 (tptp.product @t4)) (forall @t26 (=> @t24 @t23))))) % 0.40/0.58 (assume @p12 (not @t31)) % 0.40/0.58 (assume @p13 true) % 0.40/0.58 (step @p14 :rule bool-impl-elim :args (@t5 @t3)) % 0.40/0.58 (step @p15 :rule cong :premises (@p14) :args (@t7)) % 0.40/0.58 (step @p16 :rule refl :args (@t8)) % 0.40/0.58 (step @p17 :rule cong :premises (@p16 @p15) :args (@t9)) % 0.40/0.58 (step @p18 :rule cong :premises (@p17) :args (@t11)) % 0.40/0.58 (step @p19 :rule eq_resolve :premises (@p1 @p18)) % 0.40/0.58 (step @p20 :rule instantiate :premises (@p19) :args (@t37)) % 0.40/0.58 (step @p21 :rule instantiate :premises (@p19) :args ((@list @t34 @t36))) % 0.40/0.58 (step @p22 :rule bool-double-not-elim :args (@t42)) % 0.40/0.58 (step @p23 :rule refl :args (@t45)) % 0.40/0.58 (step @p24 :rule nary_cong :premises (@p23 @p22) :args ((or @t45 (not @t44)))) % 0.40/0.58 (step @p25 :rule cnf_or_neg :args (@t45 0)) % 0.40/0.58 (step @p26 :rule eq_resolve :premises (@p25 @p24)) % 0.40/0.58 (step @p27 :rule reordering :premises (@p26) :args ((or @t42 @t45))) % 0.40/0.58 (step @p28 :rule cnf_or_neg :args (@t45 1)) % 0.40/0.58 (step @p29 :rule instantiate :premises (@p5) :args ((@list @t41 @t33 @t32))) % 0.40/0.58 (step @p30 :rule cnf_equiv_pos1 :args (@t49)) % 0.40/0.58 (step @p31 :rule reordering :premises (@p30) :args ((or @t44 @t48 (not @t49)))) % 0.40/0.58 (step @p32 :rule bool-and-de-morgan :args (@t24 @t23 true)) % 0.40/0.58 (step @p33 :rule cong :premises (@p32) :args (@t50)) % 0.40/0.58 (step @p34 :rule cong :premises (@p33) :args (@t51)) % 0.40/0.58 (step @p35 :rule exists-elim :args ((= @t27 @t51))) % 0.40/0.58 (step @p36 :rule trans :premises (@p35 @p34)) % 0.40/0.58 (step @p37 :rule refl :args (@t28)) % 0.40/0.58 (step @p38 :rule cong :premises (@p37 @p36) :args (@t29)) % 0.40/0.58 (step @p39 :rule cong :premises (@p38) :args (@t30)) % 0.40/0.58 (step @p40 :rule eq_resolve :premises (@p10 @p39)) % 0.40/0.58 (step @p41 :rule instantiate :premises (@p40) :args ((@list @t41 @t35))) % 0.40/0.58 (step @p42 :rule bool-double-not-elim :args (@t53)) % 0.40/0.58 (step @p43 :rule refl :args (@t43)) % 0.40/0.58 (step @p44 :rule refl :args (@t56)) % 0.40/0.58 (step @p45 :rule nary_cong :premises (@p44 @p43 @p42) :args ((or @t56 @t43 (not @t54)))) % 0.40/0.58 (step @p46 :rule cnf_equiv_pos2 :args (@t55)) % 0.40/0.58 (step @p47 :rule eq_resolve :premises (@p46 @p45)) % 0.40/0.58 (step @p48 :rule reordering :premises (@p47) :args ((or @t43 @t53 @t56))) % 0.40/0.58 (assume-push @p248 @t53) % 0.40/0.58 (step @p50 :rule instantiate :premises (@p248) :args ((@list @t32))) % 0.40/0.58 (step-pop @p249 :rule scope :premises (@p50)) % 0.40/0.58 (step @p51 :rule process_scope :premises (@p249) :args (@t60)) % 0.40/0.58 (step @p53 :rule implies_elim :premises (@p51)) % 0.40/0.58 (assume-push @p250 @t53) % 0.40/0.58 (step @p55 :rule instantiate :premises (@p250) :args ((@list @t33))) % 0.40/0.58 (step-pop @p251 :rule scope :premises (@p55)) % 0.40/0.58 (step @p56 :rule process_scope :premises (@p251) :args (@t64)) % 0.40/0.58 (step @p58 :rule implies_elim :premises (@p56)) % 0.40/0.58 (step @p59 :rule eq-symm :args (@t2 @t1)) % 0.40/0.58 (step @p60 :rule eq-symm :args (@t2 @t4)) % 0.40/0.58 (step @p61 :rule nary_cong :premises (@p60 @p59) :args (@t17)) % 0.40/0.58 (step @p62 :rule refl :args (@t19)) % 0.40/0.58 (step @p63 :rule cong :premises (@p62 @p61) :args (@t20)) % 0.40/0.58 (step @p64 :rule cong :premises (@p63) :args (@t21)) % 0.40/0.58 (step @p65 :rule eq_resolve :premises (@p9 @p64)) % 0.40/0.58 (step @p66 :rule bool-eq-true :args (@t58)) % 0.40/0.58 (step @p67 :rule absorb :args ((= (or @t65 true) true))) % 0.40/0.58 (step @p68 :rule eq-refl :args (@t32)) % 0.40/0.58 (step @p69 :rule refl :args (@t65)) % 0.40/0.58 (step @p70 :rule nary_cong :premises (@p69 @p68) :args (@t66)) % 0.40/0.58 (step @p71 :rule trans :premises (@p70 @p67)) % 0.40/0.58 (step @p72 :rule refl :args (@t58)) % 0.40/0.58 (step @p73 :rule cong :premises (@p72 @p71) :args (@t67)) % 0.40/0.58 (step @p74 :rule trans :premises (@p73 @p66)) % 0.40/0.58 (step @p75 :rule refl :args (@t68)) % 0.40/0.58 (step @p76 :rule cong :premises (@p75 @p74) :args ((=> @t68 @t67))) % 0.40/0.58 (assume-push @p252 @t68) % 0.40/0.58 (step @p78 :rule instantiate :premises (@p65) :args ((@list @t32 @t33 @t32))) % 0.40/0.58 (step-pop @p253 :rule scope :premises (@p78)) % 0.40/0.58 (step @p79 :rule process_scope :premises (@p253) :args (@t67)) % 0.40/0.58 (step @p81 :rule eq_resolve :premises (@p79 @p76)) % 0.40/0.58 (step @p82 :rule implies_elim :premises (@p81)) % 0.40/0.58 (step @p83 :rule chain_m_resolution :premises (@p82 @p65) :args (@t58 @t69 @t70)) % 0.40/0.58 (step @p84 :rule cnf_or_pos :args (@t60)) % 0.40/0.58 (step @p85 :rule reordering :premises (@p84) :args ((or @t57 @t59 (not @t60)))) % 0.40/0.58 (step @p86 :rule bool-eq-true :args (@t62)) % 0.40/0.58 (step @p87 :rule absorb :args ((= (or true @t65) true))) % 0.40/0.58 (step @p88 :rule eq-symm :args (@t32 @t33)) % 0.40/0.58 (step @p89 :rule eq-refl :args (@t33)) % 0.40/0.58 (step @p90 :rule nary_cong :premises (@p89 @p88) :args (@t71)) % 0.40/0.58 (step @p91 :rule trans :premises (@p90 @p87)) % 0.40/0.58 (step @p92 :rule refl :args (@t62)) % 0.40/0.58 (step @p93 :rule cong :premises (@p92 @p91) :args (@t72)) % 0.40/0.58 (step @p94 :rule trans :premises (@p93 @p86)) % 0.40/0.58 (step @p95 :rule cong :premises (@p75 @p94) :args ((=> @t68 @t72))) % 0.40/0.58 (assume-push @p254 @t68) % 0.40/0.58 (step @p97 :rule instantiate :premises (@p65) :args ((@list @t33 @t33 @t32))) % 0.40/0.58 (step-pop @p255 :rule scope :premises (@p97)) % 0.40/0.58 (step @p98 :rule process_scope :premises (@p255) :args (@t72)) % 0.40/0.58 (step @p100 :rule eq_resolve :premises (@p98 @p95)) % 0.40/0.58 (step @p101 :rule implies_elim :premises (@p100)) % 0.40/0.58 (step @p102 :rule chain_m_resolution :premises (@p101 @p65) :args (@t62 @t69 @t70)) % 0.40/0.58 (step @p103 :rule cnf_or_pos :args (@t64)) % 0.40/0.58 (step @p104 :rule reordering :premises (@p103) :args ((or @t61 @t63 (not @t64)))) % 0.40/0.58 (step @p105 :rule cnf_or_pos :args (@t48)) % 0.40/0.58 (step @p106 :rule reordering :premises (@p105) :args ((or @t47 @t46 (not @t48)))) % 0.40/0.58 (step @p107 :rule chain_m_resolution :premises (@p106 @p104 @p102 @p85 @p83 @p58 @p53 @p48 @p41 @p31 @p29 @p28 @p27) :args (@t45 (@list true false true false false false false false false false true false) (@list @t47 @t62 @t46 @t58 @t64 @t60 @t53 @t55 @t48 @t49 @t43 @t42))) % 0.40/0.58 (step @p108 :rule refl :args (@t73)) % 0.40/0.58 (step @p109 :rule bool-double-not-elim :args (@t40)) % 0.40/0.58 (step @p110 :rule nary_cong :premises (@p109 @p108) :args ((or (not @t74) @t73))) % 0.40/0.58 (assume-push @p256 @t74) % 0.40/0.58 (step @p112 :rule skolemize :premises (@p256)) % 0.40/0.58 (step-pop @p257 :rule scope :premises (@p112)) % 0.40/0.58 (step @p113 :rule process_scope :premises (@p257) :args (@t73)) % 0.40/0.58 (step @p115 :rule implies_elim :premises (@p113)) % 0.40/0.58 (step @p116 :rule eq_resolve :premises (@p115 @p110)) % 0.40/0.58 (step @p117 :rule chain_m_resolution :premises (@p116 @p107) :args (@t40 @t69 (@list @t45))) % 0.40/0.58 (step @p118 :rule cnf_equiv_pos2 :args (@t76)) % 0.40/0.58 (step @p119 :rule reordering :premises (@p118) :args ((or @t75 @t74 (not @t76)))) % 0.40/0.58 (step @p120 :rule chain_m_resolution :premises (@p119 @p117 @p21) :args (@t75 @t77 (@list @t40 @t76))) % 0.40/0.58 (step @p121 :rule instantiate :premises (@p2) :args (@t37)) % 0.40/0.58 (step @p122 :rule skolemize :premises (@p12)) % 0.40/0.58 (step @p123 :rule cnf_equiv_pos2 :args (@t81)) % 0.40/0.58 (step @p124 :rule reordering :premises (@p123) :args ((or @t80 @t82 (not @t81)))) % 0.40/0.58 (step @p125 :rule chain_m_resolution :premises (@p124 @p122 @p121) :args (@t82 @t83 (@list @t80 @t81))) % 0.40/0.58 (step @p126 :rule cnf_and_neg :args (@t79)) % 0.40/0.58 (step @p127 :rule chain_m_resolution :premises (@p126 @p125 @p120) :args ((not @t78) @t83 (@list @t79 @t75))) % 0.40/0.58 (step @p128 :rule cnf_equiv_pos2 :args (@t85)) % 0.40/0.58 (step @p129 :rule reordering :premises (@p128) :args ((or @t78 @t86 (not @t85)))) % 0.40/0.58 (step @p130 :rule chain_m_resolution :premises (@p129 @p127 @p20) :args (@t86 @t83 (@list @t78 @t85))) % 0.40/0.58 (step @p131 :rule refl :args (@t92)) % 0.40/0.58 (step @p132 :rule bool-double-not-elim :args (@t84)) % 0.40/0.58 (step @p133 :rule nary_cong :premises (@p132 @p131) :args ((or (not @t86) @t92))) % 0.40/0.58 (assume-push @p258 @t86) % 0.40/0.58 (step @p135 :rule skolemize :premises (@p258)) % 0.40/0.58 (step-pop @p259 :rule scope :premises (@p135)) % 0.40/0.58 (step @p136 :rule process_scope :premises (@p259) :args (@t92)) % 0.40/0.58 (step @p138 :rule implies_elim :premises (@p136)) % 0.40/0.58 (step @p139 :rule eq_resolve :premises (@p138 @p133)) % 0.40/0.58 (step @p140 :rule chain_m_resolution :premises (@p139 @p130) :args (@t92 @t93 (@list @t84))) % 0.40/0.58 (step @p141 :rule bool-double-not-elim :args (@t89)) % 0.40/0.58 (step @p142 :rule refl :args (@t91)) % 0.40/0.58 (step @p143 :rule nary_cong :premises (@p142 @p141) :args ((or @t91 (not @t90)))) % 0.40/0.58 (step @p144 :rule cnf_or_neg :args (@t91 0)) % 0.40/0.58 (step @p145 :rule eq_resolve :premises (@p144 @p143)) % 0.40/0.58 (step @p146 :rule reordering :premises (@p145) :args ((or @t89 @t91))) % 0.40/0.58 (step @p147 :rule cnf_or_neg :args (@t91 1)) % 0.40/0.58 (step @p148 :rule instantiate :premises (@p40) :args ((@list @t87 @t35))) % 0.40/0.58 (step @p149 :rule cnf_equiv_pos1 :args (@t96)) % 0.40/0.58 (step @p150 :rule reordering :premises (@p149) :args ((or @t90 @t95 (not @t96)))) % 0.40/0.58 (step @p151 :rule instantiate :premises (@p5) :args ((@list @t87 @t33 @t32))) % 0.40/0.58 (step @p152 :rule cnf_equiv_pos2 :args (@t100)) % 0.40/0.58 (step @p153 :rule reordering :premises (@p152) :args ((or @t88 @t101 (not @t100)))) % 0.40/0.58 (step @p154 :rule refl :args (@t108)) % 0.40/0.58 (step @p155 :rule bool-double-not-elim :args (@t94)) % 0.40/0.58 (step @p156 :rule nary_cong :premises (@p155 @p154) :args ((or (not @t95) @t108))) % 0.40/0.58 (assume-push @p260 @t95) % 0.40/0.58 (step @p158 :rule skolemize :premises (@p260)) % 0.40/0.58 (step-pop @p261 :rule scope :premises (@p158)) % 0.40/0.58 (step @p159 :rule process_scope :premises (@p261) :args (@t108)) % 0.40/0.58 (step @p161 :rule implies_elim :premises (@p159)) % 0.40/0.58 (step @p162 :rule eq_resolve :premises (@p161 @p156)) % 0.40/0.58 (step @p163 :rule cnf_or_neg :args (@t99 1)) % 0.40/0.58 (step @p164 :rule bool-double-not-elim :args (@t105)) % 0.40/0.58 (step @p165 :rule refl :args (@t107)) % 0.40/0.58 (step @p166 :rule nary_cong :premises (@p165 @p164) :args ((or @t107 (not @t106)))) % 0.40/0.58 (step @p167 :rule cnf_or_neg :args (@t107 0)) % 0.40/0.58 (step @p168 :rule eq_resolve :premises (@p167 @p166)) % 0.40/0.58 (step @p169 :rule reordering :premises (@p168) :args ((or @t105 @t107))) % 0.40/0.58 (step @p170 :rule bool-double-not-elim :args (@t103)) % 0.40/0.58 (step @p171 :rule nary_cong :premises (@p165 @p170) :args ((or @t107 (not @t104)))) % 0.40/0.58 (step @p172 :rule cnf_or_neg :args (@t107 1)) % 0.40/0.58 (step @p173 :rule eq_resolve :premises (@p172 @p171)) % 0.40/0.58 (step @p174 :rule reordering :premises (@p173) :args ((or @t103 @t107))) % 0.40/0.58 (step @p175 :rule instantiate :premises (@p65) :args ((@list @t102 @t33 @t32))) % 0.40/0.58 (step @p176 :rule cnf_equiv_pos1 :args (@t112)) % 0.40/0.58 (step @p177 :rule reordering :premises (@p176) :args ((or @t106 @t111 (not @t112)))) % 0.40/0.58 (step @p178 :rule cnf_or_pos :args (@t111)) % 0.40/0.58 (step @p179 :rule reordering :premises (@p178) :args ((or @t110 @t109 (not @t111)))) % 0.40/0.58 (step @p180 :rule refl :args (@t113)) % 0.40/0.58 (step @p181 :rule refl :args (@t104)) % 0.40/0.58 (step @p182 :rule bool-double-not-elim :args (@t97)) % 0.40/0.58 (step @p183 :rule nary_cong :premises (@p182 @p181 @p180) :args ((or (not @t114) @t104 @t113))) % 0.40/0.58 (assume-push @p262 @t114) % 0.40/0.58 (assume-push @p263 @t109) % 0.40/0.58 (assume-push @p264 @t103) % 0.40/0.58 (step @p187 :rule evaluate :args ((= true false))) % 0.40/0.58 (step @p188 :rule false_intro :premises (@p262)) % 0.40/0.58 (step @p189 :rule symm :premises (@p263)) % 0.40/0.58 (step @p190 :rule refl :args (@t87)) % 0.40/0.58 (step @p191 :rule cong :premises (@p190 @p189) :args (@t103)) % 0.40/0.58 (step @p192 :rule true_intro :premises (@p264)) % 0.40/0.58 (step @p193 :rule symm :premises (@p192)) % 0.40/0.58 (step @p194 :rule trans :premises (@p193 @p191 @p188)) % 0.40/0.58 (step @p195 false :rule eq_resolve :premises (@p194 @p187)) % 0.40/0.58 (step-pop @p265 :rule scope :premises (@p195)) % 0.40/0.58 (step-pop @p266 :rule scope :premises (@p265)) % 0.40/0.58 (step-pop @p267 :rule scope :premises (@p266)) % 0.40/0.58 (step @p196 :rule process_scope :premises (@p267) :args (false)) % 0.40/0.58 (assume-push @p268 @t114) % 0.40/0.58 (assume-push @p269 @t103) % 0.40/0.58 (assume-push @p270 @t109) % 0.40/0.58 (step @p203 :rule and_intro :premises (@p268 @p270 @p269)) % 0.40/0.58 (step-pop @p271 :rule scope :premises (@p203)) % 0.40/0.58 (step-pop @p272 :rule scope :premises (@p271)) % 0.40/0.58 (step-pop @p273 :rule scope :premises (@p272)) % 0.40/0.58 (step @p204 :rule process_scope :premises (@p273) :args (@t115)) % 0.40/0.58 (step @p208 :rule implies_elim :premises (@p204)) % 0.40/0.58 (step @p209 :rule resolution :premises (@p208 @p196) :args (true @t115)) % 0.40/0.58 (step @p210 :rule not_and :premises (@p209)) % 0.40/0.58 (step @p211 :rule eq_resolve :premises (@p210 @p183)) % 0.40/0.58 (step @p212 :rule chain_m_resolution :premises (@p211 @p179 @p177 @p175 @p174 @p169 @p163 @p162 @p153 @p151 @p150 @p148 @p147 @p146) :args ((or @t91 @t110) (@list false false false false false true true true false true false true false) (@list @t109 @t111 @t112 @t103 @t105 @t97 @t107 @t99 @t100 @t94 @t96 @t88 @t89))) % 0.40/0.58 (step @p213 :rule chain_m_resolution :premises (@p212 @p140) :args (@t110 @t93 @t116)) % 0.40/0.58 (step @p214 :rule chain_m_resolution :premises (@p147 @p140) :args ((not @t88) @t93 @t116)) % 0.40/0.58 (step @p215 :rule chain_m_resolution :premises (@p153 @p214 @p151) :args (@t101 @t83 (@list @t88 @t100))) % 0.40/0.58 (step @p216 :rule cnf_or_neg :args (@t99 0)) % 0.40/0.58 (step @p217 :rule chain_m_resolution :premises (@p216 @p215) :args (@t117 @t93 (@list @t99))) % 0.40/0.58 (step @p218 :rule chain_m_resolution :premises (@p146 @p140) :args (@t89 @t93 @t116)) % 0.40/0.58 (step @p219 :rule chain_m_resolution :premises (@p150 @p218 @p148) :args (@t95 @t77 (@list @t89 @t96))) % 0.40/0.58 (step @p220 :rule chain_m_resolution :premises (@p162 @p219) :args (@t108 @t93 (@list @t94))) % 0.40/0.58 (step @p221 :rule chain_m_resolution :premises (@p174 @p220) :args (@t103 @t93 (@list @t107))) % 0.40/0.58 (step @p222 :rule refl :args (@t118)) % 0.40/0.58 (step @p223 :rule bool-double-not-elim :args (@t98)) % 0.40/0.58 (step @p224 :rule nary_cong :premises (@p223 @p222 @p181) :args ((or (not @t117) @t118 @t104))) % 0.40/0.58 (assume-push @p274 @t117) % 0.40/0.58 (assume-push @p275 @t110) % 0.40/0.58 (assume-push @p276 @t117) % 0.40/0.58 (assume-push @p277 @t110) % 0.40/0.58 (step @p229 :rule false_intro :premises (@p274)) % 0.40/0.58 (step @p230 :rule symm :premises (@p275)) % 0.40/0.58 (step @p190 :rule refl :args (@t87)) % 0.40/0.58 (step @p231 :rule cong :premises (@p190 @p230) :args (@t103)) % 0.40/0.58 (step @p232 :rule trans :premises (@p231 @p229)) % 0.40/0.58 (step @p233 :rule false_elim :premises (@p232)) % 0.40/0.58 (step-pop @p278 :rule scope :premises (@p233)) % 0.40/0.58 (step-pop @p279 :rule scope :premises (@p278)) % 0.40/0.58 (step @p234 :rule process_scope :premises (@p279) :args (@t104)) % 0.40/0.58 (step @p237 :rule and_intro :premises (@p274 @p275)) % 0.40/0.58 (step @p238 :rule modus_ponens :premises (@p237 @p234)) % 0.40/0.58 (step-pop @p280 :rule scope :premises (@p238)) % 0.40/0.58 (step-pop @p281 :rule scope :premises (@p280)) % 0.40/0.58 (step @p239 :rule process_scope :premises (@p281) :args (@t104)) % 0.40/0.58 (step @p242 :rule implies_elim :premises (@p239)) % 0.40/0.58 (step @p243 :rule cnf_and_neg :args (@t119)) % 0.40/0.58 (step @p244 :rule resolution :premises (@p243 @p242) :args (true @t119)) % 0.40/0.58 (step @p245 :rule eq_resolve :premises (@p244 @p224)) % 0.40/0.58 (step @p246 :rule reordering :premises (@p245) :args ((or @t98 @t104 @t118))) % 0.40/0.58 (step @p247 false :rule chain_m_resolution :premises (@p246 @p221 @p217 @p213) :args (false (@list false true false) (@list @t103 @t98 @t110))) % 0.40/0.58 ) % 0.40/0.58 % SZS output end Proof % 0.40/0.58 % cvc5 exiting %------------------------------------------------------------------------------