%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET046^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n029.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 08:47:08 AM UTC 2026 % Result : Theorem 150.57s 150.88s % Output : Proof 150.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET046^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n029.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 14:48:17 EDT 2026 % 0.18/0.34 % CPUTime : % 0.29/0.48 %----Proving TH0 % 150.57/150.88 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 150.57/150.88 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 150.57/150.88 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 150.57/150.88 --- Run --ho-elim --full-saturate-quant at 18s... % 150.57/150.88 % SZS status Theorem % 150.57/150.88 % SZS output start Proof % 150.57/150.88 ( % 150.57/150.88 (declare-sort $$unsorted 0) % 150.57/150.88 (declare-const tptp.cF (-> $$unsorted $$unsorted Bool)) % 150.57/150.88 (define @t1 () (@var "Xy" $$unsorted)) % 150.57/150.88 (define @t2 () (@var "Xx" $$unsorted)) % 150.57/150.88 (define @t3 () (_ tptp.cF @t2)) % 150.57/150.88 (define @t4 () (_ @t3 @t1)) % 150.57/150.88 (define @t5 () (@var "Xz" $$unsorted)) % 150.57/150.88 (define @t6 () (_ (_ tptp.cF @t5) @t2)) % 150.57/150.88 (define @t7 () (_ @t3 @t5)) % 150.57/150.88 (define @t8 () (and @t7 @t6)) % 150.57/150.88 (define @t9 () (@list @t5)) % 150.57/150.88 (define @t10 () (exists @t9 @t8)) % 150.57/150.88 (define @t11 () (not @t10)) % 150.57/150.88 (define @t12 () (=> @t11 @t4)) % 150.57/150.88 (define @t13 () (=> @t4 @t11)) % 150.57/150.88 (define @t14 () (and @t13 @t12)) % 150.57/150.88 (define @t15 () (@list @t2)) % 150.57/150.88 (define @t16 () (forall @t15 @t14)) % 150.57/150.88 (define @t17 () (@list @t1)) % 150.57/150.88 (define @t18 () (exists @t17 @t16)) % 150.57/150.88 (define @t19 () (@var "BOUND_VARIABLE_7469" $$unsorted)) % 150.57/150.88 (define @t20 () (@const 0 (@ho-elim-sort (-> $$unsorted $$unsorted Bool)))) % 150.57/150.88 (define @t21 () (@const 1 (-> (@ho-elim-sort (-> $$unsorted $$unsorted Bool)) $$unsorted (@ho-elim-sort (-> $$unsorted Bool))))) % 150.57/150.88 (define @t22 () (_ @t21 @t20 @t19)) % 150.57/150.88 (define @t23 () (@const 2 (-> (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool))) % 150.57/150.88 (define @t24 () (_ @t21 @t20 @t5)) % 150.57/150.88 (define @t25 () (not (forall @t9 (or (not (_ @t23 @t22 @t5)) (not (_ @t23 @t24 @t19)))))) % 150.57/150.88 (define @t26 () (@list @t19)) % 150.57/150.88 (define @t27 () (@var "BOUND_VARIABLE_7455" $$unsorted)) % 150.57/150.88 (define @t28 () (@var "BOUND_VARIABLE_7488" $$unsorted)) % 150.57/150.88 (define @t29 () (not (_ @t23 (_ @t21 @t20 @t28) @t27))) % 150.57/150.88 (define @t30 () (_ @t21 @t20 @t27)) % 150.57/150.88 (define @t31 () (not (_ @t23 @t30 @t28))) % 150.57/150.88 (define @t32 () (@list @t27 @t28)) % 150.57/150.88 (define @t33 () (forall @t17 (or (not (forall @t32 (or (not (_ @t23 @t30 @t1)) @t31 @t29))) (not (forall @t26 (or @t25 (_ @t23 @t22 @t1))))))) % 150.57/150.88 (define @t34 () (tptp.cF @t19 @t1)) % 150.57/150.88 (define @t35 () (not (forall @t9 (or (not (tptp.cF @t19 @t5)) (not (tptp.cF @t5 @t19)))))) % 150.57/150.88 (define @t36 () (forall @t26 (or @t35 @t34))) % 150.57/150.88 (define @t37 () (not (tptp.cF @t28 @t27))) % 150.57/150.88 (define @t38 () (not (tptp.cF @t27 @t28))) % 150.57/150.88 (define @t39 () (tptp.cF @t27 @t1)) % 150.57/150.88 (define @t40 () (not @t39)) % 150.57/150.88 (define @t41 () (or @t40 @t38 @t37)) % 150.57/150.88 (define @t42 () (forall @t32 @t41)) % 150.57/150.88 (define @t43 () (and @t42 @t36)) % 150.57/150.88 (define @t44 () (forall @t17 (not @t43))) % 150.57/150.88 (define @t45 () (not @t44)) % 150.57/150.88 (define @t46 () (_ (_ tptp.cF @t19) @t1)) % 150.57/150.88 (define @t47 () (or @t35 @t46)) % 150.57/150.88 (define @t48 () (forall @t26 @t47)) % 150.57/150.88 (define @t49 () (or @t38 @t37)) % 150.57/150.88 (define @t50 () (or @t40 @t49)) % 150.57/150.88 (define @t51 () (forall @t32 @t50)) % 150.57/150.88 (define @t52 () (@list @t28)) % 150.57/150.88 (define @t53 () (forall @t52 @t50)) % 150.57/150.88 (define @t54 () (@list @t27)) % 150.57/150.88 (define @t55 () (forall @t52 @t49)) % 150.57/150.88 (define @t56 () (or @t40 @t55)) % 150.57/150.88 (define @t57 () (forall @t9 (or (not (tptp.cF @t27 @t5)) (not (tptp.cF @t5 @t27))))) % 150.57/150.88 (define @t58 () (_ (_ tptp.cF @t27) @t1)) % 150.57/150.88 (define @t59 () (not @t58)) % 150.57/150.88 (define @t60 () (or @t59 @t57)) % 150.57/150.88 (define @t61 () (forall @t54 @t60)) % 150.57/150.88 (define @t62 () (tptp.cF @t5 @t2)) % 150.57/150.88 (define @t63 () (tptp.cF @t2 @t5)) % 150.57/150.88 (define @t64 () (forall @t9 (or (not @t63) (not @t62)))) % 150.57/150.88 (define @t65 () (or (not @t64) @t4)) % 150.57/150.88 (define @t66 () (forall @t15 @t65)) % 150.57/150.88 (define @t67 () (@list @t2)) % 150.57/150.88 (define @t68 () (or (not @t4) @t64)) % 150.57/150.88 (define @t69 () (forall @t15 @t68)) % 150.57/150.88 (define @t70 () (and @t69 @t66)) % 150.57/150.88 (define @t71 () (and (=> @t4 @t64) (=> @t64 @t4))) % 150.57/150.88 (define @t72 () (not @t6)) % 150.57/150.88 (define @t73 () (not @t7)) % 150.57/150.88 (define @t74 () (or @t73 @t72)) % 150.57/150.88 (define @t75 () (forall @t9 (not @t8))) % 150.57/150.88 (define @t76 () (not @t75)) % 150.57/150.88 (define @t77 () (@quantifiers_skolemize @t33 0)) % 150.57/150.88 (define @t78 () (forall @t32 (or (not (_ @t23 @t30 @t77)) @t31 @t29))) % 150.57/150.88 (define @t79 () (forall @t26 (or @t25 (_ @t23 @t22 @t77)))) % 150.57/150.88 (define @t80 () (not @t79)) % 150.57/150.88 (define @t81 () (not @t78)) % 150.57/150.88 (define @t82 () (or @t81 @t80)) % 150.57/150.88 (define @t83 () (@list true)) % 150.57/150.88 (define @t84 () (@list @t82)) % 150.57/150.88 (define @t85 () (_ @t21 @t20 @t77)) % 150.57/150.88 (define @t86 () (_ @t23 @t85 @t77)) % 150.57/150.88 (define @t87 () (not @t86)) % 150.57/150.88 (define @t88 () (or @t87 @t87 @t87)) % 150.57/150.88 (define @t89 () (forall @t9 (or (not (_ @t23 @t85 @t5)) (not (_ @t23 @t24 @t77))))) % 150.57/150.88 (define @t90 () (not @t89)) % 150.57/150.88 (define @t91 () (or @t90 @t86)) % 150.57/150.88 (define @t92 () (@list true false)) % 150.57/150.88 (define @t93 () (@quantifiers_skolemize @t89 0)) % 150.57/150.88 (define @t94 () (_ @t23 (_ @t21 @t20 @t93) @t77)) % 150.57/150.88 (define @t95 () (not @t94)) % 150.57/150.88 (define @t96 () (_ @t23 @t85 @t93)) % 150.57/150.88 (define @t97 () (not @t96)) % 150.57/150.88 (define @t98 () (or @t97 @t95)) % 150.57/150.88 (define @t99 () (@list @t98)) % 150.57/150.88 (define @t100 () (or @t95 @t95 @t97)) % 150.57/150.88 (define @t101 () (not @t100)) % 150.57/150.88 (assume @p1 (not (not @t18))) % 150.57/150.88 (assume @p2 true) % 150.57/150.88 ; WARNING: add trust step for TRUST % 150.57/150.88 ; trust TRUST PREPROCESS_HO_ELIM % 150.57/150.88 (step @p3 :rule trust :premises () :args ((= (not (forall @t17 (or (not @t42) (not @t36)))) (not @t33)))) % 150.57/150.88 (step @p4 :rule bool-and-de-morgan :args (@t42 @t36 true)) % 150.57/150.88 (step @p5 :rule cong :premises (@p4) :args (@t44)) % 150.57/150.88 (step @p6 :rule cong :premises (@p5) :args (@t45)) % 150.57/150.88 (step @p7 :rule exists-elim :args ((= (exists @t17 @t43) @t45))) % 150.57/150.88 (step @p8 :rule trans :premises (@p7 @p6)) % 150.57/150.88 (step @p9 :rule refl :args (@t34)) % 150.57/150.88 (step @p10 :rule refl :args (@t46)) % 150.57/150.88 (step @p11 :rule cong :premises (@p10 @p9) :args ((= @t46 @t34))) % 150.57/150.88 (step @p12 :rule symm :premises (@p11)) % 150.57/150.88 (step @p13 :rule eq_resolve :premises (@p10 @p12)) % 150.57/150.88 (step @p14 :rule refl :args (@t35)) % 150.57/150.88 (step @p15 :rule nary_cong :premises (@p14 @p13) :args (@t47)) % 150.57/150.88 (step @p16 :rule cong :premises (@p15) :args (@t48)) % 150.57/150.88 (step @p17 :rule aci_norm :args ((= @t50 @t41))) % 150.57/150.88 (step @p18 :rule cong :premises (@p17) :args (@t51)) % 150.57/150.88 (step @p19 :rule quant-merge-prenex :args ((= (forall @t54 @t53) @t51))) % 150.57/150.88 (step @p20 :rule alpha_equiv :args (@t55 (@list @t28) (@list @t5))) % 150.57/150.88 (step @p21 :rule refl :args (@t40)) % 150.57/150.88 (step @p22 :rule nary_cong :premises (@p21 @p20) :args (@t56)) % 150.57/150.88 (step @p23 :rule quant-miniscope-or :args ((= @t53 @t56))) % 150.57/150.88 (step @p24 :rule trans :premises (@p23 @p22)) % 150.57/150.88 (step @p25 :rule symm :premises (@p24)) % 150.57/150.88 (step @p26 :rule cong :premises (@p25) :args ((forall @t54 (or @t40 @t57)))) % 150.57/150.88 (step @p27 :rule trans :premises (@p26 @p19)) % 150.57/150.88 (step @p28 :rule trans :premises (@p27 @p18)) % 150.57/150.88 (step @p29 :rule refl :args (@t57)) % 150.57/150.88 (step @p30 :rule refl :args (@t39)) % 150.57/150.88 (step @p31 :rule refl :args (@t58)) % 150.57/150.88 (step @p32 :rule cong :premises (@p31 @p30) :args ((= @t58 @t39))) % 150.57/150.88 (step @p33 :rule symm :premises (@p32)) % 150.57/150.88 (step @p34 :rule eq_resolve :premises (@p31 @p33)) % 150.57/150.88 (step @p35 :rule cong :premises (@p34) :args (@t59)) % 150.57/150.88 (step @p36 :rule nary_cong :premises (@p35 @p29) :args (@t60)) % 150.57/150.88 (step @p37 :rule cong :premises (@p36) :args (@t61)) % 150.57/150.88 (step @p38 :rule trans :premises (@p37 @p28)) % 150.57/150.88 (step @p39 :rule nary_cong :premises (@p38 @p16) :args ((and @t61 @t48))) % 150.57/150.88 (step @p40 :rule alpha_equiv :args (@t66 @t67 (@list @t19))) % 150.57/150.88 (step @p41 :rule alpha_equiv :args (@t69 @t67 (@list @t27))) % 150.57/150.88 (step @p42 :rule nary_cong :premises (@p41 @p40) :args (@t70)) % 150.57/150.88 (step @p43 :rule quant-miniscope-and :args ((= (forall @t15 (and @t68 @t65)) @t70))) % 150.57/150.88 (step @p44 :rule trans :premises (@p43 @p42)) % 150.57/150.88 (step @p45 :rule trans :premises (@p44 @p39)) % 150.57/150.88 (step @p46 :rule bool-impl-elim :args (@t64 @t4)) % 150.57/150.88 (step @p47 :rule bool-impl-elim :args (@t4 @t64)) % 150.57/150.88 (step @p48 :rule nary_cong :premises (@p47 @p46) :args (@t71)) % 150.57/150.88 (step @p49 :rule cong :premises (@p48) :args ((forall @t15 @t71))) % 150.57/150.88 (step @p50 :rule trans :premises (@p49 @p45)) % 150.57/150.88 (step @p51 :rule refl :args (@t4)) % 150.57/150.88 (step @p52 :rule bool-double-not-elim :args (@t64)) % 150.57/150.88 (step @p53 :rule refl :args (@t62)) % 150.57/150.88 (step @p54 :rule refl :args (@t6)) % 150.57/150.88 (step @p55 :rule cong :premises (@p54 @p53) :args ((= @t6 @t62))) % 150.57/150.88 (step @p56 :rule symm :premises (@p55)) % 150.57/150.88 (step @p57 :rule eq_resolve :premises (@p54 @p56)) % 150.57/150.88 (step @p58 :rule cong :premises (@p57) :args (@t72)) % 150.57/150.88 (step @p59 :rule refl :args (@t63)) % 150.57/150.88 (step @p60 :rule refl :args (@t7)) % 150.57/150.88 (step @p61 :rule cong :premises (@p60 @p59) :args ((= @t7 @t63))) % 150.57/150.88 (step @p62 :rule symm :premises (@p61)) % 150.57/150.88 (step @p63 :rule eq_resolve :premises (@p60 @p62)) % 150.57/150.88 (step @p64 :rule cong :premises (@p63) :args (@t73)) % 150.57/150.88 (step @p65 :rule nary_cong :premises (@p64 @p58) :args (@t74)) % 150.57/150.88 (step @p66 :rule cong :premises (@p65) :args ((forall @t9 @t74))) % 150.57/150.88 (step @p67 :rule bool-and-de-morgan :args (@t7 @t6 true)) % 150.57/150.88 (step @p68 :rule cong :premises (@p67) :args (@t75)) % 150.57/150.88 (step @p69 :rule trans :premises (@p68 @p66)) % 150.57/150.88 (step @p70 :rule cong :premises (@p69) :args (@t76)) % 150.57/150.88 (step @p71 :rule exists-elim :args ((= @t10 @t76))) % 150.57/150.88 (step @p72 :rule trans :premises (@p71 @p70)) % 150.57/150.88 (step @p73 :rule cong :premises (@p72) :args (@t11)) % 150.57/150.88 (step @p74 :rule trans :premises (@p73 @p52)) % 150.57/150.88 (step @p75 :rule cong :premises (@p74 @p51) :args (@t12)) % 150.57/150.88 (step @p76 :rule cong :premises (@p51 @p74) :args (@t13)) % 150.57/150.88 (step @p77 :rule nary_cong :premises (@p76 @p75) :args (@t14)) % 150.57/150.88 (step @p78 :rule cong :premises (@p77) :args (@t16)) % 150.57/150.88 (step @p79 :rule trans :premises (@p78 @p50)) % 150.57/150.88 (step @p80 :rule cong :premises (@p79) :args (@t18)) % 150.57/150.88 (step @p81 :rule trans :premises (@p80 @p8)) % 150.57/150.88 (step @p82 :rule bool-double-not-elim :args (@t18)) % 150.57/150.88 (step @p83 :rule trans :premises (@p82 @p81)) % 150.57/150.88 (step @p84 :rule trans :premises (@p83 @p3)) % 150.57/150.88 (step @p85 :rule eq_resolve :premises (@p1 @p84)) % 150.57/150.88 (step @p86 :rule skolemize :premises (@p85)) % 150.57/150.88 (step @p87 :rule bool-double-not-elim :args (@t78)) % 150.57/150.88 (step @p88 :rule refl :args (@t82)) % 150.57/150.88 (step @p89 :rule nary_cong :premises (@p88 @p87) :args ((or @t82 (not @t81)))) % 150.57/150.88 (step @p90 :rule cnf_or_neg :args (@t82 0)) % 150.57/150.88 (step @p91 :rule eq_resolve :premises (@p90 @p89)) % 150.57/150.88 (step @p92 :rule reordering :premises (@p91) :args ((or @t78 @t82))) % 150.57/150.88 (step @p93 :rule chain_m_resolution :premises (@p92 @p86) :args (@t78 @t83 @t84)) % 150.57/150.88 (step @p94 :rule bool-double-not-elim :args (@t79)) % 150.57/150.88 (step @p95 :rule nary_cong :premises (@p88 @p94) :args ((or @t82 (not @t80)))) % 150.57/150.88 (step @p96 :rule cnf_or_neg :args (@t82 1)) % 150.57/150.88 (step @p97 :rule eq_resolve :premises (@p96 @p95)) % 150.57/150.88 (step @p98 :rule reordering :premises (@p97) :args ((or @t79 @t82))) % 150.57/150.88 (step @p99 :rule chain_m_resolution :premises (@p98 @p86) :args (@t79 @t83 @t84)) % 150.57/150.88 (step @p100 :rule instantiate :premises (@p99) :args ((@list @t77))) % 150.57/150.88 (step @p101 :rule aci_norm :args ((= @t88 @t87))) % 150.57/150.88 (step @p102 :rule refl :args (@t78)) % 150.57/150.88 (step @p103 :rule cong :premises (@p102 @p101) :args ((=> @t78 @t88))) % 150.57/150.88 (assume-push @p138 @t78) % 150.57/150.88 (step @p105 :rule instantiate :premises (@p93) :args ((@list @t77 @t77))) % 150.57/150.88 (step-pop @p139 :rule scope :premises (@p105)) % 150.57/150.88 (step @p106 :rule process_scope :premises (@p139) :args (@t88)) % 150.57/150.88 (step @p108 :rule eq_resolve :premises (@p106 @p103)) % 150.57/150.88 (step @p109 :rule implies_elim :premises (@p108)) % 150.57/150.88 (step @p110 :rule chain_m_resolution :premises (@p109 @p93) :args (@t87 (@list false) (@list @t78))) % 150.57/150.88 (step @p111 :rule cnf_or_pos :args (@t91)) % 150.57/150.88 (step @p112 :rule reordering :premises (@p111) :args ((or @t86 @t90 (not @t91)))) % 150.57/150.88 (step @p113 :rule chain_m_resolution :premises (@p112 @p110 @p100) :args (@t90 @t92 (@list @t86 @t91))) % 150.57/150.88 (step @p114 :rule skolemize :premises (@p113)) % 150.57/150.88 (step @p115 :rule bool-double-not-elim :args (@t94)) % 150.57/150.88 (step @p116 :rule refl :args (@t98)) % 150.57/150.88 (step @p117 :rule nary_cong :premises (@p116 @p115) :args ((or @t98 (not @t95)))) % 150.57/150.88 (step @p118 :rule cnf_or_neg :args (@t98 1)) % 150.57/150.88 (step @p119 :rule eq_resolve :premises (@p118 @p117)) % 150.57/150.88 (step @p120 :rule reordering :premises (@p119) :args ((or @t94 @t98))) % 150.57/150.88 (step @p121 :rule chain_m_resolution :premises (@p120 @p114) :args (@t94 @t83 @t99)) % 150.57/150.88 (step @p122 :rule bool-double-not-elim :args (@t96)) % 150.57/150.88 (step @p123 :rule nary_cong :premises (@p116 @p122) :args ((or @t98 (not @t97)))) % 150.57/150.88 (step @p124 :rule cnf_or_neg :args (@t98 0)) % 150.57/150.88 (step @p125 :rule eq_resolve :premises (@p124 @p123)) % 150.57/150.88 (step @p126 :rule reordering :premises (@p125) :args ((or @t96 @t98))) % 150.57/150.88 (step @p127 :rule chain_m_resolution :premises (@p126 @p114) :args (@t96 @t83 @t99)) % 150.57/150.88 (step @p128 :rule cnf_or_pos :args (@t100)) % 150.57/150.88 (step @p129 :rule factoring :premises (@p128)) % 150.57/150.88 (step @p130 :rule reordering :premises (@p129) :args ((or @t97 @t95 @t101))) % 150.57/150.88 (step @p131 :rule chain_m_resolution :premises (@p130 @p127 @p121) :args (@t101 (@list false false) (@list @t96 @t94))) % 150.57/150.88 (assume-push @p140 @t78) % 150.57/150.88 (step @p133 :rule instantiate :premises (@p93) :args ((@list @t93 @t77))) % 150.57/150.88 (step-pop @p141 :rule scope :premises (@p133)) % 150.57/150.88 (step @p134 :rule process_scope :premises (@p141) :args (@t100)) % 150.57/150.88 (step @p136 :rule implies_elim :premises (@p134)) % 150.57/150.88 (step @p137 false :rule chain_m_resolution :premises (@p136 @p131 @p93) :args (false @t92 (@list @t100 @t78))) % 150.57/150.88 ) % 150.57/150.88 % SZS output end Proof % 150.57/150.88 % cvc5 exiting %------------------------------------------------------------------------------