%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYN732^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n014.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 09:09:45 AM UTC 2026 % Result : Theorem 0.36s 0.59s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN732^5 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n014.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 23:34:43 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.49 %----Proving TH0 % 0.36/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.59 % SZS status Theorem % 0.36/0.59 % SZS output start Proof % 0.36/0.59 ( % 0.36/0.59 (declare-sort $$unsorted 0) % 0.36/0.59 (declare-const tptp.cP (-> $$unsorted $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.cQ (-> $$unsorted $$unsorted Bool)) % 0.36/0.59 (define @t1 () (@var "Xz" $$unsorted)) % 0.36/0.59 (define @t2 () (@var "Xw" $$unsorted)) % 0.36/0.59 (define @t3 () (_ (_ tptp.cQ @t2) @t1)) % 0.36/0.59 (define @t4 () (_ tptp.cP @t1)) % 0.36/0.59 (define @t5 () (_ @t4 @t2)) % 0.36/0.59 (define @t6 () (or @t5 @t3)) % 0.36/0.59 (define @t7 () (@list @t2)) % 0.36/0.59 (define @t8 () (exists @t7 @t6)) % 0.36/0.59 (define @t9 () (@var "Xv" $$unsorted)) % 0.36/0.59 (define @t10 () (_ (_ tptp.cP @t9) @t1)) % 0.36/0.59 (define @t11 () (@list @t9)) % 0.36/0.59 (define @t12 () (exists @t11 @t10)) % 0.36/0.59 (define @t13 () (=> @t12 @t8)) % 0.36/0.59 (define @t14 () (@list @t1)) % 0.36/0.59 (define @t15 () (exists @t14 @t13)) % 0.36/0.59 (define @t16 () (@var "Xy" $$unsorted)) % 0.36/0.59 (define @t17 () (@var "Xu" $$unsorted)) % 0.36/0.59 (define @t18 () (_ (_ tptp.cQ @t17) @t16)) % 0.36/0.59 (define @t19 () (@list @t17)) % 0.36/0.59 (define @t20 () (forall @t19 @t18)) % 0.36/0.59 (define @t21 () (@var "Xx" $$unsorted)) % 0.36/0.59 (define @t22 () (_ (_ tptp.cP @t21) @t16)) % 0.36/0.59 (define @t23 () (@list @t21)) % 0.36/0.59 (define @t24 () (forall @t23 @t22)) % 0.36/0.59 (define @t25 () (=> @t24 @t20)) % 0.36/0.59 (define @t26 () (@list @t16)) % 0.36/0.59 (define @t27 () (forall @t26 @t25)) % 0.36/0.59 (define @t28 () (=> @t27 @t15)) % 0.36/0.59 (define @t29 () (not @t28)) % 0.36/0.59 (define @t30 () (@var "BOUND_VARIABLE_7516" $$unsorted)) % 0.36/0.59 (define @t31 () (@var "BOUND_VARIABLE_7478" $$unsorted)) % 0.36/0.59 (define @t32 () (not (tptp.cQ @t31 @t30))) % 0.36/0.59 (define @t33 () (@list @t31)) % 0.36/0.59 (define @t34 () (forall (@list @t30) (forall @t33 @t32))) % 0.36/0.59 (define @t35 () (@var "BOUND_VARIABLE_7472" $$unsorted)) % 0.36/0.59 (define @t36 () (@var "BOUND_VARIABLE_7509" $$unsorted)) % 0.36/0.59 (define @t37 () (not (tptp.cP @t36 @t35))) % 0.36/0.59 (define @t38 () (forall (@list @t36 @t35) @t37)) % 0.36/0.59 (define @t39 () (@list @t35)) % 0.36/0.59 (define @t40 () (forall (@list @t36) (forall @t39 @t37))) % 0.36/0.59 (define @t41 () (@var "BOUND_VARIABLE_7501" $$unsorted)) % 0.36/0.59 (define @t42 () (forall (@list @t41) (not (forall @t11 (not (tptp.cP @t9 @t41)))))) % 0.36/0.59 (define @t43 () (tptp.cQ @t31 @t1)) % 0.36/0.59 (define @t44 () (forall @t33 (not @t43))) % 0.36/0.59 (define @t45 () (forall @t14 @t44)) % 0.36/0.59 (define @t46 () (@list @t1)) % 0.36/0.59 (define @t47 () (tptp.cP @t1 @t35)) % 0.36/0.59 (define @t48 () (forall @t39 (not @t47))) % 0.36/0.59 (define @t49 () (forall @t14 @t48)) % 0.36/0.59 (define @t50 () (tptp.cP @t9 @t1)) % 0.36/0.59 (define @t51 () (not (forall @t11 (not @t50)))) % 0.36/0.59 (define @t52 () (forall @t14 @t51)) % 0.36/0.59 (define @t53 () (and @t52 @t49 @t45)) % 0.36/0.59 (define @t54 () (and @t51 @t48 @t44)) % 0.36/0.59 (define @t55 () (and @t48 @t44)) % 0.36/0.59 (define @t56 () (not @t55)) % 0.36/0.59 (define @t57 () (=> @t51 @t56)) % 0.36/0.59 (define @t58 () (forall @t14 (not @t57))) % 0.36/0.59 (define @t59 () (not @t58)) % 0.36/0.59 (define @t60 () (_ (_ tptp.cQ @t31) @t1)) % 0.36/0.59 (define @t61 () (not @t60)) % 0.36/0.59 (define @t62 () (forall @t33 @t61)) % 0.36/0.59 (define @t63 () (_ @t4 @t35)) % 0.36/0.59 (define @t64 () (not @t63)) % 0.36/0.59 (define @t65 () (forall @t39 @t64)) % 0.36/0.59 (define @t66 () (not @t3)) % 0.36/0.59 (define @t67 () (forall @t7 @t66)) % 0.36/0.59 (define @t68 () (@list @t2)) % 0.36/0.59 (define @t69 () (not @t5)) % 0.36/0.59 (define @t70 () (forall @t7 @t69)) % 0.36/0.59 (define @t71 () (and @t70 @t67)) % 0.36/0.59 (define @t72 () (forall @t7 (not @t6))) % 0.36/0.59 (define @t73 () (not @t72)) % 0.36/0.59 (define @t74 () (not @t10)) % 0.36/0.59 (define @t75 () (forall @t11 @t74)) % 0.36/0.59 (define @t76 () (not @t75)) % 0.36/0.59 (define @t77 () (@var "BOUND_VARIABLE_7452" $$unsorted)) % 0.36/0.59 (define @t78 () (tptp.cQ @t77 @t16)) % 0.36/0.59 (define @t79 () (tptp.cP @t21 @t16)) % 0.36/0.59 (define @t80 () (forall @t23 @t79)) % 0.36/0.59 (define @t81 () (not @t80)) % 0.36/0.59 (define @t82 () (or @t81 @t78)) % 0.36/0.59 (define @t83 () (@list @t77)) % 0.36/0.59 (define @t84 () (forall @t83 @t82)) % 0.36/0.59 (define @t85 () (forall @t83 @t78)) % 0.36/0.59 (define @t86 () (or @t81 @t85)) % 0.36/0.59 (define @t87 () (tptp.cQ @t17 @t16)) % 0.36/0.59 (define @t88 () (forall @t19 @t87)) % 0.36/0.59 (define @t89 () (@const 0 $$unsorted)) % 0.36/0.59 (define @t90 () (forall @t11 (not (tptp.cP @t9 @t89)))) % 0.36/0.59 (define @t91 () (@quantifiers_skolemize @t90 0)) % 0.36/0.59 (define @t92 () (tptp.cP @t91 @t89)) % 0.36/0.59 (define @t93 () (not @t90)) % 0.36/0.59 (define @t94 () (not @t92)) % 0.36/0.59 (define @t95 () (not @t94)) % 0.36/0.59 (assume @p1 @t29) % 0.36/0.59 (assume @p2 true) % 0.36/0.59 (step @p3 :rule quant-merge-prenex :args ((= @t34 (forall (@list @t30 @t31) @t32)))) % 0.36/0.59 (step @p4 :rule quant-merge-prenex :args ((= @t40 @t38))) % 0.36/0.59 (step @p5 :rule refl :args (@t42)) % 0.36/0.59 (step @p6 :rule nary_cong :premises (@p5 @p4 @p3) :args ((and @t42 @t40 @t34))) % 0.36/0.59 (step @p7 :rule alpha_equiv :args (@t45 @t46 (@list @t30))) % 0.36/0.59 (step @p8 :rule alpha_equiv :args (@t49 @t46 (@list @t36))) % 0.36/0.59 (step @p9 :rule alpha_equiv :args (@t52 @t46 (@list @t41))) % 0.36/0.59 (step @p10 :rule nary_cong :premises (@p9 @p8 @p7) :args (@t53)) % 0.36/0.59 (step @p11 :rule quant-miniscope-and :args ((= (forall @t14 @t54) @t53))) % 0.36/0.59 (step @p12 :rule trans :premises (@p11 @p10)) % 0.36/0.59 (step @p13 :rule trans :premises (@p12 @p6)) % 0.36/0.59 (step @p14 :rule aci_norm :args ((= (and @t51 @t55) @t54))) % 0.36/0.59 (step @p15 :rule bool-double-not-elim :args (@t55)) % 0.36/0.59 (step @p16 :rule refl :args (@t51)) % 0.36/0.59 (step @p17 :rule nary_cong :premises (@p16 @p15) :args ((and @t51 (not @t56)))) % 0.36/0.59 (step @p18 :rule bool-implies-de-morgan :args (@t51 @t56)) % 0.36/0.59 (step @p19 :rule trans :premises (@p18 @p17)) % 0.36/0.59 (step @p20 :rule trans :premises (@p19 @p14)) % 0.36/0.59 (step @p21 :rule cong :premises (@p20) :args (@t58)) % 0.36/0.59 (step @p22 :rule trans :premises (@p21 @p13)) % 0.36/0.59 (step @p23 :rule cong :premises (@p22) :args (@t59)) % 0.36/0.59 (step @p24 :rule exists-elim :args ((= (exists @t14 @t57) @t59))) % 0.36/0.59 (step @p25 :rule trans :premises (@p24 @p23)) % 0.36/0.59 (step @p26 :rule refl :args (@t43)) % 0.36/0.59 (step @p27 :rule refl :args (@t60)) % 0.36/0.59 (step @p28 :rule cong :premises (@p27 @p26) :args ((= @t60 @t43))) % 0.36/0.59 (step @p29 :rule symm :premises (@p28)) % 0.36/0.59 (step @p30 :rule eq_resolve :premises (@p27 @p29)) % 0.36/0.59 (step @p31 :rule cong :premises (@p30) :args (@t61)) % 0.36/0.59 (step @p32 :rule cong :premises (@p31) :args (@t62)) % 0.36/0.59 (step @p33 :rule refl :args (@t47)) % 0.36/0.59 (step @p34 :rule refl :args (@t63)) % 0.36/0.59 (step @p35 :rule cong :premises (@p34 @p33) :args ((= @t63 @t47))) % 0.36/0.59 (step @p36 :rule symm :premises (@p35)) % 0.36/0.59 (step @p37 :rule eq_resolve :premises (@p34 @p36)) % 0.36/0.59 (step @p38 :rule cong :premises (@p37) :args (@t64)) % 0.36/0.59 (step @p39 :rule cong :premises (@p38) :args (@t65)) % 0.36/0.59 (step @p40 :rule nary_cong :premises (@p39 @p32) :args ((and @t65 @t62))) % 0.36/0.59 (step @p41 :rule alpha_equiv :args (@t67 @t68 (@list @t31))) % 0.36/0.59 (step @p42 :rule alpha_equiv :args (@t70 @t68 (@list @t35))) % 0.36/0.59 (step @p43 :rule nary_cong :premises (@p42 @p41) :args (@t71)) % 0.36/0.59 (step @p44 :rule quant-miniscope-and :args ((= (forall @t7 (and @t69 @t66)) @t71))) % 0.36/0.59 (step @p45 :rule trans :premises (@p44 @p43)) % 0.36/0.59 (step @p46 :rule trans :premises (@p45 @p40)) % 0.36/0.59 (step @p47 :rule bool-or-de-morgan :args (@t5 @t3 false)) % 0.36/0.59 (step @p48 :rule cong :premises (@p47) :args (@t72)) % 0.36/0.59 (step @p49 :rule trans :premises (@p48 @p46)) % 0.36/0.59 (step @p50 :rule cong :premises (@p49) :args (@t73)) % 0.36/0.59 (step @p51 :rule exists-elim :args ((= @t8 @t73))) % 0.36/0.59 (step @p52 :rule trans :premises (@p51 @p50)) % 0.36/0.59 (step @p53 :rule refl :args (@t50)) % 0.36/0.59 (step @p54 :rule refl :args (@t10)) % 0.36/0.59 (step @p55 :rule cong :premises (@p54 @p53) :args ((= @t10 @t50))) % 0.36/0.59 (step @p56 :rule symm :premises (@p55)) % 0.36/0.59 (step @p57 :rule eq_resolve :premises (@p54 @p56)) % 0.36/0.59 (step @p58 :rule cong :premises (@p57) :args (@t74)) % 0.36/0.59 (step @p59 :rule cong :premises (@p58) :args (@t75)) % 0.36/0.59 (step @p60 :rule cong :premises (@p59) :args (@t76)) % 0.36/0.59 (step @p61 :rule exists-elim :args ((= @t12 @t76))) % 0.36/0.59 (step @p62 :rule trans :premises (@p61 @p60)) % 0.36/0.59 (step @p63 :rule cong :premises (@p62 @p52) :args (@t13)) % 0.36/0.59 (step @p64 :rule cong :premises (@p63) :args (@t15)) % 0.36/0.59 (step @p65 :rule trans :premises (@p64 @p25)) % 0.36/0.59 (step @p66 :rule quant-merge-prenex :args ((= (forall @t26 @t84) (forall (@list @t16 @t77) @t82)))) % 0.36/0.59 (step @p67 :rule alpha_equiv :args (@t85 (@list @t77) (@list @t17))) % 0.36/0.59 (step @p68 :rule refl :args (@t81)) % 0.36/0.59 (step @p69 :rule nary_cong :premises (@p68 @p67) :args (@t86)) % 0.36/0.59 (step @p70 :rule quant-miniscope-or :args ((= @t84 @t86))) % 0.36/0.59 (step @p71 :rule trans :premises (@p70 @p69)) % 0.36/0.59 (step @p72 :rule symm :premises (@p71)) % 0.36/0.59 (step @p73 :rule cong :premises (@p72) :args ((forall @t26 (or @t81 @t88)))) % 0.36/0.59 (step @p74 :rule trans :premises (@p73 @p66)) % 0.36/0.59 (step @p75 :rule bool-impl-elim :args (@t80 @t88)) % 0.36/0.59 (step @p76 :rule cong :premises (@p75) :args ((forall @t26 (=> @t80 @t88)))) % 0.36/0.59 (step @p77 :rule trans :premises (@p76 @p74)) % 0.36/0.59 (step @p78 :rule refl :args (@t87)) % 0.36/0.59 (step @p79 :rule refl :args (@t18)) % 0.36/0.59 (step @p80 :rule cong :premises (@p79 @p78) :args ((= @t18 @t87))) % 0.36/0.59 (step @p81 :rule symm :premises (@p80)) % 0.36/0.59 (step @p82 :rule eq_resolve :premises (@p79 @p81)) % 0.36/0.60 (step @p83 :rule cong :premises (@p82) :args (@t20)) % 0.36/0.60 (step @p84 :rule refl :args (@t79)) % 0.36/0.60 (step @p85 :rule refl :args (@t22)) % 0.36/0.60 (step @p86 :rule cong :premises (@p85 @p84) :args ((= @t22 @t79))) % 0.36/0.60 (step @p87 :rule symm :premises (@p86)) % 0.36/0.60 (step @p88 :rule eq_resolve :premises (@p85 @p87)) % 0.36/0.60 (step @p89 :rule cong :premises (@p88) :args (@t24)) % 0.36/0.60 (step @p90 :rule cong :premises (@p89 @p83) :args (@t25)) % 0.36/0.60 (step @p91 :rule cong :premises (@p90) :args (@t27)) % 0.36/0.60 (step @p92 :rule trans :premises (@p91 @p77)) % 0.36/0.60 (step @p93 :rule cong :premises (@p92 @p65) :args (@t28)) % 0.36/0.60 (step @p94 :rule cong :premises (@p93) :args (@t29)) % 0.36/0.60 (step @p95 :rule eq_resolve :premises (@p1 @p94)) % 0.36/0.60 (step @p96 :rule not_implies_elim2 :premises (@p95)) % 0.36/0.60 (step @p97 :rule not_not_elim :premises (@p96)) % 0.36/0.60 (step @p98 :rule and_elim :premises (@p97) :args (1)) % 0.36/0.60 (step @p99 :rule and_elim :premises (@p97) :args (0)) % 0.36/0.60 (step @p100 :rule instantiate :premises (@p99) :args ((@list @t89))) % 0.36/0.60 (step @p101 :rule refl :args (@t92)) % 0.36/0.60 (step @p102 :rule bool-double-not-elim :args (@t90)) % 0.36/0.60 (step @p103 :rule nary_cong :premises (@p102 @p101) :args ((or (not @t93) @t92))) % 0.36/0.60 (step @p104 :rule bool-double-not-elim :args (@t92)) % 0.36/0.60 (step @p105 :rule refl :args (@t93)) % 0.36/0.60 (step @p106 :rule cong :premises (@p105 @p104) :args ((=> @t93 @t95))) % 0.36/0.60 (assume-push @p121 @t93) % 0.36/0.60 (step @p108 :rule skolemize :premises (@p100)) % 0.36/0.60 (step-pop @p122 :rule scope :premises (@p108)) % 0.36/0.60 (step @p109 :rule process_scope :premises (@p122) :args (@t95)) % 0.36/0.60 (step @p111 :rule eq_resolve :premises (@p109 @p106)) % 0.36/0.60 (step @p112 :rule implies_elim :premises (@p111)) % 0.36/0.60 (step @p113 :rule eq_resolve :premises (@p112 @p103)) % 0.36/0.60 (step @p114 :rule chain_m_resolution :premises (@p113 @p100) :args (@t92 (@list true) (@list @t90))) % 0.36/0.60 (assume-push @p123 @t38) % 0.36/0.60 (step @p116 :rule instantiate :premises (@p98) :args ((@list @t91 @t89))) % 0.36/0.60 (step-pop @p124 :rule scope :premises (@p116)) % 0.36/0.60 (step @p117 :rule process_scope :premises (@p124) :args (@t94)) % 0.36/0.60 (step @p119 :rule implies_elim :premises (@p117)) % 0.36/0.60 (step @p120 false :rule chain_m_resolution :premises (@p119 @p114 @p98) :args (false (@list false false) (@list @t92 @t38))) % 0.36/0.60 ) % 0.36/0.60 % SZS output end Proof % 0.36/0.60 % cvc5 exiting %------------------------------------------------------------------------------