%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL730^5 : TPTP v9.3.1. 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 : n013.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:23:43 AM UTC 2026 % Result : Theorem 14.63s 15.00s % Output : Proof 14.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL730^5 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.07/0.33 % Computer : n013.cluster.edu % 0.07/0.33 % Model : x86_64 x86_64 % 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.33 % Memory : 8046.5625MB % 0.07/0.33 % OS : Linux 6.8.0-71-generic % 0.07/0.34 % CPULimit : 300 % 0.07/0.34 % WCLimit : 300 % 0.07/0.34 % DateTime : Sat Sep 5 00:17:19 UTC 2026 % 0.07/0.34 % CPUTime : % 0.12/0.40 %----Proving TH0 % 14.63/15.00 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 14.63/15.00 % SZS status Theorem % 14.63/15.00 % SZS output start Proof % 14.63/15.00 ( % 14.63/15.00 (declare-sort tptp.b 0) % 14.63/15.00 (define @t1 () (@var "Xp" (-> tptp.b Bool))) % 14.63/15.00 (define @t2 () (@var "Xj" (-> (-> tptp.b Bool) tptp.b))) % 14.63/15.00 (define @t3 () (_ @t2 @t1)) % 14.63/15.00 (define @t4 () (_ @t1 @t3)) % 14.63/15.00 (define @t5 () (@var "Xz" tptp.b)) % 14.63/15.00 (define @t6 () (_ @t1 @t5)) % 14.63/15.00 (define @t7 () (@list @t5)) % 14.63/15.00 (define @t8 () (exists @t7 @t6)) % 14.63/15.00 (define @t9 () (=> @t8 @t4)) % 14.63/15.00 (define @t10 () (@list @t1)) % 14.63/15.00 (define @t11 () (forall @t10 @t9)) % 14.63/15.00 (define @t12 () (@list @t2)) % 14.63/15.00 (define @t13 () (exists @t12 @t11)) % 14.63/15.00 (define @t14 () (@var "Xx" (-> tptp.b Bool))) % 14.63/15.00 (define @t15 () (@var "Xf" (-> (-> tptp.b Bool) tptp.b))) % 14.63/15.00 (define @t16 () (_ @t15 @t14)) % 14.63/15.00 (define @t17 () (@var "Xr" (-> (-> tptp.b Bool) tptp.b Bool))) % 14.63/15.00 (define @t18 () (_ @t17 @t14)) % 14.63/15.00 (define @t19 () (_ @t18 @t16)) % 14.63/15.00 (define @t20 () (@list @t14)) % 14.63/15.00 (define @t21 () (forall @t20 @t19)) % 14.63/15.00 (define @t22 () (@list @t15)) % 14.63/15.00 (define @t23 () (exists @t22 @t21)) % 14.63/15.00 (define @t24 () (@var "Xy" tptp.b)) % 14.63/15.00 (define @t25 () (_ @t18 @t24)) % 14.63/15.00 (define @t26 () (@list @t24)) % 14.63/15.00 (define @t27 () (exists @t26 @t25)) % 14.63/15.00 (define @t28 () (forall @t20 @t27)) % 14.63/15.00 (define @t29 () (=> @t28 @t23)) % 14.63/15.00 (define @t30 () (@list @t17)) % 14.63/15.00 (define @t31 () (forall @t30 @t29)) % 14.63/15.00 (define @t32 () (=> @t31 @t13)) % 14.63/15.00 (define @t33 () (not @t32)) % 14.63/15.00 (define @t34 () (_ @t2 @t1)) % 14.63/15.00 (define @t35 () (_ @t1 @t34)) % 14.63/15.00 (define @t36 () (@var "BOUND_VARIABLE_7480" tptp.b)) % 14.63/15.00 (define @t37 () (not (_ @t1 @t36))) % 14.63/15.00 (define @t38 () (or @t37 @t35)) % 14.63/15.00 (define @t39 () (@list @t1 @t36)) % 14.63/15.00 (define @t40 () (forall @t39 @t38)) % 14.63/15.00 (define @t41 () (forall @t12 (not @t40))) % 14.63/15.00 (define @t42 () (@list @t36)) % 14.63/15.00 (define @t43 () (forall @t42 @t38)) % 14.63/15.00 (define @t44 () (forall @t42 @t37)) % 14.63/15.00 (define @t45 () (or @t44 @t35)) % 14.63/15.00 (define @t46 () (_ @t1 @t5)) % 14.63/15.00 (define @t47 () (forall @t7 (not @t46))) % 14.63/15.00 (define @t48 () (or @t47 @t4)) % 14.63/15.00 (define @t49 () (not @t47)) % 14.63/15.00 (define @t50 () (not @t6)) % 14.63/15.00 (define @t51 () (forall @t7 @t50)) % 14.63/15.00 (define @t52 () (not @t51)) % 14.63/15.00 (define @t53 () (_ @t17 @t14 @t24)) % 14.63/15.00 (define @t54 () (forall @t20 (not (forall @t26 (not @t53))))) % 14.63/15.00 (define @t55 () (_ @t15 @t14)) % 14.63/15.00 (define @t56 () (_ @t17 @t14 @t55)) % 14.63/15.00 (define @t57 () (forall @t20 @t56)) % 14.63/15.00 (define @t58 () (not (forall @t22 (not @t57)))) % 14.63/15.00 (define @t59 () (not @t25)) % 14.63/15.00 (define @t60 () (forall @t26 @t59)) % 14.63/15.00 (define @t61 () (not @t60)) % 14.63/15.00 (define @t62 () (@const 0 (-> (-> tptp.b Bool) tptp.b))) % 14.63/15.00 (define @t63 () (_ @t62 @t1)) % 14.63/15.00 (define @t64 () (@var "BOUND_VARIABLE_824238" (-> tptp.b Bool))) % 14.63/15.00 (define @t65 () (_ @t62 @t64)) % 14.63/15.00 (define @t66 () (@list @t64)) % 14.63/15.00 (define @t67 () (lambda @t66 @t65)) % 14.63/15.00 (define @t68 () (_ @t67 @t1)) % 14.63/15.00 (define @t69 () (_ @t1 @t68)) % 14.63/15.00 (define @t70 () (or @t37 @t69)) % 14.63/15.00 (define @t71 () (forall @t39 @t70)) % 14.63/15.00 (define @t72 () (not @t71)) % 14.63/15.00 (define @t73 () (forall @t39 (or @t37 (_ @t1 @t63)))) % 14.63/15.00 (define @t74 () (@quantifiers_skolemize @t73 1)) % 14.63/15.00 (define @t75 () (@quantifiers_skolemize @t73 0)) % 14.63/15.00 (define @t76 () (_ @t75 @t74)) % 14.63/15.00 (define @t77 () (_ @t75 (_ @t62 @t75))) % 14.63/15.00 (define @t78 () (not @t76)) % 14.63/15.00 (define @t79 () (or @t78 @t77)) % 14.63/15.00 (define @t80 () (@list true)) % 14.63/15.00 (define @t81 () (@list @t79)) % 14.63/15.00 (define @t82 () (@var "x" tptp.b)) % 14.63/15.00 (define @t83 () (@list @t82)) % 14.63/15.00 (define @t84 () (forall @t83 (not (_ @t75 @t82)))) % 14.63/15.00 (define @t85 () (or @t84 @t77)) % 14.63/15.00 (assume @p1 @t33) % 14.63/15.00 (assume @p2 true) % 14.63/15.00 (step @p3 :rule exists-elim :args ((= (exists @t12 @t40) (not @t41)))) % 14.63/15.00 (step @p4 :rule quant-merge-prenex :args ((= (forall @t10 @t43) @t40))) % 14.63/15.00 (step @p5 :rule refl :args (@t35)) % 14.63/15.00 (step @p6 :rule alpha_equiv :args (@t44 (@list @t36) (@list @t5))) % 14.63/15.00 (step @p7 :rule nary_cong :premises (@p6 @p5) :args (@t45)) % 14.63/15.00 (step @p8 :rule quant-miniscope-or :args ((= @t43 @t45))) % 14.63/15.00 (step @p9 :rule trans :premises (@p8 @p7)) % 14.63/15.00 (step @p10 :rule symm :premises (@p9)) % 14.63/15.00 (step @p11 :rule cong :premises (@p10) :args ((forall @t10 (or @t47 @t35)))) % 14.63/15.00 (step @p12 :rule trans :premises (@p11 @p4)) % 14.63/15.00 (step @p13 :rule refl :args ((_ @t1 @t3))) % 14.63/15.00 (step @p14 :rule refl :args (@t34)) % 14.63/15.00 (step @p15 :rule cong :premises (@p14) :args (@t35)) % 14.63/15.00 (step @p16 :rule trans :premises (@p15 @p13)) % 14.63/15.00 (step @p17 :rule refl :args (@t1)) % 14.63/15.00 (step @p18 :rule ho_cong :premises (@p17 @p14)) % 14.63/15.00 (step @p19 :rule cong :premises (@p18 @p16) :args ((= (_ @t1 @t34) @t35))) % 14.63/15.00 (step @p20 :rule symm :premises (@p19)) % 14.63/15.00 (step @p21 :rule refl :args (@t4)) % 14.63/15.00 (step @p22 :rule eq_resolve :premises (@p21 @p20)) % 14.63/15.00 (step @p23 :rule refl :args (@t3)) % 14.63/15.00 (step @p24 :rule cong :premises (@p23 @p14) :args ((= @t3 @t34))) % 14.63/15.00 (step @p25 :rule symm :premises (@p24)) % 14.63/15.00 (step @p26 :rule eq_resolve :premises (@p23 @p25)) % 14.63/15.00 (step @p27 :rule ho_cong :premises (@p17 @p26)) % 14.63/15.00 (step @p28 :rule trans :premises (@p27 @p22)) % 14.63/15.00 (step @p29 :rule refl :args (@t47)) % 14.63/15.00 (step @p30 :rule nary_cong :premises (@p29 @p28) :args (@t48)) % 14.63/15.00 (step @p31 :rule cong :premises (@p30) :args ((forall @t10 @t48))) % 14.63/15.00 (step @p32 :rule trans :premises (@p31 @p12)) % 14.63/15.00 (step @p33 :rule bool-double-not-elim :args (@t47)) % 14.63/15.00 (step @p34 :rule nary_cong :premises (@p33 @p21) :args ((or (not @t49) @t4))) % 14.63/15.00 (step @p35 :rule bool-impl-elim :args (@t49 @t4)) % 14.63/15.00 (step @p36 :rule trans :premises (@p35 @p34)) % 14.63/15.00 (step @p37 :rule cong :premises (@p36) :args ((forall @t10 (=> @t49 @t4)))) % 14.63/15.00 (step @p38 :rule trans :premises (@p37 @p32)) % 14.63/15.00 (step @p39 :rule refl :args (@t4)) % 14.63/15.00 (step @p40 :rule refl :args (@t46)) % 14.63/15.00 (step @p41 :rule refl :args (@t6)) % 14.63/15.00 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t6 @t46))) % 14.63/15.00 (step @p43 :rule symm :premises (@p42)) % 14.63/15.00 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 14.63/15.00 (step @p45 :rule cong :premises (@p44) :args (@t50)) % 14.63/15.00 (step @p46 :rule cong :premises (@p45) :args (@t51)) % 14.63/15.00 (step @p47 :rule cong :premises (@p46) :args (@t52)) % 14.63/15.00 (step @p48 :rule exists-elim :args ((= @t8 @t52))) % 14.63/15.00 (step @p49 :rule trans :premises (@p48 @p47)) % 14.63/15.00 (step @p50 :rule cong :premises (@p49 @p39) :args (@t9)) % 14.63/15.00 (step @p51 :rule cong :premises (@p50) :args (@t11)) % 14.63/15.00 (step @p52 :rule trans :premises (@p51 @p38)) % 14.63/15.00 (step @p53 :rule cong :premises (@p52) :args (@t13)) % 14.63/15.00 (step @p54 :rule trans :premises (@p53 @p3)) % 14.63/15.00 (step @p55 :rule bool-impl-elim :args (@t54 @t58)) % 14.63/15.00 (step @p56 :rule cong :premises (@p55) :args ((forall @t30 (=> @t54 @t58)))) % 14.63/15.00 (step @p57 :rule exists-elim :args ((= (exists @t22 @t57) @t58))) % 14.63/15.00 (step @p58 :rule refl :args ((_ @t17 @t14 @t16))) % 14.63/15.00 (step @p59 :rule refl :args (@t55)) % 14.63/15.00 (step @p60 :rule refl :args (@t14)) % 14.63/15.00 (step @p61 :rule cong :premises (@p60 @p59) :args (@t56)) % 14.63/15.00 (step @p62 :rule trans :premises (@p61 @p58)) % 14.63/15.00 (step @p63 :rule refl :args (@t18)) % 14.63/15.00 (step @p64 :rule ho_cong :premises (@p63 @p59)) % 14.63/15.00 (step @p65 :rule cong :premises (@p64 @p62) :args ((= (_ @t18 @t55) @t56))) % 14.63/15.00 (step @p66 :rule symm :premises (@p65)) % 14.63/15.00 (step @p67 :rule refl :args (@t19)) % 14.63/15.00 (step @p68 :rule eq_resolve :premises (@p67 @p66)) % 14.63/15.00 (step @p69 :rule refl :args (@t16)) % 14.63/15.00 (step @p70 :rule cong :premises (@p69 @p59) :args ((= @t16 @t55))) % 14.63/15.00 (step @p71 :rule symm :premises (@p70)) % 14.63/15.00 (step @p72 :rule eq_resolve :premises (@p69 @p71)) % 14.63/15.00 (step @p73 :rule ho_cong :premises (@p63 @p72)) % 14.63/15.00 (step @p74 :rule trans :premises (@p73 @p68)) % 14.63/15.00 (step @p75 :rule cong :premises (@p74) :args (@t21)) % 14.63/15.00 (step @p76 :rule cong :premises (@p75) :args (@t23)) % 14.63/15.00 (step @p77 :rule trans :premises (@p76 @p57)) % 14.63/15.00 (step @p78 :rule refl :args (@t53)) % 14.63/15.00 (step @p79 :rule refl :args (@t25)) % 14.63/15.00 (step @p80 :rule cong :premises (@p79 @p78) :args ((= @t25 @t53))) % 14.63/15.00 (step @p81 :rule symm :premises (@p80)) % 14.63/15.00 (step @p82 :rule eq_resolve :premises (@p79 @p81)) % 14.63/15.00 (step @p83 :rule cong :premises (@p82) :args (@t59)) % 14.63/15.00 (step @p84 :rule cong :premises (@p83) :args (@t60)) % 14.63/15.00 (step @p85 :rule cong :premises (@p84) :args (@t61)) % 14.63/15.00 (step @p86 :rule exists-elim :args ((= @t27 @t61))) % 14.63/15.00 (step @p87 :rule trans :premises (@p86 @p85)) % 14.63/15.00 (step @p88 :rule cong :premises (@p87) :args (@t28)) % 14.63/15.00 (step @p89 :rule cong :premises (@p88 @p77) :args (@t29)) % 14.63/15.00 (step @p90 :rule cong :premises (@p89) :args (@t31)) % 14.63/15.00 (step @p91 :rule trans :premises (@p90 @p56)) % 14.63/15.00 (step @p92 :rule cong :premises (@p91 @p54) :args (@t32)) % 14.63/15.00 (step @p93 :rule cong :premises (@p92) :args (@t33)) % 14.63/15.00 (step @p94 :rule eq_resolve :premises (@p1 @p93)) % 14.63/15.00 (step @p95 :rule not_implies_elim2 :premises (@p94)) % 14.63/15.00 (step @p96 :rule not_not_elim :premises (@p95)) % 14.63/15.00 (step @p97 :rule beta-reduce :args ((= @t68 @t63))) % 14.63/15.00 (step @p98 :rule cong :premises (@p97) :args (@t69)) % 14.63/15.00 (step @p99 :rule refl :args (@t37)) % 14.63/15.01 (step @p100 :rule nary_cong :premises (@p99 @p98) :args (@t70)) % 14.63/15.01 (step @p101 :rule cong :premises (@p100) :args (@t71)) % 14.63/15.01 (step @p102 :rule cong :premises (@p101) :args (@t72)) % 14.63/15.01 (step @p103 :rule refl :args (@t41)) % 14.63/15.01 (step @p104 :rule cong :premises (@p103 @p102) :args ((=> @t41 @t72))) % 14.63/15.01 (assume-push @p134 @t41) % 14.63/15.01 (step @p106 :rule instantiate :premises (@p96) :args ((@list @t67))) % 14.63/15.01 (step-pop @p135 :rule scope :premises (@p106)) % 14.63/15.01 (step @p107 :rule process_scope :premises (@p135) :args (@t72)) % 14.63/15.01 (step @p109 :rule eq_resolve :premises (@p107 @p104)) % 14.63/15.01 (step @p110 :rule implies_elim :premises (@p109)) % 14.63/15.01 (step @p111 :rule chain_m_resolution :premises (@p110 @p96) :args ((not @t73) (@list false) (@list @t41))) % 14.63/15.01 (step @p112 :rule skolemize :premises (@p111)) % 14.63/15.01 (step @p113 :rule bool-double-not-elim :args (@t76)) % 14.63/15.01 (step @p114 :rule refl :args (@t79)) % 14.63/15.01 (step @p115 :rule nary_cong :premises (@p114 @p113) :args ((or @t79 (not @t78)))) % 14.63/15.01 (step @p116 :rule cnf_or_neg :args (@t79 0)) % 14.63/15.01 (step @p117 :rule eq_resolve :premises (@p116 @p115)) % 14.63/15.01 (step @p118 :rule reordering :premises (@p117) :args ((or @t76 @t79))) % 14.63/15.01 (step @p119 :rule chain_m_resolution :premises (@p118 @p112) :args (@t76 @t80 @t81)) % 14.63/15.01 ; WARNING: add trust step for TRUST % 14.63/15.01 ; trust TRUST THEORY_LEMMA % 14.63/15.01 (step @p120 :rule trust :premises () :args ((forall @t66 (or (forall @t83 (not (_ @t64 @t82))) (_ @t64 @t65))))) % 14.63/15.01 (step @p121 :rule instantiate :premises (@p120) :args ((@list @t75))) % 14.63/15.01 (step @p122 :rule cnf_or_neg :args (@t79 1)) % 14.63/15.01 (step @p123 :rule chain_m_resolution :premises (@p122 @p112) :args ((not @t77) @t80 @t81)) % 14.63/15.01 (step @p124 :rule cnf_or_pos :args (@t85)) % 14.63/15.01 (step @p125 :rule reordering :premises (@p124) :args ((or @t77 @t84 (not @t85)))) % 14.63/15.01 (step @p126 :rule chain_m_resolution :premises (@p125 @p123 @p121) :args (@t84 (@list true false) (@list @t77 @t85))) % 14.63/15.01 (assume-push @p136 @t84) % 14.63/15.01 (step @p128 :rule instantiate :premises (@p126) :args ((@list @t74))) % 14.63/15.01 (step-pop @p137 :rule scope :premises (@p128)) % 14.63/15.01 (step @p129 :rule process_scope :premises (@p137) :args (@t78)) % 14.63/15.01 (step @p131 :rule implies_elim :premises (@p129)) % 14.63/15.01 (step @p132 :rule reordering :premises (@p131) :args ((or @t78 (not @t84)))) % 14.63/15.01 (step @p133 false :rule chain_m_resolution :premises (@p132 @p126 @p119) :args (false (@list false false) (@list @t84 @t76))) % 14.63/15.01 ) % 14.63/15.01 % SZS output end Proof % 14.63/15.01 % cvc5 exiting %------------------------------------------------------------------------------