%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV231^5 : 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 : n017.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 08:55:38 AM UTC 2026 % Result : Theorem 0.30s 0.55s % Output : Proof 0.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV231^5 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n017.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 18:20:01 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.30/0.55 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.30/0.55 % SZS status Theorem % 0.30/0.55 % SZS output start Proof % 0.30/0.55 ( % 0.30/0.55 (declare-sort tptp.a 0) % 0.30/0.55 (declare-const tptp.x (-> tptp.a Bool)) % 0.30/0.55 (declare-const tptp.y (-> tptp.a Bool)) % 0.30/0.55 (define @t1 () (@var "Xx0" tptp.a)) % 0.30/0.55 (define @t2 () (@var "S" (-> tptp.a Bool))) % 0.30/0.55 (define @t3 () (_ @t2 @t1)) % 0.30/0.55 (define @t4 () (or (= @t2 tptp.x) (= @t2 tptp.y))) % 0.30/0.55 (define @t5 () (=> @t4 @t3)) % 0.30/0.55 (define @t6 () (@list @t2)) % 0.30/0.55 (define @t7 () (forall @t6 @t5)) % 0.30/0.55 (define @t8 () (@list @t1)) % 0.30/0.55 (define @t9 () (lambda @t8 @t7)) % 0.30/0.55 (define @t10 () (lambda @t8 (and (_ tptp.x @t1) (_ tptp.y @t1)))) % 0.30/0.55 (define @t11 () (= @t10 @t9)) % 0.30/0.55 (define @t12 () (not @t11)) % 0.30/0.55 (define @t13 () (@purify @t10)) % 0.30/0.55 (define @t14 () (tptp.y @t1)) % 0.30/0.55 (define @t15 () (tptp.x @t1)) % 0.30/0.55 (define @t16 () (lambda @t8 (and @t15 @t14))) % 0.30/0.55 (define @t17 () (@purify @t16)) % 0.30/0.55 (define @t18 () (= @t10 @t16)) % 0.30/0.55 (define @t19 () (not (= tptp.y tptp.y))) % 0.30/0.55 (define @t20 () (or @t19 @t14)) % 0.30/0.55 (define @t21 () (@var "BOUND_VARIABLE_7453" (-> tptp.a Bool))) % 0.30/0.55 (define @t22 () (_ @t21 @t1)) % 0.30/0.55 (define @t23 () (not (= tptp.y @t21))) % 0.30/0.55 (define @t24 () (@list @t21)) % 0.30/0.55 (define @t25 () (or @t23 @t23 @t22)) % 0.30/0.55 (define @t26 () (or @t23 @t22)) % 0.30/0.55 (define @t27 () (forall @t24 @t26)) % 0.30/0.55 (define @t28 () (not (= tptp.x tptp.x))) % 0.30/0.55 (define @t29 () (or @t28 @t15)) % 0.30/0.55 (define @t30 () (@var "BOUND_VARIABLE_7445" (-> tptp.a Bool))) % 0.30/0.55 (define @t31 () (_ @t30 @t1)) % 0.30/0.55 (define @t32 () (not (= tptp.x @t30))) % 0.30/0.55 (define @t33 () (@list @t30)) % 0.30/0.55 (define @t34 () (or @t32 @t32 @t31)) % 0.30/0.55 (define @t35 () (or @t32 @t31)) % 0.30/0.55 (define @t36 () (forall @t33 @t35)) % 0.30/0.55 (define @t37 () (_ @t2 @t1)) % 0.30/0.55 (define @t38 () (= tptp.y @t2)) % 0.30/0.55 (define @t39 () (not @t38)) % 0.30/0.55 (define @t40 () (or @t39 @t37)) % 0.30/0.55 (define @t41 () (forall @t6 @t40)) % 0.30/0.55 (define @t42 () (@list @t2)) % 0.30/0.55 (define @t43 () (= tptp.x @t2)) % 0.30/0.55 (define @t44 () (not @t43)) % 0.30/0.55 (define @t45 () (or @t44 @t37)) % 0.30/0.55 (define @t46 () (forall @t6 @t45)) % 0.30/0.55 (define @t47 () (and @t46 @t41)) % 0.30/0.55 (define @t48 () (and @t44 @t39)) % 0.30/0.55 (define @t49 () (or @t48 @t3)) % 0.30/0.55 (define @t50 () (or @t43 @t38)) % 0.30/0.55 (define @t51 () (= @t17 @t13)) % 0.30/0.55 (define @t52 () (@const 0 tptp.a)) % 0.30/0.55 (define @t53 () (tptp.y @t52)) % 0.30/0.55 (define @t54 () (tptp.x @t52)) % 0.30/0.55 (define @t55 () (and @t54 @t53)) % 0.30/0.55 (define @t56 () (_ tptp.y @t52)) % 0.30/0.55 (define @t57 () (_ tptp.x @t52)) % 0.30/0.55 (define @t58 () (and @t57 @t56)) % 0.30/0.55 (define @t59 () (= (_ @t10 @t52) @t58)) % 0.30/0.55 (define @t60 () (_ @t13 @t52)) % 0.30/0.55 (define @t61 () (_ @t16 @t52)) % 0.30/0.55 (define @t62 () (_ @t17 @t52)) % 0.30/0.55 (define @t63 () (= @t62 @t60)) % 0.30/0.55 (define @t64 () (not @t63)) % 0.30/0.55 (define @t65 () (or @t51 @t64)) % 0.30/0.55 (assume @p1 @t12) % 0.30/0.55 (assume @p2 true) % 0.30/0.55 (step @p3 :rule eq-symm :args (@t13 @t17)) % 0.30/0.55 (step @p4 :rule eq-refl :args (@t16)) % 0.30/0.55 (step @p5 :rule skolem_intro :args (@t17)) % 0.30/0.55 (step @p6 :rule refl :args (@t16)) % 0.30/0.55 (step @p7 :rule cong :premises (@p6 @p5) :args ((= @t16 @t17))) % 0.30/0.55 (step @p8 :rule trans :premises (@p7 @p4)) % 0.30/0.55 (step @p9 :rule true_elim :premises (@p8)) % 0.30/0.55 (step @p10 :rule eq-refl :args (@t10)) % 0.30/0.55 (step @p11 :rule skolem_intro :args (@t13)) % 0.30/0.55 (step @p12 :rule refl :args (@t10)) % 0.30/0.55 (step @p13 :rule cong :premises (@p12 @p11) :args ((= @t10 @t13))) % 0.30/0.55 (step @p14 :rule trans :premises (@p13 @p10)) % 0.30/0.55 (step @p15 :rule true_elim :premises (@p14)) % 0.30/0.55 (step @p16 :rule cong :premises (@p15 @p9) :args (@t18)) % 0.30/0.55 (step @p17 :rule trans :premises (@p16 @p3)) % 0.30/0.55 (step @p18 :rule cong :premises (@p17) :args ((not @t18))) % 0.30/0.55 (step @p19 :rule aci_norm :args ((= (or false @t14) @t14))) % 0.30/0.55 (step @p20 :rule refl :args (@t14)) % 0.30/0.55 (step @p21 :rule evaluate :args ((not true))) % 0.30/0.55 (step @p22 :rule eq-refl :args (tptp.y)) % 0.30/0.55 (step @p23 :rule cong :premises (@p22) :args (@t19)) % 0.30/0.55 (step @p24 :rule trans :premises (@p23 @p21)) % 0.30/0.55 (step @p25 :rule nary_cong :premises (@p24 @p20) :args (@t20)) % 0.30/0.55 (step @p26 :rule trans :premises (@p25 @p19)) % 0.30/0.55 (step @p27 :rule quant-var-elim-eq :args ((= (forall @t24 (or (not (= @t21 tptp.y)) @t23 @t22)) @t20))) % 0.30/0.55 (step @p28 :rule refl :args (@t22)) % 0.30/0.55 (step @p29 :rule refl :args (@t23)) % 0.30/0.55 (step @p30 :rule eq-symm :args (tptp.y @t21)) % 0.30/0.55 (step @p31 :rule cong :premises (@p30) :args (@t23)) % 0.30/0.55 (step @p32 :rule nary_cong :premises (@p31 @p29 @p28) :args (@t25)) % 0.30/0.55 (step @p33 :rule aci_norm :args ((= @t26 @t25))) % 0.30/0.55 (step @p34 :rule trans :premises (@p33 @p32)) % 0.30/0.55 (step @p35 :rule cong :premises (@p34) :args (@t27)) % 0.30/0.55 (step @p36 :rule trans :premises (@p35 @p27)) % 0.30/0.55 (step @p37 :rule trans :premises (@p36 @p26)) % 0.30/0.55 (step @p38 :rule aci_norm :args ((= (or false @t15) @t15))) % 0.30/0.55 (step @p39 :rule refl :args (@t15)) % 0.30/0.55 (step @p40 :rule eq-refl :args (tptp.x)) % 0.30/0.55 (step @p41 :rule cong :premises (@p40) :args (@t28)) % 0.30/0.55 (step @p42 :rule trans :premises (@p41 @p21)) % 0.30/0.55 (step @p43 :rule nary_cong :premises (@p42 @p39) :args (@t29)) % 0.30/0.55 (step @p44 :rule trans :premises (@p43 @p38)) % 0.30/0.55 (step @p45 :rule quant-var-elim-eq :args ((= (forall @t33 (or (not (= @t30 tptp.x)) @t32 @t31)) @t29))) % 0.30/0.55 (step @p46 :rule refl :args (@t31)) % 0.30/0.55 (step @p47 :rule refl :args (@t32)) % 0.30/0.55 (step @p48 :rule eq-symm :args (tptp.x @t30)) % 0.30/0.55 (step @p49 :rule cong :premises (@p48) :args (@t32)) % 0.30/0.55 (step @p50 :rule nary_cong :premises (@p49 @p47 @p46) :args (@t34)) % 0.30/0.55 (step @p51 :rule aci_norm :args ((= @t35 @t34))) % 0.30/0.55 (step @p52 :rule trans :premises (@p51 @p50)) % 0.30/0.55 (step @p53 :rule cong :premises (@p52) :args (@t36)) % 0.30/0.55 (step @p54 :rule trans :premises (@p53 @p45)) % 0.30/0.55 (step @p55 :rule trans :premises (@p54 @p44)) % 0.30/0.55 (step @p56 :rule nary_cong :premises (@p55 @p37) :args ((and @t36 @t27))) % 0.30/0.55 (step @p57 :rule alpha_equiv :args (@t41 @t42 (@list @t21))) % 0.30/0.55 (step @p58 :rule alpha_equiv :args (@t46 @t42 (@list @t30))) % 0.30/0.55 (step @p59 :rule nary_cong :premises (@p58 @p57) :args (@t47)) % 0.30/0.55 (step @p60 :rule quant-miniscope-and :args ((= (forall @t6 (and @t45 @t40)) @t47))) % 0.30/0.55 (step @p61 :rule trans :premises (@p60 @p59)) % 0.30/0.55 (step @p62 :rule trans :premises (@p61 @p56)) % 0.30/0.55 (step @p63 :rule bool-or-and-distrib :args (@t44 @t39 true @t37 false)) % 0.30/0.55 (step @p64 :rule cong :premises (@p63) :args ((forall @t6 (or @t48 @t37)))) % 0.30/0.55 (step @p65 :rule trans :premises (@p64 @p62)) % 0.30/0.55 (step @p66 :rule refl :args (@t37)) % 0.30/0.55 (step @p67 :rule refl :args (@t3)) % 0.30/0.55 (step @p68 :rule cong :premises (@p67 @p66) :args ((= @t3 @t37))) % 0.30/0.55 (step @p69 :rule symm :premises (@p68)) % 0.30/0.55 (step @p70 :rule eq_resolve :premises (@p67 @p69)) % 0.30/0.55 (step @p71 :rule refl :args (@t48)) % 0.30/0.55 (step @p72 :rule nary_cong :premises (@p71 @p70) :args (@t49)) % 0.30/0.55 (step @p73 :rule cong :premises (@p72) :args ((forall @t6 @t49))) % 0.30/0.55 (step @p74 :rule trans :premises (@p73 @p65)) % 0.30/0.55 (step @p75 :rule bool-or-de-morgan :args (@t43 @t38 false)) % 0.30/0.55 (step @p76 :rule nary_cong :premises (@p75 @p67) :args ((or (not @t50) @t3))) % 0.30/0.55 (step @p77 :rule bool-impl-elim :args (@t50 @t3)) % 0.30/0.55 (step @p78 :rule trans :premises (@p77 @p76)) % 0.30/0.55 (step @p79 :rule cong :premises (@p78) :args ((forall @t6 (=> @t50 @t3)))) % 0.30/0.55 (step @p80 :rule trans :premises (@p79 @p74)) % 0.30/0.55 (step @p81 :rule refl :args (@t3)) % 0.30/0.55 (step @p82 :rule eq-symm :args (@t2 tptp.y)) % 0.30/0.55 (step @p83 :rule eq-symm :args (@t2 tptp.x)) % 0.30/0.55 (step @p84 :rule nary_cong :premises (@p83 @p82) :args (@t4)) % 0.30/0.55 (step @p85 :rule cong :premises (@p84 @p81) :args (@t5)) % 0.30/0.55 (step @p86 :rule cong :premises (@p85) :args (@t7)) % 0.30/0.55 (step @p87 :rule trans :premises (@p86 @p80)) % 0.30/0.55 (step @p88 :rule cong :premises (@p87) :args (@t9)) % 0.30/0.55 (step @p89 :rule cong :premises (@p12 @p88) :args (@t11)) % 0.30/0.55 (step @p90 :rule cong :premises (@p89) :args (@t12)) % 0.30/0.55 (step @p91 :rule trans :premises (@p90 @p18)) % 0.30/0.55 (step @p92 :rule eq_resolve :premises (@p1 @p91)) % 0.30/0.55 (step @p93 :rule aci_norm :args ((= (or @t51 false) @t51))) % 0.30/0.55 (step @p94 :rule eq-refl :args (@t55)) % 0.30/0.55 (step @p95 :rule refl :args (@t53)) % 0.30/0.55 (step @p96 :rule refl :args (@t56)) % 0.30/0.55 (step @p97 :rule cong :premises (@p96 @p95) :args ((= @t56 @t53))) % 0.30/0.55 (step @p98 :rule symm :premises (@p97)) % 0.30/0.55 (step @p99 :rule eq_resolve :premises (@p96 @p98)) % 0.30/0.55 (step @p100 :rule refl :args (@t54)) % 0.30/0.55 (step @p101 :rule refl :args (@t57)) % 0.30/0.55 (step @p102 :rule cong :premises (@p101 @p100) :args ((= @t57 @t54))) % 0.30/0.55 (step @p103 :rule symm :premises (@p102)) % 0.30/0.55 (step @p104 :rule eq_resolve :premises (@p101 @p103)) % 0.30/0.55 (step @p105 :rule nary_cong :premises (@p104 @p99) :args (@t58)) % 0.30/0.55 (step @p106 :rule eq-refl :args (@t58)) % 0.30/0.55 (step @p107 :rule refl :args (@t58)) % 0.30/0.55 (step @p108 :rule beta-reduce :args (@t59)) % 0.30/0.55 (step @p109 :rule cong :premises (@p108 @p107) :args (@t59)) % 0.30/0.55 (step @p110 :rule trans :premises (@p109 @p106)) % 0.30/0.55 (step @p111 :rule refl :args (@t52)) % 0.30/0.55 (step @p112 :rule ho_cong :premises (@p11 @p111)) % 0.30/0.56 (step @p113 :rule cong :premises (@p112 @p107) :args ((= @t60 @t58))) % 0.30/0.56 (step @p114 :rule trans :premises (@p113 @p110)) % 0.30/0.56 (step @p115 :rule true_elim :premises (@p114)) % 0.30/0.56 (step @p116 :rule trans :premises (@p115 @p105)) % 0.30/0.56 (step @p117 :rule beta-reduce :args ((= @t61 @t55))) % 0.30/0.56 (step @p118 :rule refl :args (@t55)) % 0.30/0.56 (step @p119 :rule cong :premises (@p118 @p117) :args ((= @t55 @t61))) % 0.30/0.56 (step @p120 :rule trans :premises (@p119 @p94)) % 0.30/0.56 (step @p121 :rule eq-symm :args (@t61 @t55)) % 0.30/0.56 (step @p122 :rule trans :premises (@p121 @p120)) % 0.30/0.56 (step @p123 :rule ho_cong :premises (@p5 @p111)) % 0.30/0.56 (step @p124 :rule cong :premises (@p123 @p118) :args ((= @t62 @t55))) % 0.30/0.56 (step @p125 :rule trans :premises (@p124 @p122)) % 0.30/0.56 (step @p126 :rule true_elim :premises (@p125)) % 0.30/0.56 (step @p127 :rule cong :premises (@p126 @p116) :args (@t63)) % 0.30/0.56 (step @p128 :rule trans :premises (@p127 @p94)) % 0.30/0.56 (step @p129 :rule cong :premises (@p128) :args (@t64)) % 0.30/0.56 (step @p130 :rule trans :premises (@p129 @p21)) % 0.30/0.56 (step @p131 :rule refl :args (@t51)) % 0.30/0.56 (step @p132 :rule nary_cong :premises (@p131 @p130) :args (@t65)) % 0.30/0.56 (step @p133 :rule trans :premises (@p132 @p93)) % 0.30/0.56 ; WARNING: add trust step for TRUST % 0.30/0.56 ; trust TRUST THEORY_LEMMA % 0.30/0.56 (step @p134 :rule trust :premises () :args (@t65)) % 0.30/0.56 (step @p135 :rule eq_resolve :premises (@p134 @p133)) % 0.30/0.56 (step @p136 false :rule chain_m_resolution :premises (@p135 @p92) :args (false (@list true) (@list @t51))) % 0.30/0.56 ) % 0.30/0.56 % SZS output end Proof % 0.33/0.56 % cvc5 exiting %------------------------------------------------------------------------------