%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYN059+1 : TPTP v9.2.1. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n028.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 09:07:56 AM UTC 2026 % Result : Theorem 0.29s 0.55s % Output : Proof 0.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN059+1 : TPTP v9.2.1. Released v2.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n028.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 23:19:50 EDT 2026 % 0.15/0.34 % CPUTime : % 0.29/0.48 %----Proving TF0_NAR, FOF, or CNF % 0.29/0.55 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.29/0.55 % SZS status Theorem % 0.29/0.55 % SZS output start Proof % 0.29/0.55 ( % 0.29/0.55 (declare-sort $$unsorted 0) % 0.29/0.55 (declare-const tptp.big_h (-> $$unsorted Bool)) % 0.29/0.55 (declare-const tptp.big_j (-> $$unsorted Bool)) % 0.29/0.55 (declare-const tptp.big_g (-> $$unsorted Bool)) % 0.29/0.55 (declare-const tptp.big_f (-> $$unsorted Bool)) % 0.29/0.55 (define @t1 () (@var "X" $$unsorted)) % 0.29/0.55 (define @t2 () (tptp.big_f @t1)) % 0.29/0.55 (define @t3 () (@list @t1)) % 0.29/0.55 (define @t4 () (exists @t3 @t2)) % 0.29/0.55 (define @t5 () (@var "Y" $$unsorted)) % 0.29/0.55 (define @t6 () (tptp.big_g @t5)) % 0.29/0.55 (define @t7 () (@list @t5)) % 0.29/0.55 (define @t8 () (exists @t7 @t6)) % 0.29/0.55 (define @t9 () (@var "W" $$unsorted)) % 0.29/0.55 (define @t10 () (and (tptp.big_h @t9) (tptp.big_j @t5))) % 0.29/0.55 (define @t11 () (tptp.big_f @t9)) % 0.29/0.55 (define @t12 () (and @t11 @t6)) % 0.29/0.55 (define @t13 () (@list @t9 @t5)) % 0.29/0.55 (define @t14 () (forall @t13 (=> @t12 @t10))) % 0.29/0.55 (define @t15 () (@var "U" $$unsorted)) % 0.29/0.55 (define @t16 () (tptp.big_j @t15)) % 0.29/0.55 (define @t17 () (tptp.big_g @t15)) % 0.29/0.55 (define @t18 () (@list @t15)) % 0.29/0.55 (define @t19 () (forall @t18 (=> @t17 @t16))) % 0.29/0.55 (define @t20 () (tptp.big_h @t1)) % 0.29/0.55 (define @t21 () (forall @t3 (=> @t2 @t20))) % 0.29/0.55 (define @t22 () (and @t21 @t19)) % 0.29/0.55 (define @t23 () (= @t22 @t14)) % 0.29/0.55 (define @t24 () (not @t23)) % 0.29/0.55 (define @t25 () (not @t6)) % 0.29/0.55 (define @t26 () (not @t11)) % 0.29/0.55 (define @t27 () (or @t26 @t25 @t10)) % 0.29/0.55 (define @t28 () (forall @t18 (or (not @t17) @t16))) % 0.29/0.55 (define @t29 () (not @t2)) % 0.29/0.55 (define @t30 () (forall @t3 (or @t29 @t20))) % 0.29/0.55 (define @t31 () (and @t30 @t28)) % 0.29/0.55 (define @t32 () (not @t31)) % 0.29/0.55 (define @t33 () (@quantifiers_skolemize @t30 0)) % 0.29/0.55 (define @t34 () (tptp.big_h @t33)) % 0.29/0.55 (define @t35 () (tptp.big_f @t33)) % 0.29/0.55 (define @t36 () (not @t35)) % 0.29/0.55 (define @t37 () (or @t36 @t34)) % 0.29/0.55 (define @t38 () (not @t37)) % 0.29/0.55 (define @t39 () (not @t30)) % 0.29/0.55 (define @t40 () (forall @t7 @t25)) % 0.29/0.55 (define @t41 () (@quantifiers_skolemize @t40 0)) % 0.29/0.55 (define @t42 () (and @t34 (tptp.big_j @t41))) % 0.29/0.55 (define @t43 () (forall @t13 @t27)) % 0.29/0.55 (define @t44 () (tptp.big_g @t41)) % 0.29/0.55 (define @t45 () (not @t44)) % 0.29/0.55 (define @t46 () (or @t36 @t45 @t42)) % 0.29/0.55 (define @t47 () (not @t40)) % 0.29/0.55 (define @t48 () (not @t45)) % 0.29/0.55 (define @t49 () (@list true)) % 0.29/0.55 (define @t50 () (@quantifiers_skolemize @t28 0)) % 0.29/0.55 (define @t51 () (tptp.big_j @t50)) % 0.29/0.55 (define @t52 () (tptp.big_g @t50)) % 0.29/0.55 (define @t53 () (not @t52)) % 0.29/0.55 (define @t54 () (or @t53 @t51)) % 0.29/0.55 (define @t55 () (not @t54)) % 0.29/0.55 (define @t56 () (not @t28)) % 0.29/0.55 (define @t57 () (forall @t3 @t29)) % 0.29/0.55 (define @t58 () (@quantifiers_skolemize @t57 0)) % 0.29/0.55 (define @t59 () (and (tptp.big_h @t58) @t51)) % 0.29/0.55 (define @t60 () (tptp.big_f @t58)) % 0.29/0.55 (define @t61 () (not @t60)) % 0.29/0.55 (define @t62 () (or @t61 @t53 @t59)) % 0.29/0.55 (define @t63 () (not @t57)) % 0.29/0.55 (define @t64 () (not @t61)) % 0.29/0.55 (define @t65 () (not @t43)) % 0.29/0.55 (define @t66 () (@list false)) % 0.29/0.55 (define @t67 () (@list @t31)) % 0.29/0.55 (define @t68 () (@quantifiers_skolemize @t43 1)) % 0.29/0.55 (define @t69 () (tptp.big_j @t68)) % 0.29/0.55 (define @t70 () (@quantifiers_skolemize @t43 0)) % 0.29/0.55 (define @t71 () (tptp.big_h @t70)) % 0.29/0.55 (define @t72 () (and @t71 @t69)) % 0.29/0.55 (define @t73 () (tptp.big_g @t68)) % 0.29/0.55 (define @t74 () (not @t73)) % 0.29/0.55 (define @t75 () (tptp.big_f @t70)) % 0.29/0.55 (define @t76 () (not @t75)) % 0.29/0.55 (define @t77 () (or @t76 @t74 @t72)) % 0.29/0.55 (define @t78 () (not @t77)) % 0.29/0.55 (define @t79 () (@list @t77)) % 0.29/0.55 (define @t80 () (or @t76 @t71)) % 0.29/0.55 (define @t81 () (@list false false)) % 0.29/0.55 (define @t82 () (or @t74 @t69)) % 0.29/0.55 (assume @p1 @t4) % 0.29/0.55 (assume @p2 @t8) % 0.29/0.55 (assume @p3 @t24) % 0.29/0.55 (assume @p4 true) % 0.29/0.55 (step @p5 :rule aci_norm :args ((= (or (or @t26 @t25) @t10) @t27))) % 0.29/0.55 (step @p6 :rule refl :args (@t10)) % 0.29/0.55 (step @p7 :rule bool-and-de-morgan :args (@t11 @t6 true)) % 0.29/0.55 (step @p8 :rule nary_cong :premises (@p7 @p6) :args ((or (not @t12) @t10))) % 0.29/0.55 (step @p9 :rule trans :premises (@p8 @p5)) % 0.29/0.55 (step @p10 :rule bool-impl-elim :args (@t12 @t10)) % 0.29/0.55 (step @p11 :rule trans :premises (@p10 @p9)) % 0.29/0.55 (step @p12 :rule cong :premises (@p11) :args (@t14)) % 0.29/0.55 (step @p13 :rule bool-impl-elim :args (@t17 @t16)) % 0.29/0.55 (step @p14 :rule cong :premises (@p13) :args (@t19)) % 0.29/0.55 (step @p15 :rule bool-impl-elim :args (@t2 @t20)) % 0.29/0.55 (step @p16 :rule cong :premises (@p15) :args (@t21)) % 0.29/0.55 (step @p17 :rule nary_cong :premises (@p16 @p14) :args (@t22)) % 0.29/0.55 (step @p18 :rule cong :premises (@p17 @p12) :args (@t23)) % 0.29/0.55 (step @p19 :rule cong :premises (@p18) :args (@t24)) % 0.29/0.55 (step @p20 :rule eq_resolve :premises (@p3 @p19)) % 0.29/0.55 (step @p21 :rule not_equiv_elim1 :premises (@p20)) % 0.29/0.55 (step @p22 :rule cnf_and_pos :args (@t31 0)) % 0.29/0.55 (step @p23 :rule reordering :premises (@p22) :args ((or @t30 @t32))) % 0.29/0.55 (step @p24 :rule refl :args (@t38)) % 0.29/0.55 (step @p25 :rule bool-double-not-elim :args (@t30)) % 0.29/0.55 (step @p26 :rule nary_cong :premises (@p25 @p24) :args ((or (not @t39) @t38))) % 0.29/0.55 (assume-push @p159 @t39) % 0.29/0.55 (step @p28 :rule skolemize :premises (@p159)) % 0.29/0.55 (step-pop @p160 :rule scope :premises (@p28)) % 0.29/0.55 (step @p29 :rule process_scope :premises (@p160) :args (@t38)) % 0.29/0.55 (step @p31 :rule implies_elim :premises (@p29)) % 0.29/0.55 (step @p32 :rule eq_resolve :premises (@p31 @p26)) % 0.29/0.55 (step @p33 :rule bool-double-not-elim :args (@t35)) % 0.29/0.55 (step @p34 :rule refl :args (@t37)) % 0.29/0.55 (step @p35 :rule nary_cong :premises (@p34 @p33) :args ((or @t37 (not @t36)))) % 0.29/0.55 (step @p36 :rule cnf_or_neg :args (@t37 0)) % 0.29/0.55 (step @p37 :rule eq_resolve :premises (@p36 @p35)) % 0.29/0.55 (step @p38 :rule reordering :premises (@p37) :args ((or @t35 @t37))) % 0.29/0.55 (step @p39 :rule cnf_or_neg :args (@t37 1)) % 0.29/0.55 (step @p40 :rule cnf_and_pos :args (@t42 0)) % 0.29/0.55 (step @p41 :rule reordering :premises (@p40) :args ((or @t34 (not @t42)))) % 0.29/0.55 (assume-push @p161 @t43) % 0.29/0.55 (step @p43 :rule instantiate :premises (@p161) :args ((@list @t33 @t41))) % 0.29/0.55 (step-pop @p162 :rule scope :premises (@p43)) % 0.29/0.55 (step @p44 :rule process_scope :premises (@p162) :args (@t46)) % 0.29/0.55 (step @p46 :rule implies_elim :premises (@p44)) % 0.29/0.55 (step @p47 :rule exists-elim :args ((= @t8 @t47))) % 0.29/0.55 (step @p48 :rule eq_resolve :premises (@p2 @p47)) % 0.29/0.55 (step @p49 :rule refl :args (@t44)) % 0.29/0.55 (step @p50 :rule bool-double-not-elim :args (@t40)) % 0.29/0.55 (step @p51 :rule nary_cong :premises (@p50 @p49) :args ((or (not @t47) @t44))) % 0.29/0.55 (step @p52 :rule bool-double-not-elim :args (@t44)) % 0.29/0.55 (step @p53 :rule refl :args (@t47)) % 0.29/0.55 (step @p54 :rule cong :premises (@p53 @p52) :args ((=> @t47 @t48))) % 0.29/0.55 (assume-push @p163 @t47) % 0.29/0.55 (step @p56 :rule skolemize :premises (@p48)) % 0.29/0.55 (step-pop @p164 :rule scope :premises (@p56)) % 0.29/0.55 (step @p57 :rule process_scope :premises (@p164) :args (@t48)) % 0.29/0.55 (step @p59 :rule eq_resolve :premises (@p57 @p54)) % 0.29/0.55 (step @p60 :rule implies_elim :premises (@p59)) % 0.29/0.55 (step @p61 :rule eq_resolve :premises (@p60 @p51)) % 0.29/0.55 (step @p62 :rule chain_m_resolution :premises (@p61 @p48) :args (@t44 @t49 (@list @t40))) % 0.29/0.55 (step @p63 :rule cnf_or_pos :args (@t46)) % 0.29/0.55 (step @p64 :rule reordering :premises (@p63) :args ((or @t45 @t36 @t42 (not @t46)))) % 0.29/0.55 (step @p65 :rule chain_m_resolution :premises (@p64 @p62 @p46 @p41 @p39 @p38 @p32 @p21 @p23) :args (@t30 (@list false false true true false true false true) (@list @t44 @t46 @t42 @t34 @t35 @t37 @t43 @t31))) % 0.29/0.55 (step @p66 :rule cnf_and_neg :args (@t31)) % 0.29/0.55 (step @p67 :rule refl :args (@t55)) % 0.29/0.55 (step @p68 :rule bool-double-not-elim :args (@t28)) % 0.29/0.55 (step @p69 :rule nary_cong :premises (@p68 @p67) :args ((or (not @t56) @t55))) % 0.29/0.55 (assume-push @p165 @t56) % 0.29/0.55 (step @p71 :rule skolemize :premises (@p165)) % 0.29/0.55 (step-pop @p166 :rule scope :premises (@p71)) % 0.29/0.55 (step @p72 :rule process_scope :premises (@p166) :args (@t55)) % 0.29/0.55 (step @p74 :rule implies_elim :premises (@p72)) % 0.29/0.55 (step @p75 :rule eq_resolve :premises (@p74 @p69)) % 0.29/0.55 (step @p76 :rule bool-double-not-elim :args (@t52)) % 0.29/0.55 (step @p77 :rule refl :args (@t54)) % 0.29/0.55 (step @p78 :rule nary_cong :premises (@p77 @p76) :args ((or @t54 (not @t53)))) % 0.29/0.55 (step @p79 :rule cnf_or_neg :args (@t54 0)) % 0.29/0.55 (step @p80 :rule eq_resolve :premises (@p79 @p78)) % 0.29/0.55 (step @p81 :rule reordering :premises (@p80) :args ((or @t52 @t54))) % 0.29/0.55 (step @p82 :rule cnf_or_neg :args (@t54 1)) % 0.29/0.55 (step @p83 :rule cnf_and_pos :args (@t59 1)) % 0.29/0.55 (step @p84 :rule reordering :premises (@p83) :args ((or @t51 (not @t59)))) % 0.29/0.55 (assume-push @p167 @t43) % 0.29/0.55 (step @p86 :rule instantiate :premises (@p167) :args ((@list @t58 @t50))) % 0.29/0.55 (step-pop @p168 :rule scope :premises (@p86)) % 0.29/0.55 (step @p87 :rule process_scope :premises (@p168) :args (@t62)) % 0.29/0.55 (step @p89 :rule implies_elim :premises (@p87)) % 0.29/0.55 (step @p90 :rule exists-elim :args ((= @t4 @t63))) % 0.29/0.55 (step @p91 :rule eq_resolve :premises (@p1 @p90)) % 0.29/0.55 (step @p92 :rule refl :args (@t60)) % 0.29/0.55 (step @p93 :rule bool-double-not-elim :args (@t57)) % 0.29/0.55 (step @p94 :rule nary_cong :premises (@p93 @p92) :args ((or (not @t63) @t60))) % 0.29/0.55 (step @p95 :rule bool-double-not-elim :args (@t60)) % 0.29/0.55 (step @p96 :rule refl :args (@t63)) % 0.29/0.55 (step @p97 :rule cong :premises (@p96 @p95) :args ((=> @t63 @t64))) % 0.29/0.55 (assume-push @p169 @t63) % 0.29/0.55 (step @p99 :rule skolemize :premises (@p91)) % 0.29/0.55 (step-pop @p170 :rule scope :premises (@p99)) % 0.29/0.55 (step @p100 :rule process_scope :premises (@p170) :args (@t64)) % 0.29/0.55 (step @p102 :rule eq_resolve :premises (@p100 @p97)) % 0.29/0.55 (step @p103 :rule implies_elim :premises (@p102)) % 0.29/0.55 (step @p104 :rule eq_resolve :premises (@p103 @p94)) % 0.29/0.55 (step @p105 :rule chain_m_resolution :premises (@p104 @p91) :args (@t60 @t49 (@list @t57))) % 0.29/0.55 (step @p106 :rule cnf_or_pos :args (@t62)) % 0.29/0.55 (step @p107 :rule reordering :premises (@p106) :args ((or @t61 @t53 @t59 (not @t62)))) % 0.29/0.55 (step @p108 :rule chain_m_resolution :premises (@p107 @p105 @p89 @p84 @p82 @p81 @p75 @p66 @p65 @p21) :args (@t31 (@list false false true true false true true false false) (@list @t60 @t62 @t59 @t51 @t52 @t54 @t28 @t30 @t43))) % 0.29/0.55 (step @p109 :rule not_equiv_elim2 :premises (@p20)) % 0.29/0.55 (step @p110 :rule chain_m_resolution :premises (@p109 @p108) :args (@t65 @t66 @t67)) % 0.29/0.55 (step @p111 :rule refl :args (@t78)) % 0.29/0.55 (step @p112 :rule bool-double-not-elim :args (@t43)) % 0.29/0.55 (step @p113 :rule nary_cong :premises (@p112 @p111) :args ((or (not @t65) @t78))) % 0.29/0.55 (assume-push @p171 @t65) % 0.29/0.55 (step @p115 :rule skolemize :premises (@p171)) % 0.29/0.55 (step-pop @p172 :rule scope :premises (@p115)) % 0.29/0.55 (step @p116 :rule process_scope :premises (@p172) :args (@t78)) % 0.29/0.55 (step @p118 :rule implies_elim :premises (@p116)) % 0.29/0.55 (step @p119 :rule eq_resolve :premises (@p118 @p113)) % 0.29/0.55 (step @p120 :rule chain_m_resolution :premises (@p119 @p110) :args (@t78 @t49 (@list @t43))) % 0.29/0.55 (step @p121 :rule cnf_or_neg :args (@t77 2)) % 0.29/0.55 (step @p122 :rule chain_m_resolution :premises (@p121 @p120) :args ((not @t72) @t49 @t79)) % 0.29/0.55 (assume-push @p173 @t30) % 0.29/0.55 (step @p124 :rule instantiate :premises (@p173) :args ((@list @t70))) % 0.29/0.55 (step-pop @p174 :rule scope :premises (@p124)) % 0.29/0.55 (step @p125 :rule process_scope :premises (@p174) :args (@t80)) % 0.29/0.55 (step @p127 :rule implies_elim :premises (@p125)) % 0.29/0.55 (step @p128 :rule chain_m_resolution :premises (@p127 @p65) :args (@t80 @t66 (@list @t30))) % 0.29/0.55 (step @p129 :rule bool-double-not-elim :args (@t75)) % 0.29/0.55 (step @p130 :rule refl :args (@t77)) % 0.29/0.55 (step @p131 :rule nary_cong :premises (@p130 @p129) :args ((or @t77 (not @t76)))) % 0.29/0.55 (step @p132 :rule cnf_or_neg :args (@t77 0)) % 0.29/0.55 (step @p133 :rule eq_resolve :premises (@p132 @p131)) % 0.29/0.55 (step @p134 :rule reordering :premises (@p133) :args ((or @t75 @t77))) % 0.29/0.55 (step @p135 :rule chain_m_resolution :premises (@p134 @p120) :args (@t75 @t49 @t79)) % 0.29/0.55 (step @p136 :rule cnf_or_pos :args (@t80)) % 0.29/0.55 (step @p137 :rule reordering :premises (@p136) :args ((or @t76 @t71 (not @t80)))) % 0.29/0.55 (step @p138 :rule chain_m_resolution :premises (@p137 @p135 @p128) :args (@t71 @t81 (@list @t75 @t80))) % 0.29/0.55 (step @p139 :rule cnf_and_pos :args (@t31 1)) % 0.29/0.55 (step @p140 :rule reordering :premises (@p139) :args ((or @t28 @t32))) % 0.29/0.55 (step @p141 :rule chain_m_resolution :premises (@p140 @p108) :args (@t28 @t66 @t67)) % 0.29/0.55 (assume-push @p175 @t28) % 0.29/0.55 (step @p143 :rule instantiate :premises (@p175) :args ((@list @t68))) % 0.29/0.55 (step-pop @p176 :rule scope :premises (@p143)) % 0.29/0.55 (step @p144 :rule process_scope :premises (@p176) :args (@t82)) % 0.29/0.55 (step @p146 :rule implies_elim :premises (@p144)) % 0.29/0.55 (step @p147 :rule chain_m_resolution :premises (@p146 @p141) :args (@t82 @t66 (@list @t28))) % 0.29/0.55 (step @p148 :rule bool-double-not-elim :args (@t73)) % 0.29/0.55 (step @p149 :rule nary_cong :premises (@p130 @p148) :args ((or @t77 (not @t74)))) % 0.29/0.55 (step @p150 :rule cnf_or_neg :args (@t77 1)) % 0.29/0.55 (step @p151 :rule eq_resolve :premises (@p150 @p149)) % 0.29/0.55 (step @p152 :rule reordering :premises (@p151) :args ((or @t73 @t77))) % 0.29/0.55 (step @p153 :rule chain_m_resolution :premises (@p152 @p120) :args (@t73 @t49 @t79)) % 0.29/0.55 (step @p154 :rule cnf_or_pos :args (@t82)) % 0.29/0.55 (step @p155 :rule reordering :premises (@p154) :args ((or @t74 @t69 (not @t82)))) % 0.29/0.55 (step @p156 :rule chain_m_resolution :premises (@p155 @p153 @p147) :args (@t69 @t81 (@list @t73 @t82))) % 0.29/0.55 (step @p157 :rule cnf_and_neg :args (@t72)) % 0.29/0.55 (step @p158 false :rule chain_m_resolution :premises (@p157 @p156 @p138 @p122) :args (false (@list false false true) (@list @t69 @t71 @t72))) % 0.29/0.55 ) % 0.29/0.55 % SZS output end Proof % 0.29/0.55 % cvc5 exiting %------------------------------------------------------------------------------