%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYN056+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 : n012.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 09:07:55 AM UTC 2026 % Result : Theorem 0.15s 0.36s % Output : Proof 0.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SYN056+1 : TPTP v9.2.1. Released v2.0.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.06/0.25 % Computer : n012.cluster.edu % 0.06/0.25 % Model : x86_64 x86_64 % 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.06/0.25 % Memory : 8042.1875MB % 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.06/0.25 % CPULimit : 300 % 0.06/0.25 % WCLimit : 300 % 0.06/0.25 % DateTime : Tue Jun 2 23:19:18 EDT 2026 % 0.06/0.25 % CPUTime : % 0.06/0.32 %----Proving TF0_NAR, FOF, or CNF % 0.15/0.36 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.15/0.36 % SZS status Theorem % 0.15/0.36 % SZS output start Proof % 0.15/0.36 ( % 0.15/0.36 (declare-sort $$unsorted 0) % 0.15/0.36 (declare-const tptp.big_r (-> $$unsorted Bool)) % 0.15/0.36 (declare-const tptp.big_s (-> $$unsorted Bool)) % 0.15/0.36 (declare-const tptp.big_p (-> $$unsorted Bool)) % 0.15/0.36 (declare-const tptp.big_q (-> $$unsorted Bool)) % 0.15/0.36 (define @t1 () (@var "Y" $$unsorted)) % 0.15/0.36 (define @t2 () (tptp.big_q @t1)) % 0.15/0.36 (define @t3 () (@list @t1)) % 0.15/0.36 (define @t4 () (exists @t3 @t2)) % 0.15/0.36 (define @t5 () (@var "X" $$unsorted)) % 0.15/0.36 (define @t6 () (tptp.big_p @t5)) % 0.15/0.36 (define @t7 () (@list @t5)) % 0.15/0.36 (define @t8 () (exists @t7 @t6)) % 0.15/0.36 (define @t9 () (= @t8 @t4)) % 0.15/0.36 (define @t10 () (tptp.big_s @t1)) % 0.15/0.36 (define @t11 () (tptp.big_r @t5)) % 0.15/0.36 (define @t12 () (= @t11 @t10)) % 0.15/0.36 (define @t13 () (and @t6 @t2)) % 0.15/0.36 (define @t14 () (@list @t5 @t1)) % 0.15/0.36 (define @t15 () (forall @t14 (=> @t13 @t12))) % 0.15/0.36 (define @t16 () (forall @t3 (=> @t2 @t10))) % 0.15/0.36 (define @t17 () (forall @t7 (=> @t6 @t11))) % 0.15/0.36 (define @t18 () (= @t17 @t16)) % 0.15/0.36 (define @t19 () (not @t18)) % 0.15/0.36 (define @t20 () (not @t6)) % 0.15/0.36 (define @t21 () (forall @t7 (or @t20 @t11))) % 0.15/0.36 (define @t22 () (forall @t7 @t20)) % 0.15/0.36 (define @t23 () (@quantifiers_skolemize @t22 0)) % 0.15/0.36 (define @t24 () (tptp.big_r @t23)) % 0.15/0.36 (define @t25 () (tptp.big_p @t23)) % 0.15/0.36 (define @t26 () (not @t25)) % 0.15/0.36 (define @t27 () (or @t26 @t24)) % 0.15/0.36 (define @t28 () (not @t2)) % 0.15/0.36 (define @t29 () (forall @t3 (or @t28 @t10))) % 0.15/0.36 (define @t30 () (@quantifiers_skolemize @t29 0)) % 0.15/0.36 (define @t31 () (tptp.big_s @t30)) % 0.15/0.36 (define @t32 () (tptp.big_q @t30)) % 0.15/0.36 (define @t33 () (not @t32)) % 0.15/0.36 (define @t34 () (or @t33 @t31)) % 0.15/0.36 (define @t35 () (not @t34)) % 0.15/0.36 (define @t36 () (not @t29)) % 0.15/0.36 (define @t37 () (or @t20 @t28 @t12)) % 0.15/0.36 (define @t38 () (or @t26 @t33 (= @t24 @t31))) % 0.15/0.36 (define @t39 () (forall @t14 @t37)) % 0.15/0.36 (define @t40 () (= @t31 @t24)) % 0.15/0.36 (define @t41 () (or @t26 @t33 @t40)) % 0.15/0.36 (define @t42 () (@list false)) % 0.15/0.36 (define @t43 () (@list @t39)) % 0.15/0.36 (define @t44 () (not @t27)) % 0.15/0.36 (define @t45 () (not @t22)) % 0.15/0.36 (define @t46 () (not @t45)) % 0.15/0.36 (define @t47 () (not @t26)) % 0.15/0.36 (define @t48 () (forall @t3 @t28)) % 0.15/0.36 (define @t49 () (not @t48)) % 0.15/0.36 (define @t50 () (not @t49)) % 0.15/0.36 (define @t51 () (not @t21)) % 0.15/0.36 (define @t52 () (@quantifiers_skolemize @t21 0)) % 0.15/0.36 (define @t53 () (tptp.big_r @t52)) % 0.15/0.36 (define @t54 () (tptp.big_p @t52)) % 0.15/0.36 (define @t55 () (not @t54)) % 0.15/0.36 (define @t56 () (or @t55 @t53)) % 0.15/0.36 (define @t57 () (not @t56)) % 0.15/0.36 (define @t58 () (@list true)) % 0.15/0.36 (define @t59 () (@list @t21)) % 0.15/0.36 (define @t60 () (@quantifiers_skolemize @t48 0)) % 0.15/0.36 (define @t61 () (tptp.big_s @t60)) % 0.15/0.36 (define @t62 () (tptp.big_q @t60)) % 0.15/0.36 (define @t63 () (not @t62)) % 0.15/0.36 (define @t64 () (or @t63 @t61)) % 0.15/0.36 (define @t65 () (not @t63)) % 0.15/0.36 (define @t66 () (not @t64)) % 0.15/0.36 (define @t67 () (or @t55 @t63 (= @t53 @t61))) % 0.15/0.36 (define @t68 () (= @t61 @t53)) % 0.15/0.36 (define @t69 () (or @t55 @t63 @t68)) % 0.15/0.36 (assume @p1 @t9) % 0.15/0.36 (assume @p2 @t15) % 0.15/0.36 (assume @p3 @t19) % 0.15/0.36 (assume @p4 true) % 0.15/0.36 (step @p5 :rule bool-impl-elim :args (@t2 @t10)) % 0.15/0.36 (step @p6 :rule cong :premises (@p5) :args (@t16)) % 0.15/0.36 (step @p7 :rule bool-impl-elim :args (@t6 @t11)) % 0.15/0.36 (step @p8 :rule cong :premises (@p7) :args (@t17)) % 0.15/0.36 (step @p9 :rule cong :premises (@p8 @p6) :args (@t18)) % 0.15/0.36 (step @p10 :rule cong :premises (@p9) :args (@t19)) % 0.15/0.36 (step @p11 :rule eq_resolve :premises (@p3 @p10)) % 0.15/0.36 (step @p12 :rule not_equiv_elim2 :premises (@p11)) % 0.15/0.36 (assume-push @p155 @t21) % 0.15/0.36 (step @p14 :rule instantiate :premises (@p155) :args ((@list @t23))) % 0.15/0.36 (step-pop @p156 :rule scope :premises (@p14)) % 0.15/0.36 (step @p15 :rule process_scope :premises (@p156) :args (@t27)) % 0.15/0.36 (step @p17 :rule implies_elim :premises (@p15)) % 0.15/0.36 (step @p18 :rule refl :args (@t35)) % 0.15/0.36 (step @p19 :rule bool-double-not-elim :args (@t29)) % 0.15/0.36 (step @p20 :rule nary_cong :premises (@p19 @p18) :args ((or (not @t36) @t35))) % 0.15/0.36 (assume-push @p157 @t36) % 0.15/0.36 (step @p22 :rule skolemize :premises (@p157)) % 0.15/0.36 (step-pop @p158 :rule scope :premises (@p22)) % 0.15/0.36 (step @p23 :rule process_scope :premises (@p158) :args (@t35)) % 0.15/0.36 (step @p25 :rule implies_elim :premises (@p23)) % 0.15/0.36 (step @p26 :rule eq_resolve :premises (@p25 @p20)) % 0.15/0.36 (step @p27 :rule bool-double-not-elim :args (@t32)) % 0.15/0.36 (step @p28 :rule refl :args (@t34)) % 0.15/0.36 (step @p29 :rule nary_cong :premises (@p28 @p27) :args ((or @t34 (not @t33)))) % 0.15/0.36 (step @p30 :rule cnf_or_neg :args (@t34 0)) % 0.15/0.36 (step @p31 :rule eq_resolve :premises (@p30 @p29)) % 0.15/0.36 (step @p32 :rule reordering :premises (@p31) :args ((or @t32 @t34))) % 0.15/0.36 (step @p33 :rule cnf_or_neg :args (@t34 1)) % 0.15/0.36 (step @p34 :rule aci_norm :args ((= (or (or @t20 @t28) @t12) @t37))) % 0.15/0.36 (step @p35 :rule refl :args (@t12)) % 0.15/0.36 (step @p36 :rule bool-and-de-morgan :args (@t6 @t2 true)) % 0.15/0.36 (step @p37 :rule nary_cong :premises (@p36 @p35) :args ((or (not @t13) @t12))) % 0.15/0.36 (step @p38 :rule trans :premises (@p37 @p34)) % 0.15/0.36 (step @p39 :rule bool-impl-elim :args (@t13 @t12)) % 0.15/0.36 (step @p40 :rule trans :premises (@p39 @p38)) % 0.15/0.36 (step @p41 :rule cong :premises (@p40) :args (@t15)) % 0.15/0.36 (step @p42 :rule eq_resolve :premises (@p2 @p41)) % 0.15/0.36 (step @p43 :rule eq-symm :args (@t24 @t31)) % 0.15/0.36 (step @p44 :rule refl :args (@t33)) % 0.15/0.36 (step @p45 :rule refl :args (@t26)) % 0.15/0.36 (step @p46 :rule nary_cong :premises (@p45 @p44 @p43) :args (@t38)) % 0.15/0.36 (step @p47 :rule refl :args (@t39)) % 0.15/0.36 (step @p48 :rule cong :premises (@p47 @p46) :args ((=> @t39 @t38))) % 0.15/0.36 (assume-push @p159 @t39) % 0.15/0.36 (step @p50 :rule instantiate :premises (@p42) :args ((@list @t23 @t30))) % 0.15/0.36 (step-pop @p160 :rule scope :premises (@p50)) % 0.15/0.36 (step @p51 :rule process_scope :premises (@p160) :args (@t38)) % 0.15/0.36 (step @p53 :rule eq_resolve :premises (@p51 @p48)) % 0.15/0.36 (step @p54 :rule implies_elim :premises (@p53)) % 0.15/0.36 (step @p55 :rule chain_m_resolution :premises (@p54 @p42) :args (@t41 @t42 @t43)) % 0.15/0.36 (step @p56 :rule cnf_or_pos :args (@t41)) % 0.15/0.36 (step @p57 :rule reordering :premises (@p56) :args ((or @t26 @t33 @t40 (not @t41)))) % 0.15/0.36 (step @p58 :rule cnf_or_pos :args (@t27)) % 0.15/0.36 (step @p59 :rule reordering :premises (@p58) :args ((or @t26 @t24 @t44))) % 0.15/0.36 (step @p60 :rule cnf_equiv_pos2 :args (@t40)) % 0.15/0.36 (step @p61 :rule reordering :premises (@p60) :args ((or @t31 (not @t24) (not @t40)))) % 0.15/0.36 (step @p62 :rule chain_m_resolution :premises (@p61 @p59 @p57 @p55) :args ((or @t26 @t33 @t31 @t44) (@list false false false) (@list @t24 @t40 @t41))) % 0.15/0.36 (step @p63 :rule refl :args (@t25)) % 0.15/0.36 (step @p64 :rule bool-double-not-elim :args (@t22)) % 0.15/0.36 (step @p65 :rule nary_cong :premises (@p64 @p63) :args ((or @t46 @t25))) % 0.15/0.36 (step @p66 :rule bool-double-not-elim :args (@t25)) % 0.15/0.36 (step @p67 :rule refl :args (@t45)) % 0.15/0.36 (step @p68 :rule cong :premises (@p67 @p66) :args ((=> @t45 @t47))) % 0.15/0.36 (assume-push @p161 @t45) % 0.15/0.36 (step @p70 :rule skolemize :premises (@p161)) % 0.15/0.36 (step-pop @p162 :rule scope :premises (@p70)) % 0.15/0.36 (step @p71 :rule process_scope :premises (@p162) :args (@t47)) % 0.15/0.36 (step @p73 :rule eq_resolve :premises (@p71 @p68)) % 0.15/0.36 (step @p74 :rule implies_elim :premises (@p73)) % 0.15/0.36 (step @p75 :rule eq_resolve :premises (@p74 @p65)) % 0.15/0.36 (step @p76 :rule bool-double-not-elim :args (@t48)) % 0.15/0.36 (step @p77 :rule nary_cong :premises (@p67 @p76) :args ((or @t45 @t50))) % 0.15/0.36 (step @p78 :rule exists-elim :args ((= @t4 @t49))) % 0.15/0.36 (step @p79 :rule exists-elim :args ((= @t8 @t45))) % 0.15/0.36 (step @p80 :rule cong :premises (@p79 @p78) :args (@t9)) % 0.15/0.36 (step @p81 :rule eq_resolve :premises (@p1 @p80)) % 0.15/0.36 (step @p82 :rule equiv_elim2 :premises (@p81)) % 0.15/0.36 (step @p83 :rule eq_resolve :premises (@p82 @p77)) % 0.15/0.36 (assume-push @p163 @t48) % 0.15/0.36 (step @p85 :rule instantiate :premises (@p163) :args ((@list @t30))) % 0.15/0.36 (step-pop @p164 :rule scope :premises (@p85)) % 0.15/0.36 (step @p86 :rule process_scope :premises (@p164) :args (@t33)) % 0.15/0.36 (step @p88 :rule implies_elim :premises (@p86)) % 0.15/0.36 (step @p89 :rule chain_m_resolution :premises (@p88 @p83 @p75 @p62 @p33 @p32 @p26 @p17 @p12) :args (@t51 (@list false false true true false true false true) (@list @t48 @t22 @t25 @t31 @t32 @t34 @t27 @t29))) % 0.15/0.36 (step @p90 :rule refl :args (@t57)) % 0.15/0.36 (step @p91 :rule bool-double-not-elim :args (@t21)) % 0.15/0.36 (step @p92 :rule nary_cong :premises (@p91 @p90) :args ((or (not @t51) @t57))) % 0.15/0.36 (assume-push @p165 @t51) % 0.15/0.36 (step @p94 :rule skolemize :premises (@p165)) % 0.15/0.36 (step-pop @p166 :rule scope :premises (@p94)) % 0.15/0.36 (step @p95 :rule process_scope :premises (@p166) :args (@t57)) % 0.15/0.36 (step @p97 :rule implies_elim :premises (@p95)) % 0.15/0.36 (step @p98 :rule eq_resolve :premises (@p97 @p92)) % 0.15/0.36 (step @p99 :rule chain_m_resolution :premises (@p98 @p89) :args (@t57 @t58 @t59)) % 0.15/0.36 (step @p100 :rule not_equiv_elim1 :premises (@p11)) % 0.15/0.36 (step @p101 :rule chain_m_resolution :premises (@p100 @p89) :args (@t29 @t58 @t59)) % 0.15/0.36 (assume-push @p167 @t29) % 0.15/0.36 (step @p103 :rule instantiate :premises (@p167) :args ((@list @t60))) % 0.15/0.36 (step-pop @p168 :rule scope :premises (@p103)) % 0.15/0.36 (step @p104 :rule process_scope :premises (@p168) :args (@t64)) % 0.15/0.36 (step @p106 :rule implies_elim :premises (@p104)) % 0.15/0.36 (step @p107 :rule chain_m_resolution :premises (@p106 @p101) :args (@t64 @t42 (@list @t29))) % 0.15/0.36 (step @p108 :rule bool-double-not-elim :args (@t54)) % 0.15/0.36 (step @p109 :rule refl :args (@t56)) % 0.15/0.36 (step @p110 :rule nary_cong :premises (@p109 @p108) :args ((or @t56 (not @t55)))) % 0.15/0.36 (step @p111 :rule cnf_or_neg :args (@t56 0)) % 0.15/0.36 (step @p112 :rule eq_resolve :premises (@p111 @p110)) % 0.15/0.36 (step @p113 :rule reordering :premises (@p112) :args ((or @t54 @t56))) % 0.15/0.36 (step @p114 :rule cnf_or_neg :args (@t56 1)) % 0.15/0.36 (assume-push @p169 @t22) % 0.15/0.36 (step @p116 :rule instantiate :premises (@p169) :args ((@list @t52))) % 0.15/0.36 (step-pop @p170 :rule scope :premises (@p116)) % 0.15/0.36 (step @p117 :rule process_scope :premises (@p170) :args (@t55)) % 0.15/0.36 (step @p119 :rule implies_elim :premises (@p117)) % 0.15/0.36 (step @p120 :rule refl :args (@t49)) % 0.15/0.36 (step @p121 :rule nary_cong :premises (@p64 @p120) :args ((or @t46 @t49))) % 0.15/0.36 (step @p122 :rule equiv_elim1 :premises (@p81)) % 0.15/0.36 (step @p123 :rule eq_resolve :premises (@p122 @p121)) % 0.15/0.36 (step @p124 :rule refl :args (@t62)) % 0.15/0.36 (step @p125 :rule nary_cong :premises (@p76 @p124) :args ((or @t50 @t62))) % 0.15/0.36 (step @p126 :rule bool-double-not-elim :args (@t62)) % 0.15/0.36 (step @p127 :rule cong :premises (@p120 @p126) :args ((=> @t49 @t65))) % 0.15/0.36 (assume-push @p171 @t49) % 0.15/0.36 (step @p129 :rule skolemize :premises (@p171)) % 0.15/0.36 (step-pop @p172 :rule scope :premises (@p129)) % 0.15/0.36 (step @p130 :rule process_scope :premises (@p172) :args (@t65)) % 0.15/0.36 (step @p132 :rule eq_resolve :premises (@p130 @p127)) % 0.15/0.36 (step @p133 :rule implies_elim :premises (@p132)) % 0.15/0.36 (step @p134 :rule eq_resolve :premises (@p133 @p125)) % 0.15/0.36 (step @p135 :rule cnf_or_pos :args (@t64)) % 0.15/0.36 (step @p136 :rule reordering :premises (@p135) :args ((or @t63 @t61 @t66))) % 0.15/0.36 (step @p137 :rule eq-symm :args (@t53 @t61)) % 0.15/0.36 (step @p138 :rule refl :args (@t63)) % 0.15/0.36 (step @p139 :rule refl :args (@t55)) % 0.15/0.36 (step @p140 :rule nary_cong :premises (@p139 @p138 @p137) :args (@t67)) % 0.15/0.36 (step @p141 :rule cong :premises (@p47 @p140) :args ((=> @t39 @t67))) % 0.15/0.36 (assume-push @p173 @t39) % 0.15/0.36 (step @p143 :rule instantiate :premises (@p42) :args ((@list @t52 @t60))) % 0.15/0.36 (step-pop @p174 :rule scope :premises (@p143)) % 0.15/0.36 (step @p144 :rule process_scope :premises (@p174) :args (@t67)) % 0.15/0.36 (step @p146 :rule eq_resolve :premises (@p144 @p141)) % 0.15/0.36 (step @p147 :rule implies_elim :premises (@p146)) % 0.15/0.36 (step @p148 :rule chain_m_resolution :premises (@p147 @p42) :args (@t69 @t42 @t43)) % 0.15/0.36 (step @p149 :rule cnf_or_pos :args (@t69)) % 0.15/0.36 (step @p150 :rule reordering :premises (@p149) :args ((or @t63 @t55 @t68 (not @t69)))) % 0.15/0.36 (step @p151 :rule cnf_equiv_pos1 :args (@t68)) % 0.15/0.36 (step @p152 :rule reordering :premises (@p151) :args ((or (not @t61) @t53 (not @t68)))) % 0.15/0.36 (step @p153 :rule chain_m_resolution :premises (@p152 @p150 @p148 @p136 @p134 @p123 @p119 @p114 @p113) :args ((or @t56 @t66) (@list false false false false true true true false) (@list @t68 @t69 @t61 @t62 @t48 @t22 @t53 @t54))) % 0.15/0.36 (step @p154 false :rule chain_m_resolution :premises (@p153 @p107 @p99) :args (false (@list false true) (@list @t64 @t56))) % 0.15/0.36 ) % 0.15/0.36 % SZS output end Proof % 0.15/0.36 % cvc5 exiting %------------------------------------------------------------------------------