%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET921+1 : TPTP v9.2.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n022.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 08:48:59 AM UTC 2026 % Result : Theorem 15.52s 15.72s % Output : Proof 15.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET921+1 : TPTP v9.2.1. Released v3.2.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n022.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 16:17:53 EDT 2026 % 0.16/0.35 % CPUTime : % 0.33/0.50 %----Proving TF0_NAR, FOF, or CNF % 15.52/15.72 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.52/15.72 --- Run --no-e-matching --full-saturate-quant at 6... % 15.52/15.72 % SZS status Theorem % 15.52/15.72 % SZS output start Proof % 15.52/15.72 ( % 15.52/15.72 (declare-sort $$unsorted 0) % 15.52/15.72 (declare-const tptp.empty (-> $$unsorted Bool)) % 15.52/15.72 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 15.52/15.72 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 15.52/15.72 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 15.52/15.72 (define @t1 () (@var "A" $$unsorted)) % 15.52/15.72 (define @t2 () (@var "B" $$unsorted)) % 15.52/15.72 (define @t3 () (tptp.in @t1 @t2)) % 15.52/15.72 (define @t4 () (@list @t1 @t2)) % 15.52/15.72 (define @t5 () (@var "C" $$unsorted)) % 15.52/15.72 (define @t6 () (tptp.in @t5 @t2)) % 15.52/15.72 (define @t7 () (= @t6 (= @t5 @t1))) % 15.52/15.72 (define @t8 () (@list @t5)) % 15.52/15.72 (define @t9 () (forall @t8 @t7)) % 15.52/15.72 (define @t10 () (= @t2 (tptp.singleton @t1))) % 15.52/15.72 (define @t11 () (= @t10 @t9)) % 15.52/15.72 (define @t12 () (forall @t4 @t11)) % 15.52/15.72 (define @t13 () (@var "D" $$unsorted)) % 15.52/15.72 (define @t14 () (@list @t13)) % 15.52/15.72 (define @t15 () (@list @t1 @t2 @t5)) % 15.52/15.72 (define @t16 () (forall @t15 (= (= @t5 (tptp.set_difference @t1 @t2)) (forall @t14 (= (tptp.in @t13 @t5) (and (tptp.in @t13 @t1) (not (tptp.in @t13 @t2)))))))) % 15.52/15.72 (define @t17 () (tptp.empty @t1)) % 15.52/15.72 (define @t18 () (@list @t1)) % 15.52/15.72 (define @t19 () (= @t1 @t5)) % 15.52/15.72 (define @t20 () (forall @t15 (= (tptp.in @t1 (tptp.set_difference @t2 (tptp.singleton @t5))) (and @t3 (not @t19))))) % 15.52/15.72 (define @t21 () (@quantifiers_skolemize @t20 2)) % 15.52/15.72 (define @t22 () (tptp.singleton @t21)) % 15.52/15.72 (define @t23 () (tptp.in @t5 @t22)) % 15.52/15.72 (define @t24 () (forall @t8 (= @t23 (= @t5 @t21)))) % 15.52/15.72 (define @t25 () (= @t23 (= @t21 @t5))) % 15.52/15.72 (define @t26 () (forall @t8 @t25)) % 15.52/15.72 (define @t27 () (= (= @t22 @t22) @t26)) % 15.52/15.72 (define @t28 () (forall @t4 (= @t10 (forall @t8 (= @t6 @t19))))) % 15.52/15.72 (define @t29 () (@list false)) % 15.52/15.72 (define @t30 () (@quantifiers_skolemize @t20 1)) % 15.52/15.72 (define @t31 () (tptp.set_difference @t30 @t22)) % 15.52/15.72 (define @t32 () (forall @t14 (= (tptp.in @t13 @t31) (and (tptp.in @t13 @t30) (not (tptp.in @t13 @t22)))))) % 15.52/15.72 (define @t33 () (= (= @t31 @t31) @t32)) % 15.52/15.72 (define @t34 () (@quantifiers_skolemize @t20 0)) % 15.52/15.72 (define @t35 () (@list @t34)) % 15.52/15.72 (define @t36 () (= @t34 @t21)) % 15.52/15.72 (define @t37 () (not @t36)) % 15.52/15.72 (define @t38 () (tptp.in @t34 @t30)) % 15.52/15.72 (define @t39 () (and @t38 @t37)) % 15.52/15.72 (define @t40 () (tptp.in @t34 @t31)) % 15.52/15.72 (define @t41 () (= @t40 @t39)) % 15.52/15.72 (define @t42 () (tptp.in @t34 @t22)) % 15.52/15.72 (define @t43 () (not @t42)) % 15.52/15.72 (define @t44 () (and @t38 @t43)) % 15.52/15.72 (define @t45 () (= @t40 @t44)) % 15.52/15.72 (define @t46 () (not @t45)) % 15.52/15.72 (define @t47 () (not @t40)) % 15.52/15.72 (define @t48 () (not @t44)) % 15.52/15.72 (define @t49 () (not @t38)) % 15.52/15.72 (define @t50 () (tptp.in @t21 @t22)) % 15.52/15.72 (define @t51 () (= @t50 (= @t21 @t21))) % 15.52/15.72 (define @t52 () (not @t50)) % 15.52/15.72 (define @t53 () (not @t43)) % 15.52/15.72 (define @t54 () (and @t43 @t36 @t50)) % 15.52/15.72 (define @t55 () (@list true false)) % 15.52/15.72 (define @t56 () (not @t39)) % 15.52/15.72 (define @t57 () (@list @t39)) % 15.52/15.72 (define @t58 () (= @t36 @t42)) % 15.52/15.72 (define @t59 () (not @t58)) % 15.52/15.72 (define @t60 () (= @t42 @t36)) % 15.52/15.72 (assume @p1 (forall @t4 (=> @t3 (not (tptp.in @t2 @t1))))) % 15.52/15.72 (assume @p2 @t12) % 15.52/15.72 (assume @p3 @t16) % 15.52/15.72 (assume @p4 (exists @t18 @t17)) % 15.52/15.72 (assume @p5 (exists @t18 (not @t17))) % 15.52/15.72 (assume @p6 (not @t20)) % 15.52/15.72 (assume @p7 true) % 15.52/15.72 (step @p8 :rule eq-symm :args (@t5 @t1)) % 15.52/15.72 (step @p9 :rule refl :args (@t6)) % 15.52/15.72 (step @p10 :rule cong :premises (@p9 @p8) :args (@t7)) % 15.52/15.72 (step @p11 :rule cong :premises (@p10) :args (@t9)) % 15.52/15.72 (step @p12 :rule refl :args (@t10)) % 15.52/15.72 (step @p13 :rule cong :premises (@p12 @p11) :args (@t11)) % 15.52/15.72 (step @p14 :rule cong :premises (@p13) :args (@t12)) % 15.52/15.72 (step @p15 :rule eq_resolve :premises (@p2 @p14)) % 15.52/15.72 (step @p16 :rule bool-eq-true :args (@t24)) % 15.52/15.72 (step @p17 :rule eq-symm :args (true @t24)) % 15.52/15.72 (step @p18 :rule trans :premises (@p17 @p16)) % 15.52/15.72 (step @p19 :rule eq-symm :args (@t21 @t5)) % 15.52/15.72 (step @p20 :rule refl :args (@t23)) % 15.52/15.72 (step @p21 :rule cong :premises (@p20 @p19) :args (@t25)) % 15.52/15.72 (step @p22 :rule cong :premises (@p21) :args (@t26)) % 15.52/15.72 (step @p23 :rule eq-refl :args (@t22)) % 15.52/15.72 (step @p24 :rule cong :premises (@p23 @p22) :args (@t27)) % 15.52/15.72 (step @p25 :rule trans :premises (@p24 @p18)) % 15.52/15.72 (step @p26 :rule refl :args (@t28)) % 15.52/15.72 (step @p27 :rule cong :premises (@p26 @p25) :args ((=> @t28 @t27))) % 15.52/15.72 (assume-push @p144 @t28) % 15.52/15.72 (step @p29 :rule instantiate :premises (@p15) :args ((@list @t21 @t22))) % 15.52/15.72 (step-pop @p145 :rule scope :premises (@p29)) % 15.52/15.72 (step @p30 :rule process_scope :premises (@p145) :args (@t27)) % 15.52/15.72 (step @p32 :rule eq_resolve :premises (@p30 @p27)) % 15.52/15.72 (step @p33 :rule implies_elim :premises (@p32)) % 15.52/15.72 (step @p34 :rule chain_m_resolution :premises (@p33 @p15) :args (@t24 @t29 (@list @t28))) % 15.52/15.72 (step @p35 :rule bool-eq-true :args (@t32)) % 15.52/15.72 (step @p36 :rule eq-symm :args (true @t32)) % 15.52/15.72 (step @p37 :rule trans :premises (@p36 @p35)) % 15.52/15.72 (step @p38 :rule refl :args (@t32)) % 15.52/15.72 (step @p39 :rule eq-refl :args (@t31)) % 15.52/15.72 (step @p40 :rule cong :premises (@p39 @p38) :args (@t33)) % 15.52/15.72 (step @p41 :rule trans :premises (@p40 @p37)) % 15.52/15.72 (step @p42 :rule refl :args (@t16)) % 15.52/15.72 (step @p43 :rule cong :premises (@p42 @p41) :args ((=> @t16 @t33))) % 15.52/15.72 (assume-push @p146 @t16) % 15.52/15.72 (step @p45 :rule instantiate :premises (@p3) :args ((@list @t30 @t22 @t31))) % 15.52/15.72 (step-pop @p147 :rule scope :premises (@p45)) % 15.52/15.72 (step @p46 :rule process_scope :premises (@p147) :args (@t33)) % 15.52/15.72 (step @p48 :rule eq_resolve :premises (@p46 @p43)) % 15.52/15.72 (step @p49 :rule implies_elim :premises (@p48)) % 15.52/15.72 (step @p50 :rule chain_m_resolution :premises (@p49 @p3) :args (@t32 @t29 (@list @t16))) % 15.52/15.72 (step @p51 :rule instantiate :premises (@p50) :args (@t35)) % 15.52/15.72 (step @p52 :rule skolemize :premises (@p6)) % 15.52/15.72 (step @p53 :rule cnf_equiv_neg2 :args (@t41)) % 15.52/15.72 (step @p54 :rule cnf_equiv_pos1 :args (@t45)) % 15.52/15.72 (step @p55 :rule reordering :premises (@p54) :args ((or @t47 @t44 @t46))) % 15.52/15.72 (step @p56 :rule cnf_and_pos :args (@t44 0)) % 15.52/15.72 (step @p57 :rule reordering :premises (@p56) :args ((or @t38 @t48))) % 15.52/15.72 (step @p58 :rule cnf_and_pos :args (@t44 1)) % 15.52/15.72 (step @p59 :rule reordering :premises (@p58) :args ((or @t43 @t48))) % 15.52/15.72 (step @p60 :rule bool-double-not-elim :args (@t36)) % 15.52/15.72 (step @p61 :rule refl :args (@t49)) % 15.52/15.72 (step @p62 :rule refl :args (@t39)) % 15.52/15.72 (step @p63 :rule nary_cong :premises (@p62 @p61 @p60) :args ((or @t39 @t49 (not @t37)))) % 15.52/15.72 (step @p64 :rule cnf_and_neg :args (@t39)) % 15.52/15.72 (step @p65 :rule eq_resolve :premises (@p64 @p63)) % 15.52/15.72 (step @p66 :rule reordering :premises (@p65) :args ((or @t36 @t39 @t49))) % 15.52/15.72 (step @p67 :rule bool-eq-true :args (@t50)) % 15.52/15.72 (step @p68 :rule eq-refl :args (@t21)) % 15.52/15.72 (step @p69 :rule refl :args (@t50)) % 15.52/15.72 (step @p70 :rule cong :premises (@p69 @p68) :args (@t51)) % 15.52/15.72 (step @p71 :rule trans :premises (@p70 @p67)) % 15.52/15.72 (step @p72 :rule refl :args (@t24)) % 15.52/15.72 (step @p73 :rule cong :premises (@p72 @p71) :args ((=> @t24 @t51))) % 15.52/15.72 (assume-push @p148 @t24) % 15.52/15.72 (step @p75 :rule instantiate :premises (@p34) :args ((@list @t21))) % 15.52/15.72 (step-pop @p149 :rule scope :premises (@p75)) % 15.52/15.72 (step @p76 :rule process_scope :premises (@p149) :args (@t51)) % 15.52/15.72 (step @p78 :rule eq_resolve :premises (@p76 @p73)) % 15.52/15.72 (step @p79 :rule implies_elim :premises (@p78)) % 15.52/15.72 (step @p80 :rule chain_m_resolution :premises (@p79 @p34) :args (@t50 @t29 (@list @t24))) % 15.52/15.72 (step @p81 :rule refl :args (@t52)) % 15.52/15.72 (step @p82 :rule bool-double-not-elim :args (@t42)) % 15.52/15.72 (step @p83 :rule refl :args (@t37)) % 15.52/15.72 (step @p84 :rule nary_cong :premises (@p83 @p82 @p81) :args ((or @t37 @t53 @t52))) % 15.52/15.72 (assume-push @p150 @t43) % 15.52/15.72 (assume-push @p151 @t36) % 15.52/15.72 (assume-push @p152 @t50) % 15.52/15.72 (step @p88 :rule evaluate :args ((= true false))) % 15.52/15.72 (step @p89 :rule false_intro :premises (@p150)) % 15.52/15.72 (step @p90 :rule refl :args (@t22)) % 15.52/15.72 (step @p91 :rule symm :premises (@p151)) % 15.52/15.72 (step @p92 :rule cong :premises (@p91 @p90) :args (@t50)) % 15.52/15.72 (step @p93 :rule true_intro :premises (@p80)) % 15.52/15.72 (step @p94 :rule symm :premises (@p93)) % 15.52/15.72 (step @p95 :rule trans :premises (@p94 @p92 @p89)) % 15.52/15.72 (step @p96 false :rule eq_resolve :premises (@p95 @p88)) % 15.52/15.72 (step-pop @p153 :rule scope :premises (@p96)) % 15.52/15.72 (step-pop @p154 :rule scope :premises (@p153)) % 15.52/15.72 (step-pop @p155 :rule scope :premises (@p154)) % 15.52/15.72 (step @p97 :rule process_scope :premises (@p155) :args (false)) % 15.52/15.72 (assume-push @p156 @t36) % 15.52/15.72 (assume-push @p157 @t43) % 15.52/15.72 (assume-push @p158 @t50) % 15.52/15.72 (step @p104 :rule and_intro :premises (@p157 @p156 @p80)) % 15.52/15.72 (step-pop @p159 :rule scope :premises (@p104)) % 15.52/15.72 (step-pop @p160 :rule scope :premises (@p159)) % 15.52/15.72 (step-pop @p161 :rule scope :premises (@p160)) % 15.52/15.72 (step @p105 :rule process_scope :premises (@p161) :args (@t54)) % 15.52/15.72 (step @p109 :rule implies_elim :premises (@p105)) % 15.52/15.72 (step @p110 :rule resolution :premises (@p109 @p97) :args (true @t54)) % 15.52/15.72 (step @p111 :rule not_and :premises (@p110)) % 15.52/15.72 (step @p112 :rule eq_resolve :premises (@p111 @p84)) % 15.52/15.72 (step @p113 :rule chain_m_resolution :premises (@p112 @p80 @p66 @p59 @p57 @p55 @p51 @p53 @p52) :args (@t47 (@list false false true false false false true true) (@list @t50 @t36 @t42 @t38 @t44 @t45 @t39 @t41))) % 15.52/15.72 (step @p114 :rule cnf_equiv_pos2 :args (@t45)) % 15.52/15.72 (step @p115 :rule reordering :premises (@p114) :args ((or @t40 @t48 @t46))) % 15.52/15.72 (step @p116 :rule chain_m_resolution :premises (@p115 @p113 @p51) :args (@t48 @t55 (@list @t40 @t45))) % 15.52/15.72 (step @p117 :rule cnf_equiv_neg1 :args (@t41)) % 15.52/15.72 (step @p118 :rule reordering :premises (@p117) :args ((or @t40 @t39 @t41))) % 15.52/15.72 (step @p119 :rule chain_m_resolution :premises (@p118 @p113 @p52) :args (@t39 (@list true true) (@list @t40 @t41))) % 15.52/15.72 (step @p120 :rule cnf_and_pos :args (@t39 0)) % 15.52/15.72 (step @p121 :rule reordering :premises (@p120) :args ((or @t38 @t56))) % 15.52/15.72 (step @p122 :rule chain_m_resolution :premises (@p121 @p119) :args (@t38 @t29 @t57)) % 15.52/15.72 (step @p123 :rule refl :args (@t44)) % 15.52/15.72 (step @p124 :rule nary_cong :premises (@p123 @p61 @p82) :args ((or @t44 @t49 @t53))) % 15.52/15.72 (step @p125 :rule cnf_and_neg :args (@t44)) % 15.52/15.72 (step @p126 :rule eq_resolve :premises (@p125 @p124)) % 15.52/15.72 (step @p127 :rule reordering :premises (@p126) :args ((or @t49 @t42 @t44))) % 15.52/15.72 (step @p128 :rule chain_m_resolution :premises (@p127 @p122 @p116) :args (@t42 (@list false true) (@list @t38 @t44))) % 15.52/15.72 (step @p129 :rule cnf_and_pos :args (@t39 1)) % 15.52/15.72 (step @p130 :rule reordering :premises (@p129) :args ((or @t37 @t56))) % 15.52/15.72 (step @p131 :rule chain_m_resolution :premises (@p130 @p119) :args (@t37 @t29 @t57)) % 15.52/15.72 (step @p132 :rule cnf_equiv_pos2 :args (@t58)) % 15.52/15.72 (step @p133 :rule reordering :premises (@p132) :args ((or @t36 @t43 @t59))) % 15.52/15.72 (step @p134 :rule chain_m_resolution :premises (@p133 @p131 @p128) :args (@t59 @t55 (@list @t36 @t42))) % 15.52/15.72 (step @p135 :rule eq-symm :args (@t42 @t36)) % 15.52/15.72 (step @p136 :rule cong :premises (@p72 @p135) :args ((=> @t24 @t60))) % 15.52/15.72 (assume-push @p162 @t24) % 15.52/15.72 (step @p138 :rule instantiate :premises (@p34) :args (@t35)) % 15.52/15.72 (step-pop @p163 :rule scope :premises (@p138)) % 15.52/15.72 (step @p139 :rule process_scope :premises (@p163) :args (@t60)) % 15.52/15.72 (step @p141 :rule eq_resolve :premises (@p139 @p136)) % 15.52/15.72 (step @p142 :rule implies_elim :premises (@p141)) % 15.52/15.72 (step @p143 false :rule chain_m_resolution :premises (@p142 @p134 @p34) :args (false @t55 (@list @t58 @t24))) % 15.52/15.72 ) % 15.52/15.72 % SZS output end Proof % 15.52/15.72 % cvc5 exiting %------------------------------------------------------------------------------