%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYN918+1 : TPTP v9.2.1. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n023.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 09:10:03 AM UTC 2026 % Result : Theorem 0.37s 0.57s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN918+1 : TPTP v9.2.1. Released v3.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n023.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 23:49:28 EDT 2026 % 0.18/0.35 % CPUTime : % 0.27/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.57 % SZS status Theorem % 0.37/0.57 % SZS output start Proof % 0.37/0.57 ( % 0.37/0.57 (declare-sort $$unsorted 0) % 0.37/0.57 (declare-const tptp.f (-> $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.g (-> $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.h (-> $$unsorted Bool)) % 0.37/0.57 (define @t1 () (@var "V" $$unsorted)) % 0.37/0.57 (define @t2 () (tptp.h @t1)) % 0.37/0.57 (define @t3 () (not @t2)) % 0.37/0.57 (define @t4 () (tptp.g @t1)) % 0.37/0.57 (define @t5 () (tptp.f @t1)) % 0.37/0.57 (define @t6 () (and @t5 @t4 @t3)) % 0.37/0.57 (define @t7 () (@list @t1)) % 0.37/0.57 (define @t8 () (exists @t7 @t6)) % 0.37/0.57 (define @t9 () (@var "R" $$unsorted)) % 0.37/0.57 (define @t10 () (tptp.g @t9)) % 0.37/0.57 (define @t11 () (tptp.h @t9)) % 0.37/0.57 (define @t12 () (tptp.f @t9)) % 0.37/0.57 (define @t13 () (and @t12 @t11)) % 0.37/0.57 (define @t14 () (forall (@list @t9) (=> @t13 @t10))) % 0.37/0.57 (define @t15 () (=> @t14 @t8)) % 0.37/0.57 (define @t16 () (@var "Z" $$unsorted)) % 0.37/0.57 (define @t17 () (tptp.h @t16)) % 0.37/0.57 (define @t18 () (tptp.f @t16)) % 0.37/0.57 (define @t19 () (@list @t16)) % 0.37/0.57 (define @t20 () (forall @t19 (=> @t18 @t17))) % 0.37/0.57 (define @t21 () (@var "W" $$unsorted)) % 0.37/0.57 (define @t22 () (tptp.g @t21)) % 0.37/0.57 (define @t23 () (tptp.f @t21)) % 0.37/0.57 (define @t24 () (@list @t21)) % 0.37/0.57 (define @t25 () (forall @t24 (=> @t23 @t22))) % 0.37/0.57 (define @t26 () (or @t25 @t20)) % 0.37/0.57 (define @t27 () (@var "Y" $$unsorted)) % 0.37/0.57 (define @t28 () (tptp.g @t27)) % 0.37/0.57 (define @t29 () (not @t28)) % 0.37/0.57 (define @t30 () (tptp.f @t27)) % 0.37/0.57 (define @t31 () (and @t30 @t29)) % 0.37/0.57 (define @t32 () (@list @t27)) % 0.37/0.57 (define @t33 () (exists @t32 @t31)) % 0.37/0.57 (define @t34 () (@var "X" $$unsorted)) % 0.37/0.57 (define @t35 () (tptp.h @t34)) % 0.37/0.57 (define @t36 () (tptp.g @t34)) % 0.37/0.57 (define @t37 () (tptp.f @t34)) % 0.37/0.57 (define @t38 () (and @t37 @t36)) % 0.37/0.57 (define @t39 () (=> @t38 @t35)) % 0.37/0.57 (define @t40 () (=> @t39 @t33)) % 0.37/0.57 (define @t41 () (@list @t34)) % 0.37/0.57 (define @t42 () (forall @t41 @t40)) % 0.37/0.57 (define @t43 () (and @t42 @t26)) % 0.37/0.57 (define @t44 () (=> @t43 @t15)) % 0.37/0.57 (define @t45 () (not @t44)) % 0.37/0.57 (define @t46 () (not @t4)) % 0.37/0.57 (define @t47 () (not @t5)) % 0.37/0.57 (define @t48 () (not @t3)) % 0.37/0.57 (define @t49 () (or @t47 @t46 @t48)) % 0.37/0.57 (define @t50 () (forall @t7 (not @t6))) % 0.37/0.57 (define @t51 () (not @t50)) % 0.37/0.57 (define @t52 () (not @t11)) % 0.37/0.57 (define @t53 () (not @t12)) % 0.37/0.57 (define @t54 () (not @t35)) % 0.37/0.57 (define @t55 () (forall @t41 @t54)) % 0.37/0.57 (define @t56 () (@list @t34)) % 0.37/0.57 (define @t57 () (@var "BOUND_VARIABLE_7486" $$unsorted)) % 0.37/0.57 (define @t58 () (forall @t41 @t36)) % 0.37/0.57 (define @t59 () (@var "BOUND_VARIABLE_7481" $$unsorted)) % 0.37/0.57 (define @t60 () (forall @t41 @t37)) % 0.37/0.57 (define @t61 () (@var "BOUND_VARIABLE_7476" $$unsorted)) % 0.37/0.57 (define @t62 () (and @t60 @t58 @t55)) % 0.37/0.57 (define @t63 () (and @t37 @t36 @t54)) % 0.37/0.57 (define @t64 () (forall @t41 @t63)) % 0.37/0.57 (define @t65 () (not @t30)) % 0.37/0.57 (define @t66 () (forall @t32 (or @t65 @t28))) % 0.37/0.57 (define @t67 () (not @t66)) % 0.37/0.57 (define @t68 () (or @t67 @t64)) % 0.37/0.57 (define @t69 () (or @t67 @t63)) % 0.37/0.57 (define @t70 () (or @t63 @t67)) % 0.37/0.57 (define @t71 () (forall @t32 (not @t31))) % 0.37/0.57 (define @t72 () (not @t71)) % 0.37/0.57 (define @t73 () (@quantifiers_skolemize @t66 0)) % 0.37/0.57 (define @t74 () (tptp.g @t73)) % 0.37/0.57 (define @t75 () (tptp.f @t73)) % 0.37/0.57 (define @t76 () (not @t75)) % 0.37/0.57 (define @t77 () (or @t76 @t74)) % 0.37/0.57 (define @t78 () (not @t77)) % 0.37/0.57 (define @t79 () (forall @t19 (or (not @t18) @t17))) % 0.37/0.57 (define @t80 () (@list @t73)) % 0.37/0.57 (define @t81 () (tptp.h @t73)) % 0.37/0.57 (define @t82 () (or @t76 @t81)) % 0.37/0.57 (define @t83 () (not @t81)) % 0.37/0.57 (define @t84 () (or @t76 @t83 @t74)) % 0.37/0.57 (define @t85 () (forall (@list @t57) (not (tptp.h @t57)))) % 0.37/0.57 (define @t86 () (forall (@list @t59) (tptp.g @t59))) % 0.37/0.57 (define @t87 () (forall (@list @t61) (tptp.f @t61))) % 0.37/0.57 (define @t88 () (and @t87 @t86 @t85)) % 0.37/0.57 (define @t89 () (@list false)) % 0.37/0.57 (define @t90 () (not @t88)) % 0.37/0.57 (define @t91 () (@list @t88)) % 0.37/0.57 (define @t92 () (@quantifiers_skolemize @t85 0)) % 0.37/0.57 (define @t93 () (@list @t92)) % 0.37/0.57 (define @t94 () (tptp.g @t92)) % 0.37/0.57 (define @t95 () (tptp.f @t92)) % 0.37/0.57 (define @t96 () (tptp.h @t92)) % 0.37/0.57 (define @t97 () (not @t96)) % 0.37/0.57 (define @t98 () (not @t94)) % 0.37/0.57 (define @t99 () (not @t95)) % 0.37/0.57 (define @t100 () (or @t99 @t98 @t96)) % 0.37/0.57 (define @t101 () (not @t100)) % 0.37/0.57 (define @t102 () (forall @t7 (or @t47 @t46 @t2))) % 0.37/0.57 (assume @p1 @t45) % 0.37/0.57 (assume @p2 true) % 0.37/0.57 (step @p3 :rule bool-double-not-elim :args (@t2)) % 0.37/0.57 (step @p4 :rule refl :args (@t46)) % 0.37/0.57 (step @p5 :rule refl :args (@t47)) % 0.37/0.57 (step @p6 :rule nary_cong :premises (@p5 @p4 @p3) :args (@t49)) % 0.37/0.57 (step @p7 :rule aci_norm :args ((= (or @t47 (or @t46 @t48)) @t49))) % 0.37/0.57 (step @p8 :rule trans :premises (@p7 @p6)) % 0.37/0.57 (step @p9 :rule bool-and-de-morgan :args (@t4 @t3 true)) % 0.37/0.57 (step @p10 :rule nary_cong :premises (@p5 @p9) :args ((or @t47 (not (and @t4 @t3))))) % 0.37/0.57 (step @p11 :rule bool-and-de-morgan :args (@t5 @t4 (and @t3))) % 0.37/0.57 (step @p12 :rule trans :premises (@p11 @p10)) % 0.37/0.57 (step @p13 :rule trans :premises (@p12 @p8)) % 0.37/0.57 (step @p14 :rule cong :premises (@p13) :args (@t50)) % 0.37/0.57 (step @p15 :rule cong :premises (@p14) :args (@t51)) % 0.37/0.57 (step @p16 :rule exists-elim :args ((= @t8 @t51))) % 0.37/0.57 (step @p17 :rule trans :premises (@p16 @p15)) % 0.37/0.57 (step @p18 :rule aci_norm :args ((= (or (or @t53 @t52) @t10) (or @t53 @t52 @t10)))) % 0.37/0.57 (step @p19 :rule refl :args (@t10)) % 0.37/0.57 (step @p20 :rule bool-and-de-morgan :args (@t12 @t11 true)) % 0.37/0.57 (step @p21 :rule nary_cong :premises (@p20 @p19) :args ((or (not @t13) @t10))) % 0.37/0.57 (step @p22 :rule trans :premises (@p21 @p18)) % 0.37/0.57 (step @p23 :rule bool-impl-elim :args (@t13 @t10)) % 0.37/0.57 (step @p24 :rule trans :premises (@p23 @p22)) % 0.37/0.57 (step @p25 :rule cong :premises (@p24) :args (@t14)) % 0.37/0.57 (step @p26 :rule cong :premises (@p25 @p17) :args (@t15)) % 0.37/0.57 (step @p27 :rule bool-impl-elim :args (@t18 @t17)) % 0.37/0.57 (step @p28 :rule cong :premises (@p27) :args (@t20)) % 0.37/0.57 (step @p29 :rule bool-impl-elim :args (@t23 @t22)) % 0.37/0.57 (step @p30 :rule cong :premises (@p29) :args (@t25)) % 0.37/0.57 (step @p31 :rule nary_cong :premises (@p30 @p28) :args (@t26)) % 0.37/0.57 (step @p32 :rule alpha_equiv :args (@t55 @t56 (@list @t57))) % 0.37/0.57 (step @p33 :rule alpha_equiv :args (@t58 @t56 (@list @t59))) % 0.37/0.57 (step @p34 :rule alpha_equiv :args (@t60 @t56 (@list @t61))) % 0.37/0.57 (step @p35 :rule nary_cong :premises (@p34 @p33 @p32) :args (@t62)) % 0.37/0.57 (step @p36 :rule quant-miniscope-and :args ((= @t64 @t62))) % 0.37/0.57 (step @p37 :rule trans :premises (@p36 @p35)) % 0.37/0.57 (step @p38 :rule refl :args (@t67)) % 0.37/0.57 (step @p39 :rule nary_cong :premises (@p38 @p37) :args (@t68)) % 0.37/0.57 (step @p40 :rule quant-miniscope-or :args ((= (forall @t41 @t69) @t68))) % 0.37/0.57 (step @p41 :rule aci_norm :args ((= @t70 @t69))) % 0.37/0.57 (step @p42 :rule cong :premises (@p41) :args ((forall @t41 @t70))) % 0.37/0.57 (step @p43 :rule trans :premises (@p42 @p40)) % 0.37/0.57 (step @p44 :rule trans :premises (@p43 @p39)) % 0.37/0.57 (step @p45 :rule refl :args (@t67)) % 0.37/0.57 (step @p46 :rule aci_norm :args ((= (and @t38 @t54) @t63))) % 0.37/0.57 (step @p47 :rule bool-implies-de-morgan :args (@t38 @t35)) % 0.37/0.57 (step @p48 :rule trans :premises (@p47 @p46)) % 0.37/0.57 (step @p49 :rule nary_cong :premises (@p48 @p45) :args ((or (not @t39) @t67))) % 0.37/0.57 (step @p50 :rule bool-impl-elim :args (@t39 @t67)) % 0.37/0.57 (step @p51 :rule trans :premises (@p50 @p49)) % 0.37/0.57 (step @p52 :rule cong :premises (@p51) :args ((forall @t41 (=> @t39 @t67)))) % 0.37/0.57 (step @p53 :rule trans :premises (@p52 @p44)) % 0.37/0.57 (step @p54 :rule bool-double-not-elim :args (@t28)) % 0.37/0.57 (step @p55 :rule refl :args (@t65)) % 0.37/0.57 (step @p56 :rule nary_cong :premises (@p55 @p54) :args ((or @t65 (not @t29)))) % 0.37/0.57 (step @p57 :rule bool-and-de-morgan :args (@t30 @t29 true)) % 0.37/0.57 (step @p58 :rule trans :premises (@p57 @p56)) % 0.37/0.57 (step @p59 :rule cong :premises (@p58) :args (@t71)) % 0.37/0.57 (step @p60 :rule cong :premises (@p59) :args (@t72)) % 0.37/0.57 (step @p61 :rule exists-elim :args ((= @t33 @t72))) % 0.37/0.57 (step @p62 :rule trans :premises (@p61 @p60)) % 0.37/0.57 (step @p63 :rule refl :args (@t39)) % 0.37/0.57 (step @p64 :rule cong :premises (@p63 @p62) :args (@t40)) % 0.37/0.57 (step @p65 :rule cong :premises (@p64) :args (@t42)) % 0.37/0.57 (step @p66 :rule trans :premises (@p65 @p53)) % 0.37/0.57 (step @p67 :rule nary_cong :premises (@p66 @p31) :args (@t43)) % 0.37/0.57 (step @p68 :rule cong :premises (@p67 @p26) :args (@t44)) % 0.37/0.57 (step @p69 :rule cong :premises (@p68) :args (@t45)) % 0.37/0.57 (step @p70 :rule eq_resolve :premises (@p1 @p69)) % 0.37/0.57 (step @p71 :rule not_implies_elim2 :premises (@p70)) % 0.37/0.57 (step @p72 :rule not_implies_elim2 :premises (@p71)) % 0.37/0.57 (step @p73 :rule not_not_elim :premises (@p72)) % 0.37/0.57 (step @p74 :rule alpha_equiv :args (@t66 (@list @t27) (@list @t21))) % 0.37/0.57 (step @p75 :rule equiv_elim2 :premises (@p74)) % 0.37/0.57 (step @p76 :rule refl :args (@t78)) % 0.37/0.57 (step @p77 :rule bool-double-not-elim :args (@t66)) % 0.37/0.57 (step @p78 :rule nary_cong :premises (@p77 @p76) :args ((or (not @t67) @t78))) % 0.37/0.57 (assume-push @p144 @t67) % 0.37/0.57 (step @p80 :rule skolemize :premises (@p144)) % 0.37/0.57 (step-pop @p145 :rule scope :premises (@p80)) % 0.37/0.57 (step @p81 :rule process_scope :premises (@p145) :args (@t78)) % 0.37/0.57 (step @p83 :rule implies_elim :premises (@p81)) % 0.37/0.57 (step @p84 :rule eq_resolve :premises (@p83 @p78)) % 0.37/0.57 (step @p85 :rule not_implies_elim1 :premises (@p70)) % 0.37/0.57 (step @p86 :rule and_elim :premises (@p85) :args (1)) % 0.37/0.57 (step @p87 :rule bool-double-not-elim :args (@t75)) % 0.37/0.57 (step @p88 :rule refl :args (@t77)) % 0.37/0.57 (step @p89 :rule nary_cong :premises (@p88 @p87) :args ((or @t77 (not @t76)))) % 0.37/0.57 (step @p90 :rule cnf_or_neg :args (@t77 0)) % 0.37/0.57 (step @p91 :rule eq_resolve :premises (@p90 @p89)) % 0.37/0.57 (step @p92 :rule reordering :premises (@p91) :args ((or @t75 @t77))) % 0.37/0.57 (step @p93 :rule cnf_or_neg :args (@t77 1)) % 0.37/0.57 (assume-push @p146 @t79) % 0.37/0.57 (step @p95 :rule instantiate :premises (@p146) :args (@t80)) % 0.37/0.57 (step-pop @p147 :rule scope :premises (@p95)) % 0.37/0.57 (step @p96 :rule process_scope :premises (@p147) :args (@t82)) % 0.37/0.57 (step @p98 :rule implies_elim :premises (@p96)) % 0.37/0.57 (step @p99 :rule not_implies_elim1 :premises (@p71)) % 0.37/0.57 (step @p100 :rule instantiate :premises (@p99) :args (@t80)) % 0.37/0.57 (step @p101 :rule cnf_or_pos :args (@t84)) % 0.37/0.57 (step @p102 :rule reordering :premises (@p101) :args ((or @t76 @t74 @t83 (not @t84)))) % 0.37/0.57 (step @p103 :rule cnf_or_pos :args (@t82)) % 0.37/0.57 (step @p104 :rule reordering :premises (@p103) :args ((or @t76 @t81 (not @t82)))) % 0.37/0.57 (step @p105 :rule chain_m_resolution :premises (@p104 @p102 @p100 @p98 @p93 @p92 @p86 @p84 @p75) :args (@t66 (@list true false false true false false true true) (@list @t81 @t84 @t82 @t74 @t75 @t79 @t77 (forall @t24 (or (not @t23) @t22))))) % 0.37/0.57 (step @p106 :rule and_elim :premises (@p85) :args (0)) % 0.37/0.57 (step @p107 :rule chain_m_resolution :premises (@p106 @p105) :args (@t88 @t89 (@list @t66))) % 0.37/0.57 (step @p108 :rule cnf_and_pos :args (@t88 1)) % 0.37/0.57 (step @p109 :rule reordering :premises (@p108) :args ((or @t86 @t90))) % 0.37/0.57 (step @p110 :rule chain_m_resolution :premises (@p109 @p107) :args (@t86 @t89 @t91)) % 0.37/0.57 (assume-push @p148 @t86) % 0.37/0.57 (step @p112 :rule instantiate :premises (@p148) :args (@t93)) % 0.37/0.57 (step-pop @p149 :rule scope :premises (@p112)) % 0.37/0.57 (step @p113 :rule process_scope :premises (@p149) :args (@t94)) % 0.37/0.57 (step @p115 :rule implies_elim :premises (@p113)) % 0.37/0.57 (step @p116 :rule chain_m_resolution :premises (@p115 @p110) :args (@t94 @t89 (@list @t86))) % 0.37/0.57 (step @p117 :rule cnf_and_pos :args (@t88 0)) % 0.37/0.57 (step @p118 :rule reordering :premises (@p117) :args ((or @t87 @t90))) % 0.37/0.57 (step @p119 :rule chain_m_resolution :premises (@p118 @p107) :args (@t87 @t89 @t91)) % 0.37/0.57 (assume-push @p150 @t87) % 0.37/0.57 (step @p121 :rule instantiate :premises (@p150) :args (@t93)) % 0.37/0.57 (step-pop @p151 :rule scope :premises (@p121)) % 0.37/0.57 (step @p122 :rule process_scope :premises (@p151) :args (@t95)) % 0.37/0.57 (step @p124 :rule implies_elim :premises (@p122)) % 0.37/0.57 (step @p125 :rule chain_m_resolution :premises (@p124 @p119) :args (@t95 @t89 (@list @t87))) % 0.37/0.57 (step @p126 :rule cnf_and_pos :args (@t88 2)) % 0.37/0.57 (step @p127 :rule reordering :premises (@p126) :args ((or @t85 @t90))) % 0.37/0.57 (step @p128 :rule chain_m_resolution :premises (@p127 @p107) :args (@t85 @t89 @t91)) % 0.37/0.57 (assume-push @p152 @t85) % 0.37/0.57 (step @p130 :rule instantiate :premises (@p152) :args (@t93)) % 0.37/0.57 (step-pop @p153 :rule scope :premises (@p130)) % 0.37/0.57 (step @p131 :rule process_scope :premises (@p153) :args (@t97)) % 0.37/0.57 (step @p133 :rule implies_elim :premises (@p131)) % 0.37/0.57 (step @p134 :rule chain_m_resolution :premises (@p133 @p128) :args (@t97 @t89 (@list @t85))) % 0.37/0.57 (step @p135 :rule cnf_or_pos :args (@t100)) % 0.37/0.57 (step @p136 :rule reordering :premises (@p135) :args ((or @t96 @t99 @t98 @t101))) % 0.37/0.57 (step @p137 :rule chain_m_resolution :premises (@p136 @p134 @p125 @p116) :args (@t101 (@list true false false) (@list @t96 @t95 @t94))) % 0.37/0.57 (assume-push @p154 @t102) % 0.37/0.57 (step @p139 :rule instantiate :premises (@p73) :args (@t93)) % 0.37/0.57 (step-pop @p155 :rule scope :premises (@p139)) % 0.37/0.57 (step @p140 :rule process_scope :premises (@p155) :args (@t100)) % 0.37/0.57 (step @p142 :rule implies_elim :premises (@p140)) % 0.37/0.57 (step @p143 false :rule chain_m_resolution :premises (@p142 @p137 @p73) :args (false (@list true false) (@list @t100 @t102))) % 0.37/0.57 ) % 0.37/0.57 % SZS output end Proof % 0.37/0.57 % cvc5 exiting %------------------------------------------------------------------------------