%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYN050+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 : n004.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 09:07:53 AM UTC 2026 % Result : Theorem 0.39s 0.55s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN050+1 : TPTP v9.2.1. Released v2.0.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n004.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 23:19:07 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.39/0.55 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.39/0.55 % SZS status Theorem % 0.39/0.55 % SZS output start Proof % 0.39/0.55 ( % 0.39/0.55 (declare-sort $$unsorted 0) % 0.39/0.55 (declare-const tptp.big_s (-> $$unsorted Bool)) % 0.39/0.55 (declare-const tptp.big_p (-> $$unsorted Bool)) % 0.39/0.55 (declare-const tptp.big_q (-> $$unsorted Bool)) % 0.39/0.55 (declare-const tptp.big_r (-> $$unsorted Bool)) % 0.39/0.55 (define @t1 () (@var "Z1" $$unsorted)) % 0.39/0.55 (define @t2 () (tptp.big_r @t1)) % 0.39/0.55 (define @t3 () (@list @t1)) % 0.39/0.55 (define @t4 () (exists @t3 @t2)) % 0.39/0.55 (define @t5 () (@var "Y1" $$unsorted)) % 0.39/0.55 (define @t6 () (tptp.big_q @t5)) % 0.39/0.55 (define @t7 () (@var "X1" $$unsorted)) % 0.39/0.55 (define @t8 () (tptp.big_p @t7)) % 0.39/0.55 (define @t9 () (and @t8 @t6)) % 0.39/0.55 (define @t10 () (=> @t9 @t4)) % 0.39/0.55 (define @t11 () (@list @t7 @t5)) % 0.39/0.55 (define @t12 () (exists @t11 @t10)) % 0.39/0.55 (define @t13 () (@var "W" $$unsorted)) % 0.39/0.55 (define @t14 () (tptp.big_s @t13)) % 0.39/0.55 (define @t15 () (@var "Z" $$unsorted)) % 0.39/0.55 (define @t16 () (tptp.big_r @t15)) % 0.39/0.55 (define @t17 () (and @t16 @t14)) % 0.39/0.55 (define @t18 () (@var "Y" $$unsorted)) % 0.39/0.55 (define @t19 () (tptp.big_q @t18)) % 0.39/0.55 (define @t20 () (@var "X" $$unsorted)) % 0.39/0.55 (define @t21 () (tptp.big_p @t20)) % 0.39/0.55 (define @t22 () (and @t21 @t19)) % 0.39/0.55 (define @t23 () (@list @t13)) % 0.39/0.55 (define @t24 () (forall @t23 (=> @t22 @t17))) % 0.39/0.55 (define @t25 () (@list @t15)) % 0.39/0.55 (define @t26 () (exists @t25 @t24)) % 0.39/0.55 (define @t27 () (@list @t20 @t18)) % 0.39/0.55 (define @t28 () (forall @t27 @t26)) % 0.39/0.55 (define @t29 () (=> @t28 @t12)) % 0.39/0.55 (define @t30 () (not @t29)) % 0.39/0.55 (define @t31 () (forall @t3 (not @t2))) % 0.39/0.55 (define @t32 () (@var "BOUND_VARIABLE_7510" $$unsorted)) % 0.39/0.55 (define @t33 () (tptp.big_q @t32)) % 0.39/0.55 (define @t34 () (@var "BOUND_VARIABLE_7508" $$unsorted)) % 0.39/0.55 (define @t35 () (forall (@list @t34 @t32) @t33)) % 0.39/0.55 (define @t36 () (@var "BOUND_VARIABLE_7501" $$unsorted)) % 0.39/0.55 (define @t37 () (tptp.big_p @t36)) % 0.39/0.55 (define @t38 () (@var "BOUND_VARIABLE_7503" $$unsorted)) % 0.39/0.55 (define @t39 () (forall (@list @t36 @t38) @t37)) % 0.39/0.55 (define @t40 () (forall @t11 @t31)) % 0.39/0.55 (define @t41 () (forall @t11 @t6)) % 0.39/0.55 (define @t42 () (@list @t7 @t5)) % 0.39/0.55 (define @t43 () (forall @t11 @t8)) % 0.39/0.55 (define @t44 () (and @t43 @t41 @t40)) % 0.39/0.55 (define @t45 () (and @t8 @t6 @t31)) % 0.39/0.55 (define @t46 () (not @t31)) % 0.39/0.55 (define @t47 () (=> @t9 @t46)) % 0.39/0.55 (define @t48 () (forall @t11 (not @t47))) % 0.39/0.55 (define @t49 () (not @t48)) % 0.39/0.55 (define @t50 () (not @t19)) % 0.39/0.55 (define @t51 () (forall (@list @t18) @t50)) % 0.39/0.55 (define @t52 () (not @t21)) % 0.39/0.55 (define @t53 () (forall (@list @t20) @t52)) % 0.39/0.55 (define @t54 () (@var "BOUND_VARIABLE_7468" $$unsorted)) % 0.39/0.55 (define @t55 () (not (tptp.big_r @t54))) % 0.39/0.55 (define @t56 () (@list @t54)) % 0.39/0.55 (define @t57 () (forall @t56 @t55)) % 0.39/0.55 (define @t58 () (not @t57)) % 0.39/0.55 (define @t59 () (@var "BOUND_VARIABLE_7451" $$unsorted)) % 0.39/0.55 (define @t60 () (forall (@list @t59) (tptp.big_s @t59))) % 0.39/0.55 (define @t61 () (and @t60 @t58)) % 0.39/0.55 (define @t62 () (or @t61 @t52 @t50)) % 0.39/0.55 (define @t63 () (or @t52 @t50 @t61)) % 0.39/0.55 (define @t64 () (not @t60)) % 0.39/0.55 (define @t65 () (or @t64 @t57)) % 0.39/0.55 (define @t66 () (not @t65)) % 0.39/0.55 (define @t67 () (or @t52 @t50 @t66)) % 0.39/0.55 (define @t68 () (or @t64 @t55)) % 0.39/0.55 (define @t69 () (or @t55 @t64)) % 0.39/0.55 (define @t70 () (forall @t56 @t69)) % 0.39/0.55 (define @t71 () (or (not @t16) @t64)) % 0.39/0.55 (define @t72 () (forall @t25 @t71)) % 0.39/0.55 (define @t73 () (@list @t54)) % 0.39/0.55 (define @t74 () (forall @t25 @t19)) % 0.39/0.55 (define @t75 () (forall @t25 @t21)) % 0.39/0.55 (define @t76 () (and @t75 @t74 @t72)) % 0.39/0.55 (define @t77 () (and @t16 @t60)) % 0.39/0.55 (define @t78 () (not @t77)) % 0.39/0.55 (define @t79 () (not @t50)) % 0.39/0.55 (define @t80 () (not @t52)) % 0.39/0.55 (define @t81 () (and @t80 @t79 @t78)) % 0.39/0.55 (define @t82 () (or @t52 @t50 @t77)) % 0.39/0.55 (define @t83 () (forall @t25 (not @t82))) % 0.39/0.55 (define @t84 () (not @t83)) % 0.39/0.55 (define @t85 () (forall @t23 @t14)) % 0.39/0.55 (define @t86 () (forall @t23 @t16)) % 0.39/0.55 (define @t87 () (and @t86 @t85)) % 0.39/0.55 (define @t88 () (forall @t23 @t17)) % 0.39/0.55 (define @t89 () (or @t52 @t50 @t88)) % 0.39/0.55 (define @t90 () (or @t52 @t50 @t17)) % 0.39/0.55 (define @t91 () (@quantifiers_skolemize @t51 0)) % 0.39/0.55 (define @t92 () (@list @t91)) % 0.39/0.55 (define @t93 () (@quantifiers_skolemize @t60 0)) % 0.39/0.55 (define @t94 () (@list @t93)) % 0.39/0.55 (define @t95 () (tptp.big_p @t93)) % 0.39/0.55 (define @t96 () (@list false)) % 0.39/0.55 (define @t97 () (not @t61)) % 0.39/0.55 (define @t98 () (tptp.big_q @t91)) % 0.39/0.55 (assume @p1 @t30) % 0.39/0.55 (assume @p2 true) % 0.39/0.55 (step @p3 :rule refl :args (@t31)) % 0.39/0.55 (step @p4 :rule quant-unused-vars :args ((= @t35 (forall (@list @t32) @t33)))) % 0.39/0.55 (step @p5 :rule quant-unused-vars :args ((= @t39 (forall (@list @t36) @t37)))) % 0.39/0.55 (step @p6 :rule nary_cong :premises (@p5 @p4 @p3) :args ((and @t39 @t35 @t31))) % 0.39/0.55 (step @p7 :rule quant-unused-vars :args ((= @t40 @t31))) % 0.39/0.55 (step @p8 :rule alpha_equiv :args (@t41 @t42 (@list @t34 @t32))) % 0.39/0.55 (step @p9 :rule alpha_equiv :args (@t43 @t42 (@list @t36 @t38))) % 0.39/0.55 (step @p10 :rule nary_cong :premises (@p9 @p8 @p7) :args (@t44)) % 0.39/0.55 (step @p11 :rule quant-miniscope-and :args ((= (forall @t11 @t45) @t44))) % 0.39/0.55 (step @p12 :rule trans :premises (@p11 @p10)) % 0.39/0.55 (step @p13 :rule trans :premises (@p12 @p6)) % 0.39/0.55 (step @p14 :rule aci_norm :args ((= (and @t9 @t31) @t45))) % 0.39/0.55 (step @p15 :rule bool-double-not-elim :args (@t31)) % 0.39/0.55 (step @p16 :rule refl :args (@t9)) % 0.39/0.55 (step @p17 :rule nary_cong :premises (@p16 @p15) :args ((and @t9 (not @t46)))) % 0.39/0.55 (step @p18 :rule bool-implies-de-morgan :args (@t9 @t46)) % 0.39/0.55 (step @p19 :rule trans :premises (@p18 @p17)) % 0.39/0.55 (step @p20 :rule trans :premises (@p19 @p14)) % 0.39/0.55 (step @p21 :rule cong :premises (@p20) :args (@t48)) % 0.39/0.55 (step @p22 :rule trans :premises (@p21 @p13)) % 0.39/0.55 (step @p23 :rule cong :premises (@p22) :args (@t49)) % 0.39/0.55 (step @p24 :rule exists-elim :args ((= (exists @t11 @t47) @t49))) % 0.39/0.55 (step @p25 :rule trans :premises (@p24 @p23)) % 0.39/0.55 (step @p26 :rule exists-elim :args ((= @t4 @t46))) % 0.39/0.55 (step @p27 :rule refl :args (@t9)) % 0.39/0.55 (step @p28 :rule cong :premises (@p27 @p26) :args (@t10)) % 0.39/0.55 (step @p29 :rule cong :premises (@p28) :args (@t12)) % 0.39/0.55 (step @p30 :rule trans :premises (@p29 @p25)) % 0.39/0.55 (step @p31 :rule quant-miniscope-or :args ((= (forall @t27 @t62) (or @t61 @t53 @t51)))) % 0.39/0.55 (step @p32 :rule aci_norm :args ((= @t63 @t62))) % 0.39/0.55 (step @p33 :rule cong :premises (@p32) :args ((forall @t27 @t63))) % 0.39/0.55 (step @p34 :rule trans :premises (@p33 @p31)) % 0.39/0.55 (step @p35 :rule refl :args (@t58)) % 0.39/0.55 (step @p36 :rule bool-double-not-elim :args (@t60)) % 0.39/0.55 (step @p37 :rule nary_cong :premises (@p36 @p35) :args ((and (not @t64) @t58))) % 0.39/0.55 (step @p38 :rule bool-or-de-morgan :args (@t64 @t57 false)) % 0.39/0.55 (step @p39 :rule trans :premises (@p38 @p37)) % 0.39/0.55 (step @p40 :rule refl :args (@t50)) % 0.39/0.55 (step @p41 :rule refl :args (@t52)) % 0.39/0.55 (step @p42 :rule nary_cong :premises (@p41 @p40 @p39) :args (@t67)) % 0.39/0.55 (step @p43 :rule aci_norm :args ((= (or @t52 (or @t50 @t66)) @t67))) % 0.39/0.55 (step @p44 :rule bool-and-de-morgan :args (@t19 @t65 true)) % 0.39/0.55 (step @p45 :rule nary_cong :premises (@p41 @p44) :args ((or @t52 (not (and @t19 @t65))))) % 0.39/0.55 (step @p46 :rule bool-and-de-morgan :args (@t21 @t19 (and @t65))) % 0.39/0.55 (step @p47 :rule trans :premises (@p46 @p45)) % 0.39/0.55 (step @p48 :rule trans :premises (@p47 @p43)) % 0.39/0.55 (step @p49 :rule trans :premises (@p48 @p42)) % 0.39/0.55 (step @p50 :rule cong :premises (@p49) :args ((forall @t27 (not (and @t21 @t19 @t65))))) % 0.39/0.55 (step @p51 :rule trans :premises (@p50 @p34)) % 0.39/0.55 (step @p52 :rule quant-miniscope-or :args ((= (forall @t56 @t68) @t65))) % 0.39/0.55 (step @p53 :rule aci_norm :args ((= @t69 @t68))) % 0.39/0.55 (step @p54 :rule cong :premises (@p53) :args (@t70)) % 0.39/0.55 (step @p55 :rule trans :premises (@p54 @p52)) % 0.39/0.55 (step @p56 :rule refl :args (@t19)) % 0.39/0.55 (step @p57 :rule refl :args (@t21)) % 0.39/0.55 (step @p58 :rule nary_cong :premises (@p57 @p56 @p55) :args ((and @t21 @t19 @t70))) % 0.39/0.55 (step @p59 :rule alpha_equiv :args (@t72 (@list @t15) @t73)) % 0.39/0.55 (step @p60 :rule quant-unused-vars :args ((= @t74 @t19))) % 0.39/0.55 (step @p61 :rule quant-unused-vars :args ((= @t75 @t21))) % 0.39/0.55 (step @p62 :rule nary_cong :premises (@p61 @p60 @p59) :args (@t76)) % 0.39/0.55 (step @p63 :rule quant-miniscope-and :args ((= (forall @t25 (and @t21 @t19 @t71)) @t76))) % 0.39/0.55 (step @p64 :rule trans :premises (@p63 @p62)) % 0.39/0.55 (step @p65 :rule trans :premises (@p64 @p58)) % 0.39/0.55 (step @p66 :rule bool-and-de-morgan :args (@t16 @t60 true)) % 0.39/0.55 (step @p67 :rule refl :args (@t19)) % 0.39/0.55 (step @p68 :rule refl :args (@t21)) % 0.39/0.55 (step @p69 :rule nary_cong :premises (@p68 @p67 @p66) :args ((and @t21 @t19 @t78))) % 0.39/0.55 (step @p70 :rule refl :args (@t78)) % 0.39/0.55 (step @p71 :rule bool-double-not-elim :args (@t19)) % 0.39/0.55 (step @p72 :rule bool-double-not-elim :args (@t21)) % 0.39/0.55 (step @p73 :rule nary_cong :premises (@p72 @p71 @p70) :args (@t81)) % 0.39/0.55 (step @p74 :rule aci_norm :args ((= (and @t80 (and @t79 @t78)) @t81))) % 0.39/0.55 (step @p75 :rule trans :premises (@p74 @p73)) % 0.39/0.55 (step @p76 :rule bool-or-de-morgan :args (@t50 @t77 false)) % 0.39/0.56 (step @p77 :rule refl :args (@t80)) % 0.39/0.56 (step @p78 :rule nary_cong :premises (@p77 @p76) :args ((and @t80 (not (or @t50 @t77))))) % 0.39/0.56 (step @p79 :rule bool-or-de-morgan :args (@t52 @t50 (or @t77))) % 0.39/0.56 (step @p80 :rule trans :premises (@p79 @p78)) % 0.39/0.56 (step @p81 :rule trans :premises (@p80 @p75)) % 0.39/0.56 (step @p82 :rule trans :premises (@p81 @p69)) % 0.39/0.56 (step @p83 :rule cong :premises (@p82) :args (@t83)) % 0.39/0.56 (step @p84 :rule trans :premises (@p83 @p65)) % 0.39/0.56 (step @p85 :rule cong :premises (@p84) :args (@t84)) % 0.39/0.56 (step @p86 :rule exists-elim :args ((= (exists @t25 @t82) @t84))) % 0.39/0.56 (step @p87 :rule trans :premises (@p86 @p85)) % 0.39/0.56 (step @p88 :rule alpha_equiv :args (@t85 (@list @t13) (@list @t59))) % 0.39/0.56 (step @p89 :rule quant-unused-vars :args ((= @t86 @t16))) % 0.39/0.56 (step @p90 :rule nary_cong :premises (@p89 @p88) :args (@t87)) % 0.39/0.56 (step @p91 :rule quant-miniscope-and :args ((= @t88 @t87))) % 0.39/0.56 (step @p92 :rule trans :premises (@p91 @p90)) % 0.39/0.56 (step @p93 :rule refl :args (@t50)) % 0.39/0.56 (step @p94 :rule refl :args (@t52)) % 0.39/0.56 (step @p95 :rule nary_cong :premises (@p94 @p93 @p92) :args (@t89)) % 0.39/0.56 (step @p96 :rule quant-miniscope-or :args ((= (forall @t23 @t90) @t89))) % 0.39/0.56 (step @p97 :rule trans :premises (@p96 @p95)) % 0.39/0.56 (step @p98 :rule aci_norm :args ((= (or (or @t52 @t50) @t17) @t90))) % 0.39/0.56 (step @p99 :rule refl :args (@t17)) % 0.39/0.56 (step @p100 :rule bool-and-de-morgan :args (@t21 @t19 true)) % 0.39/0.56 (step @p101 :rule nary_cong :premises (@p100 @p99) :args ((or (not @t22) @t17))) % 0.39/0.56 (step @p102 :rule trans :premises (@p101 @p98)) % 0.39/0.56 (step @p103 :rule bool-impl-elim :args (@t22 @t17)) % 0.39/0.56 (step @p104 :rule trans :premises (@p103 @p102)) % 0.39/0.56 (step @p105 :rule cong :premises (@p104) :args (@t24)) % 0.39/0.56 (step @p106 :rule trans :premises (@p105 @p97)) % 0.39/0.56 (step @p107 :rule cong :premises (@p106) :args (@t26)) % 0.39/0.56 (step @p108 :rule trans :premises (@p107 @p87)) % 0.39/0.56 (step @p109 :rule cong :premises (@p108) :args (@t28)) % 0.39/0.56 (step @p110 :rule trans :premises (@p109 @p51)) % 0.39/0.56 (step @p111 :rule cong :premises (@p110 @p30) :args (@t29)) % 0.39/0.56 (step @p112 :rule cong :premises (@p111) :args (@t30)) % 0.39/0.56 (step @p113 :rule eq_resolve :premises (@p1 @p112)) % 0.39/0.56 (step @p114 :rule not_implies_elim2 :premises (@p113)) % 0.39/0.56 (step @p115 :rule not_not_elim :premises (@p114)) % 0.39/0.56 (step @p116 :rule and_elim :premises (@p115) :args (1)) % 0.39/0.56 (step @p117 :rule instantiate :premises (@p116) :args (@t92)) % 0.39/0.56 (step @p118 :rule and_elim :premises (@p115) :args (0)) % 0.39/0.56 (step @p119 :rule instantiate :premises (@p118) :args (@t94)) % 0.39/0.56 (assume-push @p141 @t53) % 0.39/0.56 (step @p121 :rule instantiate :premises (@p141) :args (@t94)) % 0.39/0.56 (step-pop @p142 :rule scope :premises (@p121)) % 0.39/0.56 (step @p122 :rule process_scope :premises (@p142) :args ((not @t95))) % 0.39/0.56 (step @p124 :rule implies_elim :premises (@p122)) % 0.39/0.56 (step @p125 :rule chain_m_resolution :premises (@p124 @p119) :args ((not @t53) @t96 (@list @t95))) % 0.39/0.56 (step @p126 :rule and_elim :premises (@p115) :args (2)) % 0.39/0.56 (step @p127 :rule alpha_equiv :args (@t57 @t73 (@list @t1))) % 0.39/0.56 (step @p128 :rule equiv_elim2 :premises (@p127)) % 0.39/0.56 (step @p129 :rule chain_m_resolution :premises (@p128 @p126) :args (@t57 @t96 (@list @t31))) % 0.39/0.56 (step @p130 :rule cnf_and_pos :args (@t61 1)) % 0.39/0.56 (step @p131 :rule reordering :premises (@p130) :args ((or @t58 @t97))) % 0.39/0.56 (step @p132 :rule chain_m_resolution :premises (@p131 @p129) :args (@t97 @t96 (@list @t57))) % 0.39/0.56 (step @p133 :rule not_implies_elim1 :premises (@p113)) % 0.39/0.56 (step @p134 :rule chain_m_resolution :premises (@p133 @p132 @p125) :args (@t51 (@list true true) (@list @t61 @t53))) % 0.39/0.56 (assume-push @p143 @t51) % 0.39/0.56 (step @p136 :rule instantiate :premises (@p143) :args (@t92)) % 0.39/0.56 (step-pop @p144 :rule scope :premises (@p136)) % 0.39/0.56 (step @p137 :rule process_scope :premises (@p144) :args ((not @t98))) % 0.39/0.56 (step @p139 :rule implies_elim :premises (@p137)) % 0.39/0.56 (step @p140 false :rule chain_m_resolution :premises (@p139 @p134 @p117) :args (false (@list false false) (@list @t51 @t98))) % 0.39/0.56 ) % 0.39/0.56 % SZS output end Proof % 0.39/0.56 % cvc5 exiting %------------------------------------------------------------------------------