%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO888_10 : TPTP v9.2.1. Released v8.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n026.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 09:13:42 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 : SYO888_10 : TPTP v9.2.1. Released v8.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n026.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 : Wed Jun 3 01:08:55 EDT 2026 % 0.16/0.35 % CPUTime : % 0.26/0.50 %----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 |tptp.'$ki_world'| 0) % 0.37/0.57 (declare-sort $$unsorted 0) % 0.37/0.57 (declare-const tptp.f (-> |tptp.'$ki_world'| $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.g (-> |tptp.'$ki_world'| $$unsorted Bool)) % 0.37/0.57 (declare-const |tptp.'$ki_local_world'| |tptp.'$ki_world'|) % 0.37/0.57 (declare-const tptp.h (-> |tptp.'$ki_world'| $$unsorted Bool)) % 0.37/0.57 (declare-const |tptp.'$ki_exists_in_world_$i'| (-> |tptp.'$ki_world'| $$unsorted Bool)) % 0.37/0.57 (declare-const |tptp.'$ki_accessible'| (-> |tptp.'$ki_world'| |tptp.'$ki_world'| Bool)) % 0.37/0.57 (define @t1 () (@var "W" |tptp.'$ki_world'|)) % 0.37/0.57 (define @t2 () (@list @t1)) % 0.37/0.57 (define @t3 () (forall @t2 (|tptp.'$ki_accessible'| @t1 @t1))) % 0.37/0.57 (define @t4 () (@var "U" |tptp.'$ki_world'|)) % 0.37/0.57 (define @t5 () (@var "V" |tptp.'$ki_world'|)) % 0.37/0.57 (define @t6 () (@var "X" $$unsorted)) % 0.37/0.57 (define @t7 () (@list @t6)) % 0.37/0.57 (define @t8 () (tptp.h @t1 @t6)) % 0.37/0.57 (define @t9 () (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| @t1)) % 0.37/0.57 (define @t10 () (forall @t2 (=> @t9 @t8))) % 0.37/0.57 (define @t11 () (tptp.f |tptp.'$ki_local_world'| @t6)) % 0.37/0.57 (define @t12 () (=> @t11 @t10)) % 0.37/0.57 (define @t13 () (|tptp.'$ki_exists_in_world_$i'| |tptp.'$ki_local_world'| @t6)) % 0.37/0.57 (define @t14 () (=> @t13 @t12)) % 0.37/0.57 (define @t15 () (forall @t7 @t14)) % 0.37/0.57 (define @t16 () (tptp.g |tptp.'$ki_local_world'| @t6)) % 0.37/0.57 (define @t17 () (=> @t16 @t10)) % 0.37/0.57 (define @t18 () (=> @t13 @t17)) % 0.37/0.57 (define @t19 () (forall @t7 @t18)) % 0.37/0.57 (define @t20 () (tptp.g @t1 @t6)) % 0.37/0.57 (define @t21 () (forall @t2 (=> @t9 @t20))) % 0.37/0.57 (define @t22 () (=> @t11 @t21)) % 0.37/0.57 (define @t23 () (=> @t13 @t22)) % 0.37/0.57 (define @t24 () (forall @t7 @t23)) % 0.37/0.57 (define @t25 () (and @t24 @t19)) % 0.37/0.57 (define @t26 () (=> @t25 @t15)) % 0.37/0.57 (define @t27 () (not @t26)) % 0.37/0.57 (define @t28 () (@var "BOUND_VARIABLE_7517" |tptp.'$ki_world'|)) % 0.37/0.57 (define @t29 () (tptp.h @t28 @t6)) % 0.37/0.57 (define @t30 () (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| @t28))) % 0.37/0.57 (define @t31 () (not @t11)) % 0.37/0.57 (define @t32 () (not @t13)) % 0.37/0.57 (define @t33 () (or @t32 @t31 @t30 @t29)) % 0.37/0.57 (define @t34 () (or @t30 @t29)) % 0.37/0.57 (define @t35 () (or @t32 @t31 @t34)) % 0.37/0.57 (define @t36 () (@list @t6 @t28)) % 0.37/0.57 (define @t37 () (forall @t36 @t35)) % 0.37/0.57 (define @t38 () (@list @t28)) % 0.37/0.57 (define @t39 () (forall @t38 @t35)) % 0.37/0.57 (define @t40 () (forall @t38 @t34)) % 0.37/0.57 (define @t41 () (@list @t1)) % 0.37/0.57 (define @t42 () (or @t32 @t31 @t40)) % 0.37/0.57 (define @t43 () (not @t9)) % 0.37/0.57 (define @t44 () (forall @t2 (or @t43 @t8))) % 0.37/0.57 (define @t45 () (or @t32 @t31 @t44)) % 0.37/0.57 (define @t46 () (=> @t11 @t44)) % 0.37/0.57 (define @t47 () (@var "BOUND_VARIABLE_7499" |tptp.'$ki_world'|)) % 0.37/0.57 (define @t48 () (tptp.h @t47 @t6)) % 0.37/0.57 (define @t49 () (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| @t47))) % 0.37/0.57 (define @t50 () (not @t16)) % 0.37/0.57 (define @t51 () (or @t49 @t48)) % 0.37/0.57 (define @t52 () (or @t32 @t50 @t51)) % 0.37/0.57 (define @t53 () (forall (@list @t6 @t47) @t52)) % 0.37/0.57 (define @t54 () (@list @t47)) % 0.37/0.57 (define @t55 () (forall @t54 @t52)) % 0.37/0.57 (define @t56 () (forall @t54 @t51)) % 0.37/0.57 (define @t57 () (or @t32 @t50 @t56)) % 0.37/0.57 (define @t58 () (or @t32 @t50 @t44)) % 0.37/0.57 (define @t59 () (=> @t16 @t44)) % 0.37/0.57 (define @t60 () (@var "BOUND_VARIABLE_7479" |tptp.'$ki_world'|)) % 0.37/0.57 (define @t61 () (tptp.g @t60 @t6)) % 0.37/0.57 (define @t62 () (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| @t60))) % 0.37/0.57 (define @t63 () (or @t62 @t61)) % 0.37/0.57 (define @t64 () (or @t32 @t31 @t63)) % 0.37/0.57 (define @t65 () (forall (@list @t6 @t60) @t64)) % 0.37/0.57 (define @t66 () (@list @t60)) % 0.37/0.57 (define @t67 () (forall @t66 @t64)) % 0.37/0.57 (define @t68 () (forall @t66 @t63)) % 0.37/0.57 (define @t69 () (or @t32 @t31 @t68)) % 0.37/0.57 (define @t70 () (forall @t2 (or @t43 @t20))) % 0.37/0.57 (define @t71 () (or @t32 @t31 @t70)) % 0.37/0.57 (define @t72 () (=> @t11 @t70)) % 0.37/0.57 (define @t73 () (forall @t36 @t33)) % 0.37/0.57 (define @t74 () (@quantifiers_skolemize @t73 0)) % 0.37/0.57 (define @t75 () (@quantifiers_skolemize @t73 1)) % 0.37/0.57 (define @t76 () (tptp.h @t75 @t74)) % 0.37/0.57 (define @t77 () (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| @t75)) % 0.37/0.57 (define @t78 () (not @t77)) % 0.37/0.57 (define @t79 () (tptp.f |tptp.'$ki_local_world'| @t74)) % 0.37/0.57 (define @t80 () (not @t79)) % 0.37/0.57 (define @t81 () (|tptp.'$ki_exists_in_world_$i'| |tptp.'$ki_local_world'| @t74)) % 0.37/0.57 (define @t82 () (not @t81)) % 0.37/0.57 (define @t83 () (or @t82 @t80 @t78 @t76)) % 0.37/0.57 (define @t84 () (@list true)) % 0.37/0.57 (define @t85 () (@list @t83)) % 0.37/0.57 (define @t86 () (tptp.g |tptp.'$ki_local_world'| @t74)) % 0.37/0.57 (define @t87 () (not @t86)) % 0.37/0.57 (define @t88 () (or @t82 @t87 @t78 @t76)) % 0.37/0.57 (define @t89 () (@list false false true false)) % 0.37/0.57 (define @t90 () (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| |tptp.'$ki_local_world'|)) % 0.37/0.57 (define @t91 () (not @t90)) % 0.37/0.57 (define @t92 () (or @t82 @t80 @t91 @t86)) % 0.37/0.57 (assume @p1 @t3) % 0.37/0.57 (assume @p2 (forall (@list @t1 @t5 @t4) (=> (and (|tptp.'$ki_accessible'| @t1 @t5) (|tptp.'$ki_accessible'| @t5 @t4)) (|tptp.'$ki_accessible'| @t1 @t4)))) % 0.37/0.57 (assume @p3 (forall @t2 (exists @t7 (|tptp.'$ki_exists_in_world_$i'| @t1 @t6)))) % 0.37/0.57 (assume @p4 @t27) % 0.37/0.57 (assume @p5 true) % 0.37/0.57 (step @p6 :rule aci_norm :args ((= @t35 @t33))) % 0.37/0.57 (step @p7 :rule cong :premises (@p6) :args (@t37)) % 0.37/0.57 (step @p8 :rule quant-merge-prenex :args ((= (forall @t7 @t39) @t37))) % 0.37/0.57 (step @p9 :rule alpha_equiv :args (@t40 (@list @t28) @t41)) % 0.37/0.57 (step @p10 :rule refl :args (@t31)) % 0.37/0.57 (step @p11 :rule refl :args (@t32)) % 0.37/0.57 (step @p12 :rule nary_cong :premises (@p11 @p10 @p9) :args (@t42)) % 0.37/0.57 (step @p13 :rule quant-miniscope-or :args ((= @t39 @t42))) % 0.37/0.57 (step @p14 :rule trans :premises (@p13 @p12)) % 0.37/0.57 (step @p15 :rule symm :premises (@p14)) % 0.37/0.57 (step @p16 :rule cong :premises (@p15) :args ((forall @t7 @t45))) % 0.37/0.57 (step @p17 :rule trans :premises (@p16 @p8)) % 0.37/0.57 (step @p18 :rule trans :premises (@p17 @p7)) % 0.37/0.57 (step @p19 :rule aci_norm :args ((= (or @t32 (or @t31 @t44)) @t45))) % 0.37/0.57 (step @p20 :rule bool-impl-elim :args (@t11 @t44)) % 0.37/0.57 (step @p21 :rule nary_cong :premises (@p11 @p20) :args ((or @t32 @t46))) % 0.37/0.57 (step @p22 :rule trans :premises (@p21 @p19)) % 0.37/0.57 (step @p23 :rule bool-impl-elim :args (@t13 @t46)) % 0.37/0.57 (step @p24 :rule trans :premises (@p23 @p22)) % 0.37/0.57 (step @p25 :rule cong :premises (@p24) :args ((forall @t7 (=> @t13 @t46)))) % 0.37/0.57 (step @p26 :rule trans :premises (@p25 @p18)) % 0.37/0.57 (step @p27 :rule bool-impl-elim :args (@t9 @t8)) % 0.37/0.57 (step @p28 :rule cong :premises (@p27) :args (@t10)) % 0.37/0.57 (step @p29 :rule refl :args (@t11)) % 0.37/0.57 (step @p30 :rule cong :premises (@p29 @p28) :args (@t12)) % 0.37/0.57 (step @p31 :rule refl :args (@t13)) % 0.37/0.57 (step @p32 :rule cong :premises (@p31 @p30) :args (@t14)) % 0.37/0.57 (step @p33 :rule cong :premises (@p32) :args (@t15)) % 0.37/0.57 (step @p34 :rule trans :premises (@p33 @p26)) % 0.37/0.57 (step @p35 :rule aci_norm :args ((= @t52 (or @t32 @t50 @t49 @t48)))) % 0.37/0.57 (step @p36 :rule cong :premises (@p35) :args (@t53)) % 0.37/0.57 (step @p37 :rule quant-merge-prenex :args ((= (forall @t7 @t55) @t53))) % 0.37/0.57 (step @p38 :rule alpha_equiv :args (@t56 (@list @t47) @t41)) % 0.37/0.57 (step @p39 :rule refl :args (@t50)) % 0.37/0.57 (step @p40 :rule nary_cong :premises (@p11 @p39 @p38) :args (@t57)) % 0.37/0.57 (step @p41 :rule quant-miniscope-or :args ((= @t55 @t57))) % 0.37/0.57 (step @p42 :rule trans :premises (@p41 @p40)) % 0.37/0.57 (step @p43 :rule symm :premises (@p42)) % 0.37/0.57 (step @p44 :rule cong :premises (@p43) :args ((forall @t7 @t58))) % 0.37/0.57 (step @p45 :rule trans :premises (@p44 @p37)) % 0.37/0.57 (step @p46 :rule trans :premises (@p45 @p36)) % 0.37/0.57 (step @p47 :rule aci_norm :args ((= (or @t32 (or @t50 @t44)) @t58))) % 0.37/0.57 (step @p48 :rule bool-impl-elim :args (@t16 @t44)) % 0.37/0.57 (step @p49 :rule nary_cong :premises (@p11 @p48) :args ((or @t32 @t59))) % 0.37/0.57 (step @p50 :rule trans :premises (@p49 @p47)) % 0.37/0.57 (step @p51 :rule bool-impl-elim :args (@t13 @t59)) % 0.37/0.57 (step @p52 :rule trans :premises (@p51 @p50)) % 0.37/0.57 (step @p53 :rule cong :premises (@p52) :args ((forall @t7 (=> @t13 @t59)))) % 0.37/0.57 (step @p54 :rule trans :premises (@p53 @p46)) % 0.37/0.57 (step @p55 :rule refl :args (@t16)) % 0.37/0.57 (step @p56 :rule cong :premises (@p55 @p28) :args (@t17)) % 0.37/0.57 (step @p57 :rule cong :premises (@p31 @p56) :args (@t18)) % 0.37/0.57 (step @p58 :rule cong :premises (@p57) :args (@t19)) % 0.37/0.57 (step @p59 :rule trans :premises (@p58 @p54)) % 0.37/0.57 (step @p60 :rule aci_norm :args ((= @t64 (or @t32 @t31 @t62 @t61)))) % 0.37/0.57 (step @p61 :rule cong :premises (@p60) :args (@t65)) % 0.37/0.57 (step @p62 :rule quant-merge-prenex :args ((= (forall @t7 @t67) @t65))) % 0.37/0.57 (step @p63 :rule alpha_equiv :args (@t68 (@list @t60) @t41)) % 0.37/0.57 (step @p64 :rule nary_cong :premises (@p11 @p10 @p63) :args (@t69)) % 0.37/0.57 (step @p65 :rule quant-miniscope-or :args ((= @t67 @t69))) % 0.37/0.57 (step @p66 :rule trans :premises (@p65 @p64)) % 0.37/0.57 (step @p67 :rule symm :premises (@p66)) % 0.37/0.57 (step @p68 :rule cong :premises (@p67) :args ((forall @t7 @t71))) % 0.37/0.57 (step @p69 :rule trans :premises (@p68 @p62)) % 0.37/0.58 (step @p70 :rule trans :premises (@p69 @p61)) % 0.37/0.58 (step @p71 :rule aci_norm :args ((= (or @t32 (or @t31 @t70)) @t71))) % 0.37/0.58 (step @p72 :rule bool-impl-elim :args (@t11 @t70)) % 0.37/0.58 (step @p73 :rule nary_cong :premises (@p11 @p72) :args ((or @t32 @t72))) % 0.37/0.58 (step @p74 :rule trans :premises (@p73 @p71)) % 0.37/0.58 (step @p75 :rule bool-impl-elim :args (@t13 @t72)) % 0.37/0.58 (step @p76 :rule trans :premises (@p75 @p74)) % 0.37/0.58 (step @p77 :rule cong :premises (@p76) :args ((forall @t7 (=> @t13 @t72)))) % 0.37/0.58 (step @p78 :rule trans :premises (@p77 @p70)) % 0.37/0.58 (step @p79 :rule bool-impl-elim :args (@t9 @t20)) % 0.37/0.58 (step @p80 :rule cong :premises (@p79) :args (@t21)) % 0.37/0.58 (step @p81 :rule cong :premises (@p29 @p80) :args (@t22)) % 0.37/0.58 (step @p82 :rule cong :premises (@p31 @p81) :args (@t23)) % 0.37/0.58 (step @p83 :rule cong :premises (@p82) :args (@t24)) % 0.37/0.58 (step @p84 :rule trans :premises (@p83 @p78)) % 0.37/0.58 (step @p85 :rule nary_cong :premises (@p84 @p59) :args (@t25)) % 0.37/0.58 (step @p86 :rule cong :premises (@p85 @p34) :args (@t26)) % 0.37/0.58 (step @p87 :rule cong :premises (@p86) :args (@t27)) % 0.37/0.58 (step @p88 :rule eq_resolve :premises (@p4 @p87)) % 0.37/0.58 (step @p89 :rule not_implies_elim1 :premises (@p88)) % 0.37/0.58 (step @p90 :rule and_elim :premises (@p89) :args (0)) % 0.37/0.58 (step @p91 :rule instantiate :premises (@p90) :args ((@list @t74 |tptp.'$ki_local_world'|))) % 0.37/0.58 (step @p92 :rule and_elim :premises (@p89) :args (1)) % 0.37/0.58 (step @p93 :rule instantiate :premises (@p92) :args ((@list @t74 @t75))) % 0.37/0.58 (step @p94 :rule not_implies_elim2 :premises (@p88)) % 0.37/0.58 (step @p95 :rule skolemize :premises (@p94)) % 0.37/0.58 (step @p96 :rule cnf_or_neg :args (@t83 3)) % 0.37/0.58 (step @p97 :rule chain_m_resolution :premises (@p96 @p95) :args ((not @t76) @t84 @t85)) % 0.37/0.58 (step @p98 :rule bool-double-not-elim :args (@t77)) % 0.37/0.58 (step @p99 :rule refl :args (@t83)) % 0.37/0.58 (step @p100 :rule nary_cong :premises (@p99 @p98) :args ((or @t83 (not @t78)))) % 0.37/0.58 (step @p101 :rule cnf_or_neg :args (@t83 2)) % 0.37/0.58 (step @p102 :rule eq_resolve :premises (@p101 @p100)) % 0.37/0.58 (step @p103 :rule reordering :premises (@p102) :args ((or @t77 @t83))) % 0.37/0.58 (step @p104 :rule chain_m_resolution :premises (@p103 @p95) :args (@t77 @t84 @t85)) % 0.37/0.58 (step @p105 :rule bool-double-not-elim :args (@t81)) % 0.37/0.58 (step @p106 :rule nary_cong :premises (@p99 @p105) :args ((or @t83 (not @t82)))) % 0.37/0.58 (step @p107 :rule cnf_or_neg :args (@t83 0)) % 0.37/0.58 (step @p108 :rule eq_resolve :premises (@p107 @p106)) % 0.37/0.58 (step @p109 :rule reordering :premises (@p108) :args ((or @t81 @t83))) % 0.37/0.58 (step @p110 :rule chain_m_resolution :premises (@p109 @p95) :args (@t81 @t84 @t85)) % 0.37/0.58 (step @p111 :rule cnf_or_pos :args (@t88)) % 0.37/0.58 (step @p112 :rule reordering :premises (@p111) :args ((or @t82 @t78 @t76 @t87 (not @t88)))) % 0.37/0.58 (step @p113 :rule chain_m_resolution :premises (@p112 @p110 @p104 @p97 @p93) :args (@t87 @t89 (@list @t81 @t77 @t76 @t88))) % 0.37/0.58 (step @p114 :rule bool-double-not-elim :args (@t79)) % 0.37/0.58 (step @p115 :rule nary_cong :premises (@p99 @p114) :args ((or @t83 (not @t80)))) % 0.37/0.58 (step @p116 :rule cnf_or_neg :args (@t83 1)) % 0.37/0.58 (step @p117 :rule eq_resolve :premises (@p116 @p115)) % 0.37/0.58 (step @p118 :rule reordering :premises (@p117) :args ((or @t79 @t83))) % 0.37/0.58 (step @p119 :rule chain_m_resolution :premises (@p118 @p95) :args (@t79 @t84 @t85)) % 0.37/0.58 (step @p120 :rule cnf_or_pos :args (@t92)) % 0.37/0.58 (step @p121 :rule reordering :premises (@p120) :args ((or @t82 @t80 @t86 @t91 (not @t92)))) % 0.37/0.58 (step @p122 :rule chain_m_resolution :premises (@p121 @p110 @p119 @p113 @p91) :args (@t91 @t89 (@list @t81 @t79 @t86 @t92))) % 0.37/0.58 (assume-push @p129 @t3) % 0.37/0.58 (step @p124 :rule instantiate :premises (@p1) :args ((@list |tptp.'$ki_local_world'|))) % 0.37/0.58 (step-pop @p130 :rule scope :premises (@p124)) % 0.37/0.58 (step @p125 :rule process_scope :premises (@p130) :args (@t90)) % 0.37/0.58 (step @p127 :rule implies_elim :premises (@p125)) % 0.37/0.58 (step @p128 false :rule chain_m_resolution :premises (@p127 @p122 @p1) :args (false (@list true false) (@list @t90 @t3))) % 0.37/0.58 ) % 0.37/0.58 % SZS output end Proof % 0.37/0.58 % cvc5 exiting %------------------------------------------------------------------------------