%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GEO087+1 : TPTP v9.2.1. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/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 08:16:19 AM UTC 2026 % Result : Theorem 15.94s 16.15s % Output : Proof 15.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO087+1 : TPTP v9.2.1. Released v2.4.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n026.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 : Mon Jun 1 23:18:40 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 15.94/16.15 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.94/16.15 --- Run --no-e-matching --full-saturate-quant at 6... % 15.94/16.15 % SZS status Theorem % 15.94/16.15 % SZS output start Proof % 15.94/16.15 ( % 15.94/16.15 (declare-sort $$unsorted 0) % 15.94/16.15 (declare-const tptp.open (-> $$unsorted Bool)) % 15.94/16.15 (declare-const tptp.closed (-> $$unsorted Bool)) % 15.94/16.15 (declare-const tptp.meet (-> $$unsorted $$unsorted $$unsorted Bool)) % 15.94/16.15 (declare-const tptp.end_point (-> $$unsorted $$unsorted Bool)) % 15.94/16.15 (declare-const tptp.sum (-> $$unsorted $$unsorted $$unsorted)) % 15.94/16.15 (declare-const tptp.part_of (-> $$unsorted $$unsorted Bool)) % 15.94/16.15 (declare-const tptp.inner_point (-> $$unsorted $$unsorted Bool)) % 15.94/16.15 (declare-const tptp.incident_c (-> $$unsorted $$unsorted Bool)) % 15.94/16.15 (define @t1 () (@var "C" $$unsorted)) % 15.94/16.15 (define @t2 () (@var "P" $$unsorted)) % 15.94/16.15 (define @t3 () (tptp.incident_c @t2 @t1)) % 15.94/16.15 (define @t4 () (@var "C1" $$unsorted)) % 15.94/16.15 (define @t5 () (tptp.incident_c @t2 @t4)) % 15.94/16.15 (define @t6 () (@list @t2)) % 15.94/16.15 (define @t7 () (forall @t6 (=> @t5 @t3))) % 15.94/16.15 (define @t8 () (tptp.part_of @t4 @t1)) % 15.94/16.15 (define @t9 () (= @t8 @t7)) % 15.94/16.15 (define @t10 () (@list @t1 @t4)) % 15.94/16.15 (define @t11 () (forall @t10 @t9)) % 15.94/16.15 (define @t12 () (@var "C2" $$unsorted)) % 15.94/16.15 (define @t13 () (@var "Q" $$unsorted)) % 15.94/16.15 (define @t14 () (tptp.incident_c @t13 @t4)) % 15.94/16.15 (define @t15 () (tptp.incident_c @t13 @t1)) % 15.94/16.15 (define @t16 () (@list @t13)) % 15.94/16.15 (define @t17 () (= @t1 (tptp.sum @t4 @t12))) % 15.94/16.15 (define @t18 () (tptp.part_of @t12 @t4)) % 15.94/16.15 (define @t19 () (tptp.part_of @t4 @t12)) % 15.94/16.15 (define @t20 () (tptp.part_of @t12 @t1)) % 15.94/16.15 (define @t21 () (@list @t4 @t12)) % 15.94/16.15 (define @t22 () (tptp.end_point @t2 @t1)) % 15.94/16.15 (define @t23 () (@list @t2 @t1)) % 15.94/16.15 (define @t24 () (tptp.inner_point @t2 @t1)) % 15.94/16.15 (define @t25 () (tptp.end_point @t13 @t4)) % 15.94/16.15 (define @t26 () (tptp.end_point @t13 @t1)) % 15.94/16.15 (define @t27 () (and @t26 @t25)) % 15.94/16.15 (define @t28 () (and @t15 @t14)) % 15.94/16.15 (define @t29 () (forall @t16 (=> @t28 @t27))) % 15.94/16.15 (define @t30 () (and @t3 @t5 @t29)) % 15.94/16.15 (define @t31 () (tptp.meet @t2 @t1 @t4)) % 15.94/16.15 (define @t32 () (= @t31 @t30)) % 15.94/16.15 (define @t33 () (forall (@list @t2 @t1 @t4) @t32)) % 15.94/16.15 (define @t34 () (exists @t6 @t22)) % 15.94/16.15 (define @t35 () (tptp.closed @t1)) % 15.94/16.15 (define @t36 () (@list @t1)) % 15.94/16.15 (define @t37 () (@var "C3" $$unsorted)) % 15.94/16.15 (define @t38 () (exists @t6 @t24)) % 15.94/16.15 (define @t39 () (forall @t36 @t38)) % 15.94/16.15 (define @t40 () (tptp.meet @t2 @t4 @t12)) % 15.94/16.15 (define @t41 () (@list @t1 @t2)) % 15.94/16.15 (define @t42 () (@var "R" $$unsorted)) % 15.94/16.15 (define @t43 () (= @t2 @t13)) % 15.94/16.15 (define @t44 () (exists @t6 @t40)) % 15.94/16.15 (define @t45 () (not @t44)) % 15.94/16.15 (define @t46 () (=> @t19 @t45)) % 15.94/16.15 (define @t47 () (forall @t21 @t46)) % 15.94/16.15 (define @t48 () (not @t47)) % 15.94/16.15 (define @t49 () (@var "BOUND_VARIABLE_7717" $$unsorted)) % 15.94/16.15 (define @t50 () (not (tptp.meet @t49 @t4 @t12))) % 15.94/16.15 (define @t51 () (not @t19)) % 15.94/16.15 (define @t52 () (or @t51 @t50)) % 15.94/16.15 (define @t53 () (forall (@list @t4 @t12 @t49) @t52)) % 15.94/16.15 (define @t54 () (@quantifiers_skolemize @t53 0)) % 15.94/16.15 (define @t55 () (forall @t6 (not (tptp.inner_point @t2 @t54)))) % 15.94/16.15 (define @t56 () (@quantifiers_skolemize @t55 0)) % 15.94/16.15 (define @t57 () (tptp.inner_point @t56 @t54)) % 15.94/16.15 (define @t58 () (not @t55)) % 15.94/16.15 (define @t59 () (not @t57)) % 15.94/16.15 (define @t60 () (not @t59)) % 15.94/16.15 (define @t61 () (@list true)) % 15.94/16.15 (define @t62 () (tptp.end_point @t56 @t54)) % 15.94/16.15 (define @t63 () (not @t62)) % 15.94/16.15 (define @t64 () (tptp.incident_c @t56 @t54)) % 15.94/16.15 (define @t65 () (and @t64 @t63)) % 15.94/16.15 (define @t66 () (= @t57 @t65)) % 15.94/16.15 (define @t67 () (@list false false)) % 15.94/16.15 (define @t68 () (not @t65)) % 15.94/16.15 (define @t69 () (@list false)) % 15.94/16.15 (define @t70 () (@list @t65)) % 15.94/16.15 (define @t71 () (@quantifiers_skolemize @t53 1)) % 15.94/16.15 (define @t72 () (@list @t49)) % 15.94/16.15 (define @t73 () (forall @t72 @t52)) % 15.94/16.15 (define @t74 () (forall @t72 @t50)) % 15.94/16.15 (define @t75 () (or @t51 @t74)) % 15.94/16.15 (define @t76 () (forall @t6 (not @t40))) % 15.94/16.15 (define @t77 () (tptp.part_of @t54 @t71)) % 15.94/16.15 (define @t78 () (@quantifiers_skolemize @t53 2)) % 15.94/16.15 (define @t79 () (tptp.meet @t78 @t54 @t71)) % 15.94/16.15 (define @t80 () (not @t79)) % 15.94/16.15 (define @t81 () (not @t77)) % 15.94/16.15 (define @t82 () (or @t81 @t80)) % 15.94/16.15 (define @t83 () (@list @t82)) % 15.94/16.15 (define @t84 () (forall @t6 (or (not (tptp.incident_c @t2 @t54)) (tptp.incident_c @t2 @t71)))) % 15.94/16.15 (define @t85 () (= @t77 @t84)) % 15.94/16.15 (define @t86 () (@list @t56)) % 15.94/16.15 (define @t87 () (tptp.incident_c @t56 @t71)) % 15.94/16.15 (define @t88 () (not @t64)) % 15.94/16.15 (define @t89 () (or @t88 @t87)) % 15.94/16.15 (define @t90 () (and @t62 (tptp.end_point @t56 @t71))) % 15.94/16.15 (define @t91 () (not @t90)) % 15.94/16.15 (define @t92 () (not @t14)) % 15.94/16.15 (define @t93 () (not @t15)) % 15.94/16.15 (define @t94 () (forall @t16 (or (not (tptp.incident_c @t13 @t54)) (not (tptp.incident_c @t13 @t71)) (and (tptp.end_point @t13 @t54) (tptp.end_point @t13 @t71))))) % 15.94/16.15 (define @t95 () (and (tptp.incident_c @t78 @t54) (tptp.incident_c @t78 @t71) @t94)) % 15.94/16.15 (define @t96 () (= @t79 @t95)) % 15.94/16.15 (define @t97 () (not @t87)) % 15.94/16.15 (define @t98 () (or @t88 @t97 @t90)) % 15.94/16.15 (assume @p1 @t11) % 15.94/16.15 (assume @p2 (forall (@list @t1 @t4 @t12) (= @t17 (forall @t16 (= @t15 (or @t14 (tptp.incident_c @t13 @t12))))))) % 15.94/16.15 (assume @p3 (forall @t23 (= @t22 (and @t3 (forall @t21 (=> (and @t8 @t20 @t5 (tptp.incident_c @t2 @t12)) (or @t19 @t18))))))) % 15.94/16.15 (assume @p4 (forall @t23 (= @t24 (and @t3 (not @t22))))) % 15.94/16.15 (assume @p5 @t33) % 15.94/16.15 (assume @p6 (forall @t36 (= @t35 (not @t34)))) % 15.94/16.15 (assume @p7 (forall @t36 (= (tptp.open @t1) @t34))) % 15.94/16.15 (assume @p8 (forall @t10 (=> (and @t8 (not (= @t4 @t1))) (tptp.open @t4)))) % 15.94/16.15 (assume @p9 (forall (@list @t1 @t4 @t12 @t37) (=> (and @t8 @t20 (tptp.part_of @t37 @t1) (exists @t6 (and (tptp.end_point @t2 @t4) (tptp.end_point @t2 @t12) (tptp.end_point @t2 @t37)))) (or (tptp.part_of @t12 @t37) (tptp.part_of @t37 @t12) @t19 @t18 (tptp.part_of @t4 @t37) (tptp.part_of @t37 @t4))))) % 15.94/16.15 (assume @p10 @t39) % 15.94/16.15 (assume @p11 (forall @t41 (=> @t24 (exists @t21 (and @t40 @t17))))) % 15.94/16.15 (assume @p12 (forall (@list @t1 @t2 @t13 @t42) (=> (and @t22 @t26 (tptp.end_point @t42 @t1)) (or @t43 (= @t2 @t42) (= @t13 @t42))))) % 15.94/16.15 (assume @p13 (forall @t41 (=> @t22 (exists @t16 (and @t26 (not @t43)))))) % 15.94/16.15 (assume @p14 (forall (@list @t1 @t4 @t12 @t2) (=> (and @t35 @t40 @t17) (forall @t16 (=> @t25 (tptp.meet @t13 @t4 @t12)))))) % 15.94/16.15 (assume @p15 (forall @t21 (=> @t44 (exists @t36 @t17)))) % 15.94/16.15 (assume @p16 (forall @t10 (=> (forall @t6 (= @t3 @t5)) (= @t1 @t4)))) % 15.94/16.15 (assume @p17 @t48) % 15.94/16.15 (assume @p18 true) % 15.94/16.15 (step @p19 :rule instantiate :premises (@p4) :args ((@list @t56 @t54))) % 15.94/16.15 (step @p20 :rule exists-elim :args ((= @t38 (not (forall @t6 (not @t24)))))) % 15.94/16.15 (step @p21 :rule cong :premises (@p20) :args (@t39)) % 15.94/16.15 (step @p22 :rule eq_resolve :premises (@p10 @p21)) % 15.94/16.15 (step @p23 :rule instantiate :premises (@p22) :args ((@list @t54))) % 15.94/16.15 (step @p24 :rule refl :args (@t57)) % 15.94/16.15 (step @p25 :rule bool-double-not-elim :args (@t55)) % 15.94/16.15 (step @p26 :rule nary_cong :premises (@p25 @p24) :args ((or (not @t58) @t57))) % 15.94/16.15 (step @p27 :rule bool-double-not-elim :args (@t57)) % 15.94/16.15 (step @p28 :rule refl :args (@t58)) % 15.94/16.15 (step @p29 :rule cong :premises (@p28 @p27) :args ((=> @t58 @t60))) % 15.94/16.15 (assume-push @p126 @t58) % 15.94/16.15 (step @p31 :rule skolemize :premises (@p23)) % 15.94/16.15 (step-pop @p127 :rule scope :premises (@p31)) % 15.94/16.15 (step @p32 :rule process_scope :premises (@p127) :args (@t60)) % 15.94/16.15 (step @p34 :rule eq_resolve :premises (@p32 @p29)) % 15.94/16.15 (step @p35 :rule implies_elim :premises (@p34)) % 15.94/16.15 (step @p36 :rule eq_resolve :premises (@p35 @p26)) % 15.94/16.15 (step @p37 :rule chain_m_resolution :premises (@p36 @p23) :args (@t57 @t61 (@list @t55))) % 15.94/16.15 (step @p38 :rule cnf_equiv_pos1 :args (@t66)) % 15.94/16.15 (step @p39 :rule reordering :premises (@p38) :args ((or @t59 @t65 (not @t66)))) % 15.94/16.15 (step @p40 :rule chain_m_resolution :premises (@p39 @p37 @p19) :args (@t65 @t67 (@list @t57 @t66))) % 15.94/16.15 (step @p41 :rule cnf_and_pos :args (@t65 0)) % 15.94/16.15 (step @p42 :rule reordering :premises (@p41) :args ((or @t64 @t68))) % 15.94/16.15 (step @p43 :rule chain_m_resolution :premises (@p42 @p40) :args (@t64 @t69 @t70)) % 15.94/16.15 (step @p44 :rule bool-impl-elim :args (@t5 @t3)) % 15.94/16.15 (step @p45 :rule cong :premises (@p44) :args (@t7)) % 15.94/16.15 (step @p46 :rule refl :args (@t8)) % 15.94/16.15 (step @p47 :rule cong :premises (@p46 @p45) :args (@t9)) % 15.94/16.15 (step @p48 :rule cong :premises (@p47) :args (@t11)) % 15.94/16.15 (step @p49 :rule eq_resolve :premises (@p1 @p48)) % 15.94/16.15 (step @p50 :rule instantiate :premises (@p49) :args ((@list @t71 @t54))) % 15.94/16.15 (step @p51 :rule quant-merge-prenex :args ((= (forall @t21 @t73) @t53))) % 15.94/16.15 (step @p52 :rule alpha_equiv :args (@t74 (@list @t49) (@list @t2))) % 15.94/16.15 (step @p53 :rule refl :args (@t51)) % 15.94/16.15 (step @p54 :rule nary_cong :premises (@p53 @p52) :args (@t75)) % 15.94/16.15 (step @p55 :rule quant-miniscope-or :args ((= @t73 @t75))) % 15.94/16.15 (step @p56 :rule trans :premises (@p55 @p54)) % 15.94/16.15 (step @p57 :rule symm :premises (@p56)) % 15.94/16.15 (step @p58 :rule cong :premises (@p57) :args ((forall @t21 (or @t51 @t76)))) % 15.94/16.15 (step @p59 :rule trans :premises (@p58 @p51)) % 15.94/16.15 (step @p60 :rule bool-impl-elim :args (@t19 @t76)) % 15.94/16.15 (step @p61 :rule cong :premises (@p60) :args ((forall @t21 (=> @t19 @t76)))) % 15.94/16.15 (step @p62 :rule trans :premises (@p61 @p59)) % 15.94/16.15 (step @p63 :rule bool-double-not-elim :args (@t76)) % 15.94/16.15 (step @p64 :rule exists-elim :args ((= @t44 (not @t76)))) % 15.94/16.15 (step @p65 :rule cong :premises (@p64) :args (@t45)) % 15.94/16.15 (step @p66 :rule trans :premises (@p65 @p63)) % 15.94/16.15 (step @p67 :rule refl :args (@t19)) % 15.94/16.15 (step @p68 :rule cong :premises (@p67 @p66) :args (@t46)) % 15.94/16.15 (step @p69 :rule cong :premises (@p68) :args (@t47)) % 15.94/16.15 (step @p70 :rule trans :premises (@p69 @p62)) % 15.94/16.15 (step @p71 :rule cong :premises (@p70) :args (@t48)) % 15.94/16.15 (step @p72 :rule eq_resolve :premises (@p17 @p71)) % 15.94/16.15 (step @p73 :rule skolemize :premises (@p72)) % 15.94/16.15 (step @p74 :rule bool-double-not-elim :args (@t77)) % 15.94/16.15 (step @p75 :rule refl :args (@t82)) % 15.94/16.15 (step @p76 :rule nary_cong :premises (@p75 @p74) :args ((or @t82 (not @t81)))) % 15.94/16.15 (step @p77 :rule cnf_or_neg :args (@t82 0)) % 15.94/16.15 (step @p78 :rule eq_resolve :premises (@p77 @p76)) % 15.94/16.15 (step @p79 :rule reordering :premises (@p78) :args ((or @t77 @t82))) % 15.94/16.15 (step @p80 :rule chain_m_resolution :premises (@p79 @p73) :args (@t77 @t61 @t83)) % 15.94/16.15 (step @p81 :rule cnf_equiv_pos1 :args (@t85)) % 15.94/16.15 (step @p82 :rule reordering :premises (@p81) :args ((or @t81 @t84 (not @t85)))) % 15.94/16.15 (step @p83 :rule chain_m_resolution :premises (@p82 @p80 @p50) :args (@t84 @t67 (@list @t77 @t85))) % 15.94/16.15 (step @p84 :rule instantiate :premises (@p83) :args (@t86)) % 15.94/16.15 (step @p85 :rule cnf_or_pos :args (@t89)) % 15.94/16.15 (step @p86 :rule reordering :premises (@p85) :args ((or @t88 @t87 (not @t89)))) % 15.94/16.15 (step @p87 :rule chain_m_resolution :premises (@p86 @p43 @p84) :args (@t87 @t67 (@list @t64 @t89))) % 15.94/16.15 (step @p88 :rule cnf_and_pos :args (@t65 1)) % 15.94/16.15 (step @p89 :rule reordering :premises (@p88) :args ((or @t63 @t68))) % 15.94/16.15 (step @p90 :rule chain_m_resolution :premises (@p89 @p40) :args (@t63 @t69 @t70)) % 15.94/16.15 (step @p91 :rule cnf_and_pos :args (@t90 0)) % 15.94/16.15 (step @p92 :rule reordering :premises (@p91) :args ((or @t62 @t91))) % 15.94/16.15 (step @p93 :rule chain_m_resolution :premises (@p92 @p90) :args (@t91 @t61 (@list @t62))) % 15.94/16.15 (step @p94 :rule aci_norm :args ((= (or (or @t93 @t92) @t27) (or @t93 @t92 @t27)))) % 15.94/16.15 (step @p95 :rule refl :args (@t27)) % 15.94/16.15 (step @p96 :rule bool-and-de-morgan :args (@t15 @t14 true)) % 15.94/16.15 (step @p97 :rule nary_cong :premises (@p96 @p95) :args ((or (not @t28) @t27))) % 15.94/16.15 (step @p98 :rule trans :premises (@p97 @p94)) % 15.94/16.15 (step @p99 :rule bool-impl-elim :args (@t28 @t27)) % 15.94/16.15 (step @p100 :rule trans :premises (@p99 @p98)) % 15.94/16.15 (step @p101 :rule cong :premises (@p100) :args (@t29)) % 15.94/16.15 (step @p102 :rule refl :args (@t5)) % 15.94/16.15 (step @p103 :rule refl :args (@t3)) % 15.94/16.15 (step @p104 :rule nary_cong :premises (@p103 @p102 @p101) :args (@t30)) % 15.94/16.15 (step @p105 :rule refl :args (@t31)) % 15.94/16.15 (step @p106 :rule cong :premises (@p105 @p104) :args (@t32)) % 15.94/16.15 (step @p107 :rule cong :premises (@p106) :args (@t33)) % 15.94/16.15 (step @p108 :rule eq_resolve :premises (@p5 @p107)) % 15.94/16.15 (step @p109 :rule instantiate :premises (@p108) :args ((@list @t78 @t54 @t71))) % 15.94/16.15 (step @p110 :rule bool-double-not-elim :args (@t79)) % 15.94/16.15 (step @p111 :rule nary_cong :premises (@p75 @p110) :args ((or @t82 (not @t80)))) % 15.94/16.15 (step @p112 :rule cnf_or_neg :args (@t82 1)) % 15.94/16.15 (step @p113 :rule eq_resolve :premises (@p112 @p111)) % 15.94/16.15 (step @p114 :rule reordering :premises (@p113) :args ((or @t79 @t82))) % 15.94/16.15 (step @p115 :rule chain_m_resolution :premises (@p114 @p73) :args (@t79 @t61 @t83)) % 15.94/16.15 (step @p116 :rule cnf_equiv_pos1 :args (@t96)) % 15.94/16.15 (step @p117 :rule reordering :premises (@p116) :args ((or @t80 @t95 (not @t96)))) % 15.94/16.15 (step @p118 :rule chain_m_resolution :premises (@p117 @p115 @p109) :args (@t95 @t67 (@list @t79 @t96))) % 15.94/16.15 (step @p119 :rule cnf_and_pos :args (@t95 2)) % 15.94/16.15 (step @p120 :rule reordering :premises (@p119) :args ((or @t94 (not @t95)))) % 15.94/16.15 (step @p121 :rule chain_m_resolution :premises (@p120 @p118) :args (@t94 @t69 (@list @t95))) % 15.94/16.15 (step @p122 :rule instantiate :premises (@p121) :args (@t86)) % 15.94/16.15 (step @p123 :rule cnf_or_pos :args (@t98)) % 15.94/16.15 (step @p124 :rule reordering :premises (@p123) :args ((or @t88 @t97 @t90 (not @t98)))) % 15.94/16.15 (step @p125 false :rule chain_m_resolution :premises (@p124 @p122 @p93 @p87 @p43) :args (false (@list false true false false) (@list @t98 @t90 @t87 @t64))) % 15.94/16.15 ) % 15.94/16.15 % SZS output end Proof % 15.94/16.15 % cvc5 exiting %------------------------------------------------------------------------------