%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GEO198+1 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n020.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 08:16:40 AM UTC 2026 % Result : Theorem 0.39s 0.61s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO198+1 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n020.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Mon Jun 1 23:40:10 EDT 2026 % 0.17/0.35 % CPUTime : % 0.31/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.39/0.61 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.39/0.61 % SZS status Theorem % 0.39/0.61 % SZS output start Proof % 0.39/0.61 ( % 0.39/0.61 (declare-sort $$unsorted 0) % 0.39/0.61 (declare-const tptp.intersection_point (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.61 (declare-const tptp.apart_point_and_line (-> $$unsorted $$unsorted Bool)) % 0.39/0.61 (declare-const tptp.line_connecting (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.61 (declare-const tptp.convergent_lines (-> $$unsorted $$unsorted Bool)) % 0.39/0.61 (declare-const tptp.distinct_lines (-> $$unsorted $$unsorted Bool)) % 0.39/0.61 (declare-const tptp.distinct_points (-> $$unsorted $$unsorted Bool)) % 0.39/0.61 (define @t1 () (@var "X" $$unsorted)) % 0.39/0.61 (define @t2 () (@list @t1)) % 0.39/0.61 (define @t3 () (@var "Z" $$unsorted)) % 0.39/0.61 (define @t4 () (@var "Y" $$unsorted)) % 0.39/0.61 (define @t5 () (tptp.distinct_points @t1 @t3)) % 0.39/0.61 (define @t6 () (tptp.distinct_points @t1 @t4)) % 0.39/0.61 (define @t7 () (@list @t1 @t4 @t3)) % 0.39/0.61 (define @t8 () (tptp.distinct_lines @t4 @t3)) % 0.39/0.61 (define @t9 () (tptp.convergent_lines @t1 @t3)) % 0.39/0.61 (define @t10 () (tptp.convergent_lines @t1 @t4)) % 0.39/0.61 (define @t11 () (tptp.line_connecting @t1 @t4)) % 0.39/0.61 (define @t12 () (@list @t1 @t4)) % 0.39/0.61 (define @t13 () (tptp.intersection_point @t1 @t4)) % 0.39/0.61 (define @t14 () (not (tptp.apart_point_and_line @t13 @t1))) % 0.39/0.61 (define @t15 () (forall @t12 (=> @t10 @t14))) % 0.39/0.61 (define @t16 () (not (tptp.apart_point_and_line @t13 @t4))) % 0.39/0.61 (define @t17 () (forall @t12 (=> @t10 @t16))) % 0.39/0.61 (define @t18 () (@var "V" $$unsorted)) % 0.39/0.61 (define @t19 () (tptp.apart_point_and_line @t4 @t18)) % 0.39/0.61 (define @t20 () (@var "U" $$unsorted)) % 0.39/0.61 (define @t21 () (tptp.apart_point_and_line @t4 @t20)) % 0.39/0.61 (define @t22 () (tptp.apart_point_and_line @t1 @t18)) % 0.39/0.61 (define @t23 () (tptp.apart_point_and_line @t1 @t20)) % 0.39/0.61 (define @t24 () (or @t23 @t22 @t21 @t19)) % 0.39/0.61 (define @t25 () (tptp.distinct_lines @t20 @t18)) % 0.39/0.61 (define @t26 () (and @t6 @t25)) % 0.39/0.61 (define @t27 () (@list @t1 @t4 @t20 @t18)) % 0.39/0.61 (define @t28 () (forall @t27 (=> @t26 @t24))) % 0.39/0.61 (define @t29 () (tptp.apart_point_and_line @t3 @t4)) % 0.39/0.61 (define @t30 () (or @t5 @t29)) % 0.39/0.61 (define @t31 () (tptp.apart_point_and_line @t1 @t4)) % 0.39/0.61 (define @t32 () (forall @t7 (=> @t31 @t30))) % 0.39/0.61 (define @t33 () (or @t8 @t9)) % 0.39/0.61 (define @t34 () (forall @t7 (=> @t10 @t33))) % 0.39/0.61 (define @t35 () (not (tptp.apart_point_and_line (tptp.intersection_point @t1 @t3) @t4))) % 0.39/0.61 (define @t36 () (tptp.apart_point_and_line @t13 @t3)) % 0.39/0.61 (define @t37 () (not @t36)) % 0.39/0.61 (define @t38 () (tptp.convergent_lines @t3 @t4)) % 0.39/0.61 (define @t39 () (and @t10 @t38 @t9 @t37)) % 0.39/0.61 (define @t40 () (forall @t7 (=> @t39 @t35))) % 0.39/0.61 (define @t41 () (not @t40)) % 0.39/0.61 (define @t42 () (not @t25)) % 0.39/0.61 (define @t43 () (not @t6)) % 0.39/0.61 (define @t44 () (or @t43 @t42 @t23 @t22 @t21 @t19)) % 0.39/0.61 (define @t45 () (not @t31)) % 0.39/0.61 (define @t46 () (not @t9)) % 0.39/0.61 (define @t47 () (not @t38)) % 0.39/0.61 (define @t48 () (not @t10)) % 0.39/0.61 (define @t49 () (or @t48 @t47 @t46 @t36 @t35)) % 0.39/0.61 (define @t50 () (forall @t7 @t49)) % 0.39/0.61 (define @t51 () (@quantifiers_skolemize @t50 1)) % 0.39/0.61 (define @t52 () (@quantifiers_skolemize @t50 0)) % 0.39/0.61 (define @t53 () (tptp.intersection_point @t52 @t51)) % 0.39/0.61 (define @t54 () (@quantifiers_skolemize @t50 2)) % 0.39/0.61 (define @t55 () (tptp.intersection_point @t52 @t54)) % 0.39/0.61 (define @t56 () (@list @t52 @t51)) % 0.39/0.61 (define @t57 () (not @t37)) % 0.39/0.61 (define @t58 () (or @t48 @t47 @t46 @t57)) % 0.39/0.61 (define @t59 () (tptp.convergent_lines @t52 @t51)) % 0.39/0.61 (define @t60 () (tptp.apart_point_and_line @t55 @t51)) % 0.39/0.61 (define @t61 () (not @t60)) % 0.39/0.61 (define @t62 () (tptp.apart_point_and_line @t53 @t54)) % 0.39/0.61 (define @t63 () (tptp.convergent_lines @t52 @t54)) % 0.39/0.61 (define @t64 () (not @t63)) % 0.39/0.61 (define @t65 () (not @t59)) % 0.39/0.61 (define @t66 () (or @t65 (not (tptp.convergent_lines @t54 @t51)) @t64 @t62 @t61)) % 0.39/0.61 (define @t67 () (@list true)) % 0.39/0.61 (define @t68 () (@list @t66)) % 0.39/0.61 (define @t69 () (tptp.apart_point_and_line @t53 @t51)) % 0.39/0.61 (define @t70 () (not @t69)) % 0.39/0.61 (define @t71 () (or @t65 @t70)) % 0.39/0.61 (define @t72 () (@list false false)) % 0.39/0.61 (define @t73 () (tptp.distinct_points @t55 @t53)) % 0.39/0.61 (define @t74 () (or @t61 @t73 @t69)) % 0.39/0.61 (define @t75 () (@list false true false)) % 0.39/0.61 (define @t76 () (tptp.convergent_lines @t52 @t52)) % 0.39/0.61 (define @t77 () (tptp.distinct_lines @t54 @t52)) % 0.39/0.61 (define @t78 () (or @t64 @t77 @t76)) % 0.39/0.61 (define @t79 () (@list @t52 @t54)) % 0.39/0.61 (define @t80 () (tptp.apart_point_and_line @t55 @t54)) % 0.39/0.61 (define @t81 () (not @t80)) % 0.39/0.61 (define @t82 () (or @t64 @t81)) % 0.39/0.61 (define @t83 () (tptp.apart_point_and_line @t55 @t52)) % 0.39/0.61 (define @t84 () (not @t83)) % 0.39/0.61 (define @t85 () (or @t64 @t84)) % 0.39/0.61 (define @t86 () (tptp.apart_point_and_line @t53 @t52)) % 0.39/0.61 (define @t87 () (not @t86)) % 0.39/0.61 (define @t88 () (or @t65 @t87)) % 0.39/0.61 (define @t89 () (not @t77)) % 0.39/0.61 (define @t90 () (not @t73)) % 0.39/0.61 (define @t91 () (or @t90 @t89 @t80 @t83 @t62 @t86)) % 0.39/0.61 (define @t92 () (not @t91)) % 0.39/0.61 (define @t93 () (forall @t27 @t44)) % 0.39/0.61 (assume @p1 (forall @t2 (not (tptp.distinct_points @t1 @t1)))) % 0.39/0.61 (assume @p2 (forall @t2 (not (tptp.distinct_lines @t1 @t1)))) % 0.39/0.61 (assume @p3 (forall @t2 (not (tptp.convergent_lines @t1 @t1)))) % 0.39/0.61 (assume @p4 (forall @t7 (=> @t6 (or @t5 (tptp.distinct_points @t4 @t3))))) % 0.39/0.61 (assume @p5 (forall @t7 (=> (tptp.distinct_lines @t1 @t4) (or (tptp.distinct_lines @t1 @t3) @t8)))) % 0.39/0.61 (assume @p6 (forall @t7 (=> @t10 (or @t9 (tptp.convergent_lines @t4 @t3))))) % 0.39/0.61 (assume @p7 (forall @t12 (=> @t6 (not (tptp.apart_point_and_line @t1 @t11))))) % 0.39/0.61 (assume @p8 (forall @t12 (=> @t6 (not (tptp.apart_point_and_line @t4 @t11))))) % 0.39/0.61 (assume @p9 @t15) % 0.39/0.61 (assume @p10 @t17) % 0.39/0.61 (assume @p11 @t28) % 0.39/0.61 (assume @p12 @t32) % 0.39/0.61 (assume @p13 (forall @t7 (=> @t31 (or @t8 (tptp.apart_point_and_line @t1 @t3))))) % 0.39/0.61 (assume @p14 @t34) % 0.39/0.61 (assume @p15 @t41) % 0.39/0.61 (assume @p16 true) % 0.39/0.61 (step @p17 :rule aci_norm :args ((= (or (or @t43 @t42) @t24) @t44))) % 0.39/0.61 (step @p18 :rule refl :args (@t24)) % 0.39/0.61 (step @p19 :rule bool-and-de-morgan :args (@t6 @t25 true)) % 0.39/0.61 (step @p20 :rule nary_cong :premises (@p19 @p18) :args ((or (not @t26) @t24))) % 0.39/0.61 (step @p21 :rule trans :premises (@p20 @p17)) % 0.39/0.61 (step @p22 :rule bool-impl-elim :args (@t26 @t24)) % 0.39/0.61 (step @p23 :rule trans :premises (@p22 @p21)) % 0.39/0.61 (step @p24 :rule cong :premises (@p23) :args (@t28)) % 0.39/0.61 (step @p25 :rule eq_resolve :premises (@p11 @p24)) % 0.39/0.61 (step @p26 :rule aci_norm :args ((= (or @t45 @t30) (or @t45 @t5 @t29)))) % 0.39/0.61 (step @p27 :rule bool-impl-elim :args (@t31 @t30)) % 0.39/0.61 (step @p28 :rule trans :premises (@p27 @p26)) % 0.39/0.61 (step @p29 :rule cong :premises (@p28) :args (@t32)) % 0.39/0.61 (step @p30 :rule eq_resolve :premises (@p12 @p29)) % 0.39/0.61 (step @p31 :rule instantiate :premises (@p30) :args ((@list @t55 @t51 @t53))) % 0.39/0.61 (step @p32 :rule bool-impl-elim :args (@t10 @t16)) % 0.39/0.61 (step @p33 :rule cong :premises (@p32) :args (@t17)) % 0.39/0.61 (step @p34 :rule eq_resolve :premises (@p10 @p33)) % 0.39/0.61 (step @p35 :rule instantiate :premises (@p34) :args (@t56)) % 0.39/0.61 (step @p36 :rule aci_norm :args ((= (or (or @t48 @t47 @t46 @t36) @t35) @t49))) % 0.39/0.61 (step @p37 :rule refl :args (@t35)) % 0.39/0.61 (step @p38 :rule bool-double-not-elim :args (@t36)) % 0.39/0.61 (step @p39 :rule refl :args (@t46)) % 0.39/0.61 (step @p40 :rule refl :args (@t47)) % 0.39/0.61 (step @p41 :rule refl :args (@t48)) % 0.39/0.61 (step @p42 :rule nary_cong :premises (@p41 @p40 @p39 @p38) :args (@t58)) % 0.39/0.61 (step @p43 :rule aci_norm :args ((= (or @t48 (or @t47 (or @t46 @t57))) @t58))) % 0.39/0.61 (step @p44 :rule trans :premises (@p43 @p42)) % 0.39/0.61 (step @p45 :rule bool-and-de-morgan :args (@t9 @t37 true)) % 0.39/0.61 (step @p46 :rule nary_cong :premises (@p40 @p45) :args ((or @t47 (not (and @t9 @t37))))) % 0.39/0.61 (step @p47 :rule bool-and-de-morgan :args (@t38 @t9 (and @t37))) % 0.39/0.61 (step @p48 :rule trans :premises (@p47 @p46)) % 0.39/0.61 (step @p49 :rule nary_cong :premises (@p41 @p48) :args ((or @t48 (not (and @t38 @t9 @t37))))) % 0.39/0.61 (step @p50 :rule bool-and-de-morgan :args (@t10 @t38 (and @t9 @t37))) % 0.39/0.61 (step @p51 :rule trans :premises (@p50 @p49)) % 0.39/0.61 (step @p52 :rule trans :premises (@p51 @p44)) % 0.39/0.61 (step @p53 :rule nary_cong :premises (@p52 @p37) :args ((or (not @t39) @t35))) % 0.39/0.61 (step @p54 :rule trans :premises (@p53 @p36)) % 0.39/0.61 (step @p55 :rule bool-impl-elim :args (@t39 @t35)) % 0.39/0.61 (step @p56 :rule trans :premises (@p55 @p54)) % 0.39/0.61 (step @p57 :rule cong :premises (@p56) :args (@t40)) % 0.39/0.61 (step @p58 :rule cong :premises (@p57) :args (@t41)) % 0.39/0.61 (step @p59 :rule eq_resolve :premises (@p15 @p58)) % 0.39/0.61 (step @p60 :rule skolemize :premises (@p59)) % 0.39/0.61 (step @p61 :rule bool-double-not-elim :args (@t59)) % 0.39/0.61 (step @p62 :rule refl :args (@t66)) % 0.39/0.61 (step @p63 :rule nary_cong :premises (@p62 @p61) :args ((or @t66 (not @t65)))) % 0.39/0.61 (step @p64 :rule cnf_or_neg :args (@t66 0)) % 0.39/0.61 (step @p65 :rule eq_resolve :premises (@p64 @p63)) % 0.39/0.61 (step @p66 :rule reordering :premises (@p65) :args ((or @t59 @t66))) % 0.39/0.61 (step @p67 :rule chain_m_resolution :premises (@p66 @p60) :args (@t59 @t67 @t68)) % 0.39/0.61 (step @p68 :rule cnf_or_pos :args (@t71)) % 0.39/0.61 (step @p69 :rule reordering :premises (@p68) :args ((or @t65 @t70 (not @t71)))) % 0.39/0.61 (step @p70 :rule chain_m_resolution :premises (@p69 @p67 @p35) :args (@t70 @t72 (@list @t59 @t71))) % 0.39/0.61 (step @p71 :rule bool-double-not-elim :args (@t60)) % 0.39/0.61 (step @p72 :rule nary_cong :premises (@p62 @p71) :args ((or @t66 (not @t61)))) % 0.39/0.61 (step @p73 :rule cnf_or_neg :args (@t66 4)) % 0.39/0.61 (step @p74 :rule eq_resolve :premises (@p73 @p72)) % 0.39/0.61 (step @p75 :rule reordering :premises (@p74) :args ((or @t60 @t66))) % 0.39/0.61 (step @p76 :rule chain_m_resolution :premises (@p75 @p60) :args (@t60 @t67 @t68)) % 0.39/0.61 (step @p77 :rule cnf_or_pos :args (@t74)) % 0.39/0.61 (step @p78 :rule reordering :premises (@p77) :args ((or @t61 @t69 @t73 (not @t74)))) % 0.39/0.61 (step @p79 :rule chain_m_resolution :premises (@p78 @p76 @p70 @p31) :args (@t73 @t75 (@list @t60 @t69 @t74))) % 0.39/0.61 (step @p80 :rule aci_norm :args ((= (or @t48 @t33) (or @t48 @t8 @t9)))) % 0.39/0.61 (step @p81 :rule bool-impl-elim :args (@t10 @t33)) % 0.39/0.61 (step @p82 :rule trans :premises (@p81 @p80)) % 0.39/0.61 (step @p83 :rule cong :premises (@p82) :args (@t34)) % 0.39/0.61 (step @p84 :rule eq_resolve :premises (@p14 @p83)) % 0.39/0.61 (step @p85 :rule instantiate :premises (@p84) :args ((@list @t52 @t54 @t52))) % 0.39/0.61 (step @p86 :rule instantiate :premises (@p3) :args ((@list @t52))) % 0.39/0.61 (step @p87 :rule bool-double-not-elim :args (@t63)) % 0.39/0.61 (step @p88 :rule nary_cong :premises (@p62 @p87) :args ((or @t66 (not @t64)))) % 0.39/0.61 (step @p89 :rule cnf_or_neg :args (@t66 2)) % 0.39/0.61 (step @p90 :rule eq_resolve :premises (@p89 @p88)) % 0.39/0.61 (step @p91 :rule reordering :premises (@p90) :args ((or @t63 @t66))) % 0.39/0.61 (step @p92 :rule chain_m_resolution :premises (@p91 @p60) :args (@t63 @t67 @t68)) % 0.39/0.61 (step @p93 :rule cnf_or_pos :args (@t78)) % 0.39/0.61 (step @p94 :rule reordering :premises (@p93) :args ((or @t64 @t76 @t77 (not @t78)))) % 0.39/0.61 (step @p95 :rule chain_m_resolution :premises (@p94 @p92 @p86 @p85) :args (@t77 @t75 (@list @t63 @t76 @t78))) % 0.39/0.61 (step @p96 :rule instantiate :premises (@p34) :args (@t79)) % 0.39/0.61 (step @p97 :rule cnf_or_pos :args (@t82)) % 0.39/0.61 (step @p98 :rule reordering :premises (@p97) :args ((or @t64 @t81 (not @t82)))) % 0.39/0.61 (step @p99 :rule chain_m_resolution :premises (@p98 @p92 @p96) :args (@t81 @t72 (@list @t63 @t82))) % 0.39/0.61 (step @p100 :rule bool-impl-elim :args (@t10 @t14)) % 0.39/0.61 (step @p101 :rule cong :premises (@p100) :args (@t15)) % 0.39/0.61 (step @p102 :rule eq_resolve :premises (@p9 @p101)) % 0.39/0.61 (step @p103 :rule instantiate :premises (@p102) :args (@t79)) % 0.39/0.61 (step @p104 :rule cnf_or_pos :args (@t85)) % 0.39/0.61 (step @p105 :rule reordering :premises (@p104) :args ((or @t64 @t84 (not @t85)))) % 0.39/0.61 (step @p106 :rule chain_m_resolution :premises (@p105 @p92 @p103) :args (@t84 @t72 (@list @t63 @t85))) % 0.39/0.61 (step @p107 :rule instantiate :premises (@p102) :args (@t56)) % 0.39/0.61 (step @p108 :rule cnf_or_pos :args (@t88)) % 0.39/0.61 (step @p109 :rule reordering :premises (@p108) :args ((or @t65 @t87 (not @t88)))) % 0.39/0.61 (step @p110 :rule chain_m_resolution :premises (@p109 @p67 @p107) :args (@t87 @t72 (@list @t59 @t88))) % 0.39/0.61 (step @p111 :rule cnf_or_neg :args (@t66 3)) % 0.39/0.61 (step @p112 :rule chain_m_resolution :premises (@p111 @p60) :args ((not @t62) @t67 @t68)) % 0.39/0.61 (step @p113 :rule cnf_or_pos :args (@t91)) % 0.39/0.61 (step @p114 :rule reordering :premises (@p113) :args ((or @t62 @t86 @t83 @t80 @t89 @t90 @t92))) % 0.39/0.61 (step @p115 :rule chain_m_resolution :premises (@p114 @p112 @p110 @p106 @p99 @p95 @p79) :args (@t92 (@list true true true true false false) (@list @t62 @t86 @t83 @t80 @t77 @t73))) % 0.39/0.61 (assume-push @p122 @t93) % 0.39/0.61 (step @p117 :rule instantiate :premises (@p25) :args ((@list @t55 @t53 @t54 @t52))) % 0.39/0.61 (step-pop @p123 :rule scope :premises (@p117)) % 0.39/0.61 (step @p118 :rule process_scope :premises (@p123) :args (@t91)) % 0.39/0.61 (step @p120 :rule implies_elim :premises (@p118)) % 0.39/0.61 (step @p121 false :rule chain_m_resolution :premises (@p120 @p115 @p25) :args (false (@list true false) (@list @t91 @t93))) % 0.39/0.61 ) % 0.39/0.61 % SZS output end Proof % 0.39/0.61 % cvc5 exiting %------------------------------------------------------------------------------