%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GEO205+2 : 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 : n008.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 08:16:43 AM UTC 2026 % Result : Theorem 0.46s 0.68s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO205+2 : 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 : n008.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 23:40:18 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.46/0.68 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.46/0.68 % SZS status Theorem % 0.46/0.68 % SZS output start Proof % 0.46/0.68 ( % 0.46/0.68 (declare-sort $$unsorted 0) % 0.46/0.68 (declare-const tptp.intersection_point (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.68 (declare-const tptp.apart_point_and_line (-> $$unsorted $$unsorted Bool)) % 0.46/0.68 (declare-const tptp.line_connecting (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.68 (declare-const tptp.convergent_lines (-> $$unsorted $$unsorted Bool)) % 0.46/0.68 (declare-const tptp.distinct_lines (-> $$unsorted $$unsorted Bool)) % 0.46/0.68 (declare-const tptp.distinct_points (-> $$unsorted $$unsorted Bool)) % 0.46/0.68 (define @t1 () (@var "X" $$unsorted)) % 0.46/0.68 (define @t2 () (@list @t1)) % 0.46/0.68 (define @t3 () (@var "Z" $$unsorted)) % 0.46/0.68 (define @t4 () (@var "Y" $$unsorted)) % 0.46/0.68 (define @t5 () (tptp.distinct_points @t1 @t3)) % 0.46/0.68 (define @t6 () (tptp.distinct_points @t1 @t4)) % 0.46/0.68 (define @t7 () (@list @t1 @t4 @t3)) % 0.46/0.68 (define @t8 () (tptp.distinct_lines @t4 @t3)) % 0.46/0.68 (define @t9 () (tptp.distinct_lines @t1 @t4)) % 0.46/0.68 (define @t10 () (tptp.convergent_lines @t4 @t3)) % 0.46/0.68 (define @t11 () (tptp.convergent_lines @t1 @t3)) % 0.46/0.68 (define @t12 () (or @t11 @t10)) % 0.46/0.68 (define @t13 () (tptp.convergent_lines @t1 @t4)) % 0.46/0.68 (define @t14 () (forall @t7 (=> @t13 @t12))) % 0.46/0.68 (define @t15 () (tptp.intersection_point @t1 @t4)) % 0.46/0.68 (define @t16 () (tptp.distinct_points @t3 @t15)) % 0.46/0.68 (define @t17 () (tptp.apart_point_and_line @t3 @t4)) % 0.46/0.68 (define @t18 () (tptp.apart_point_and_line @t3 @t1)) % 0.46/0.68 (define @t19 () (or @t18 @t17)) % 0.46/0.68 (define @t20 () (=> @t19 @t16)) % 0.46/0.68 (define @t21 () (forall @t7 (=> @t13 @t20))) % 0.46/0.68 (define @t22 () (@var "V" $$unsorted)) % 0.46/0.68 (define @t23 () (tptp.apart_point_and_line @t4 @t22)) % 0.46/0.68 (define @t24 () (@var "U" $$unsorted)) % 0.46/0.68 (define @t25 () (tptp.apart_point_and_line @t4 @t24)) % 0.46/0.68 (define @t26 () (tptp.apart_point_and_line @t1 @t22)) % 0.46/0.68 (define @t27 () (tptp.apart_point_and_line @t1 @t24)) % 0.46/0.68 (define @t28 () (or @t27 @t26 @t25 @t23)) % 0.46/0.68 (define @t29 () (tptp.distinct_lines @t24 @t22)) % 0.46/0.68 (define @t30 () (and @t6 @t29)) % 0.46/0.68 (define @t31 () (forall (@list @t1 @t4 @t24 @t22) (=> @t30 @t28))) % 0.46/0.68 (define @t32 () (tptp.apart_point_and_line @t1 @t4)) % 0.46/0.68 (define @t33 () (tptp.apart_point_and_line @t1 @t3)) % 0.46/0.68 (define @t34 () (or @t8 @t33)) % 0.46/0.68 (define @t35 () (forall @t7 (=> @t32 @t34))) % 0.46/0.68 (define @t36 () (forall (@list @t1 @t4) (=> @t13 @t9))) % 0.46/0.68 (define @t37 () (and @t11 (not (tptp.distinct_points @t15 (tptp.intersection_point @t1 @t3))))) % 0.46/0.68 (define @t38 () (not @t8)) % 0.46/0.68 (define @t39 () (and @t13 @t38)) % 0.46/0.68 (define @t40 () (forall @t7 (=> @t39 @t37))) % 0.46/0.68 (define @t41 () (not @t40)) % 0.46/0.68 (define @t42 () (not @t13)) % 0.46/0.68 (define @t43 () (or @t42 @t8 @t37)) % 0.46/0.68 (define @t44 () (forall @t7 @t43)) % 0.46/0.68 (define @t45 () (@quantifiers_skolemize @t44 2)) % 0.46/0.68 (define @t46 () (@quantifiers_skolemize @t44 0)) % 0.46/0.68 (define @t47 () (tptp.intersection_point @t46 @t45)) % 0.46/0.68 (define @t48 () (@quantifiers_skolemize @t44 1)) % 0.46/0.68 (define @t49 () (tptp.intersection_point @t46 @t48)) % 0.46/0.68 (define @t50 () (tptp.distinct_points @t49 @t47)) % 0.46/0.68 (define @t51 () (not @t50)) % 0.46/0.68 (define @t52 () (tptp.convergent_lines @t46 @t45)) % 0.46/0.68 (define @t53 () (and @t52 @t51)) % 0.46/0.68 (define @t54 () (tptp.distinct_lines @t48 @t45)) % 0.46/0.68 (define @t55 () (tptp.convergent_lines @t46 @t48)) % 0.46/0.68 (define @t56 () (not @t55)) % 0.46/0.68 (define @t57 () (or @t56 @t54 @t53)) % 0.46/0.68 (define @t58 () (@list true)) % 0.46/0.68 (define @t59 () (@list @t57)) % 0.46/0.68 (define @t60 () (not @t32)) % 0.46/0.68 (define @t61 () (and (not @t18) (not @t17))) % 0.46/0.68 (define @t62 () (tptp.convergent_lines @t48 @t45)) % 0.46/0.68 (define @t63 () (not @t62)) % 0.46/0.68 (define @t64 () (or @t63 @t54)) % 0.46/0.68 (define @t65 () (@list true false)) % 0.46/0.68 (define @t66 () (or @t56 @t52 @t62)) % 0.46/0.68 (define @t67 () (@list false true false)) % 0.46/0.68 (define @t68 () (tptp.distinct_points @t47 @t47)) % 0.46/0.68 (define @t69 () (tptp.apart_point_and_line @t47 @t45)) % 0.46/0.68 (define @t70 () (not @t69)) % 0.46/0.68 (define @t71 () (tptp.apart_point_and_line @t47 @t46)) % 0.46/0.68 (define @t72 () (not @t71)) % 0.46/0.68 (define @t73 () (and @t72 @t70)) % 0.46/0.68 (define @t74 () (not @t52)) % 0.46/0.68 (define @t75 () (or @t74 @t73 @t68)) % 0.46/0.68 (define @t76 () (not @t73)) % 0.46/0.68 (define @t77 () (@list false)) % 0.46/0.68 (define @t78 () (@list @t73)) % 0.46/0.68 (define @t79 () (not @t29)) % 0.46/0.68 (define @t80 () (not @t6)) % 0.46/0.68 (define @t81 () (tptp.distinct_points @t49 @t49)) % 0.46/0.68 (define @t82 () (tptp.apart_point_and_line @t49 @t48)) % 0.46/0.68 (define @t83 () (not @t82)) % 0.46/0.68 (define @t84 () (tptp.apart_point_and_line @t49 @t46)) % 0.46/0.68 (define @t85 () (not @t84)) % 0.46/0.68 (define @t86 () (and @t85 @t83)) % 0.46/0.68 (define @t87 () (or @t56 @t86 @t81)) % 0.46/0.68 (define @t88 () (not @t86)) % 0.46/0.68 (define @t89 () (@list @t86)) % 0.46/0.68 (define @t90 () (tptp.distinct_lines @t46 @t48)) % 0.46/0.68 (define @t91 () (or @t56 @t90)) % 0.46/0.68 (define @t92 () (tptp.apart_point_and_line @t47 @t48)) % 0.46/0.68 (define @t93 () (not @t90)) % 0.46/0.68 (define @t94 () (or @t51 @t93 @t84 @t82 @t71 @t92)) % 0.46/0.68 (define @t95 () (not @t92)) % 0.46/0.68 (define @t96 () (or @t95 @t54 @t69)) % 0.46/0.68 (assume @p1 (forall @t2 (not (tptp.distinct_points @t1 @t1)))) % 0.46/0.68 (assume @p2 (forall @t2 (not (tptp.distinct_lines @t1 @t1)))) % 0.46/0.68 (assume @p3 (forall @t2 (not (tptp.convergent_lines @t1 @t1)))) % 0.46/0.68 (assume @p4 (forall @t7 (=> @t6 (or @t5 (tptp.distinct_points @t4 @t3))))) % 0.46/0.68 (assume @p5 (forall @t7 (=> @t9 (or (tptp.distinct_lines @t1 @t3) @t8)))) % 0.46/0.68 (assume @p6 @t14) % 0.46/0.68 (assume @p7 (forall @t7 (=> @t6 (=> (tptp.apart_point_and_line @t3 (tptp.line_connecting @t1 @t4)) (and (tptp.distinct_points @t3 @t1) (tptp.distinct_points @t3 @t4)))))) % 0.46/0.68 (assume @p8 @t21) % 0.46/0.68 (assume @p9 @t31) % 0.46/0.68 (assume @p10 (forall @t7 (=> @t32 (or @t5 @t17)))) % 0.46/0.68 (assume @p11 @t35) % 0.46/0.68 (assume @p12 @t36) % 0.46/0.68 (assume @p13 @t41) % 0.46/0.68 (assume @p14 true) % 0.46/0.68 (step @p15 :rule aci_norm :args ((= (or (or @t42 @t8) @t37) @t43))) % 0.46/0.68 (step @p16 :rule refl :args (@t37)) % 0.46/0.68 (step @p17 :rule bool-double-not-elim :args (@t8)) % 0.46/0.68 (step @p18 :rule refl :args (@t42)) % 0.46/0.68 (step @p19 :rule nary_cong :premises (@p18 @p17) :args ((or @t42 (not @t38)))) % 0.46/0.68 (step @p20 :rule bool-and-de-morgan :args (@t13 @t38 true)) % 0.46/0.68 (step @p21 :rule trans :premises (@p20 @p19)) % 0.46/0.68 (step @p22 :rule nary_cong :premises (@p21 @p16) :args ((or (not @t39) @t37))) % 0.46/0.68 (step @p23 :rule trans :premises (@p22 @p15)) % 0.46/0.68 (step @p24 :rule bool-impl-elim :args (@t39 @t37)) % 0.46/0.68 (step @p25 :rule trans :premises (@p24 @p23)) % 0.46/0.68 (step @p26 :rule cong :premises (@p25) :args (@t40)) % 0.46/0.68 (step @p27 :rule cong :premises (@p26) :args (@t41)) % 0.46/0.68 (step @p28 :rule eq_resolve :premises (@p13 @p27)) % 0.46/0.68 (step @p29 :rule skolemize :premises (@p28)) % 0.46/0.68 (step @p30 :rule cnf_or_neg :args (@t57 1)) % 0.46/0.68 (step @p31 :rule chain_m_resolution :premises (@p30 @p29) :args ((not @t54) @t58 @t59)) % 0.46/0.68 (step @p32 :rule aci_norm :args ((= (or @t60 @t34) (or @t60 @t8 @t33)))) % 0.46/0.68 (step @p33 :rule bool-impl-elim :args (@t32 @t34)) % 0.46/0.68 (step @p34 :rule trans :premises (@p33 @p32)) % 0.46/0.68 (step @p35 :rule cong :premises (@p34) :args (@t35)) % 0.46/0.68 (step @p36 :rule eq_resolve :premises (@p11 @p35)) % 0.46/0.68 (step @p37 :rule instantiate :premises (@p36) :args ((@list @t47 @t48 @t45))) % 0.46/0.68 (step @p38 :rule aci_norm :args ((= (or @t42 (or @t61 @t16)) (or @t42 @t61 @t16)))) % 0.46/0.68 (step @p39 :rule refl :args (@t16)) % 0.46/0.68 (step @p40 :rule bool-or-de-morgan :args (@t18 @t17 false)) % 0.46/0.68 (step @p41 :rule nary_cong :premises (@p40 @p39) :args ((or (not @t19) @t16))) % 0.46/0.68 (step @p42 :rule bool-impl-elim :args (@t19 @t16)) % 0.46/0.68 (step @p43 :rule trans :premises (@p42 @p41)) % 0.46/0.68 (step @p44 :rule nary_cong :premises (@p18 @p43) :args ((or @t42 @t20))) % 0.46/0.68 (step @p45 :rule trans :premises (@p44 @p38)) % 0.46/0.68 (step @p46 :rule bool-impl-elim :args (@t13 @t20)) % 0.46/0.68 (step @p47 :rule trans :premises (@p46 @p45)) % 0.46/0.68 (step @p48 :rule cong :premises (@p47) :args (@t21)) % 0.46/0.68 (step @p49 :rule eq_resolve :premises (@p8 @p48)) % 0.46/0.68 (step @p50 :rule instantiate :premises (@p49) :args ((@list @t46 @t45 @t47))) % 0.46/0.68 (step @p51 :rule instantiate :premises (@p1) :args ((@list @t47))) % 0.46/0.68 (step @p52 :rule aci_norm :args ((= (or @t42 @t12) (or @t42 @t11 @t10)))) % 0.46/0.68 (step @p53 :rule bool-impl-elim :args (@t13 @t12)) % 0.46/0.68 (step @p54 :rule trans :premises (@p53 @p52)) % 0.46/0.68 (step @p55 :rule cong :premises (@p54) :args (@t14)) % 0.46/0.68 (step @p56 :rule eq_resolve :premises (@p6 @p55)) % 0.46/0.68 (step @p57 :rule instantiate :premises (@p56) :args ((@list @t46 @t48 @t45))) % 0.46/0.68 (step @p58 :rule bool-impl-elim :args (@t13 @t9)) % 0.46/0.68 (step @p59 :rule cong :premises (@p58) :args (@t36)) % 0.46/0.68 (step @p60 :rule eq_resolve :premises (@p12 @p59)) % 0.46/0.68 (step @p61 :rule instantiate :premises (@p60) :args ((@list @t48 @t45))) % 0.46/0.68 (step @p62 :rule cnf_or_pos :args (@t64)) % 0.46/0.68 (step @p63 :rule reordering :premises (@p62) :args ((or @t54 @t63 (not @t64)))) % 0.46/0.68 (step @p64 :rule chain_m_resolution :premises (@p63 @p31 @p61) :args (@t63 @t65 (@list @t54 @t64))) % 0.46/0.68 (step @p65 :rule bool-double-not-elim :args (@t55)) % 0.46/0.68 (step @p66 :rule refl :args (@t57)) % 0.46/0.68 (step @p67 :rule nary_cong :premises (@p66 @p65) :args ((or @t57 (not @t56)))) % 0.46/0.68 (step @p68 :rule cnf_or_neg :args (@t57 0)) % 0.46/0.68 (step @p69 :rule eq_resolve :premises (@p68 @p67)) % 0.46/0.68 (step @p70 :rule reordering :premises (@p69) :args ((or @t55 @t57))) % 0.46/0.68 (step @p71 :rule chain_m_resolution :premises (@p70 @p29) :args (@t55 @t58 @t59)) % 0.46/0.68 (step @p72 :rule cnf_or_pos :args (@t66)) % 0.46/0.68 (step @p73 :rule reordering :premises (@p72) :args ((or @t56 @t52 @t62 (not @t66)))) % 0.46/0.68 (step @p74 :rule chain_m_resolution :premises (@p73 @p71 @p64 @p57) :args (@t52 @t67 (@list @t55 @t62 @t66))) % 0.46/0.68 (step @p75 :rule cnf_or_pos :args (@t75)) % 0.46/0.68 (step @p76 :rule reordering :premises (@p75) :args ((or @t74 @t68 @t73 (not @t75)))) % 0.46/0.68 (step @p77 :rule chain_m_resolution :premises (@p76 @p74 @p51 @p50) :args (@t73 @t67 (@list @t52 @t68 @t75))) % 0.46/0.68 (step @p78 :rule cnf_and_pos :args (@t73 1)) % 0.46/0.68 (step @p79 :rule reordering :premises (@p78) :args ((or @t70 @t76))) % 0.46/0.68 (step @p80 :rule chain_m_resolution :premises (@p79 @p77) :args (@t70 @t77 @t78)) % 0.46/0.68 (step @p81 :rule aci_norm :args ((= (or (or @t80 @t79) @t28) (or @t80 @t79 @t27 @t26 @t25 @t23)))) % 0.46/0.68 (step @p82 :rule refl :args (@t28)) % 0.46/0.68 (step @p83 :rule bool-and-de-morgan :args (@t6 @t29 true)) % 0.46/0.68 (step @p84 :rule nary_cong :premises (@p83 @p82) :args ((or (not @t30) @t28))) % 0.46/0.68 (step @p85 :rule trans :premises (@p84 @p81)) % 0.46/0.68 (step @p86 :rule bool-impl-elim :args (@t30 @t28)) % 0.46/0.68 (step @p87 :rule trans :premises (@p86 @p85)) % 0.46/0.68 (step @p88 :rule cong :premises (@p87) :args (@t31)) % 0.46/0.68 (step @p89 :rule eq_resolve :premises (@p9 @p88)) % 0.46/0.68 (step @p90 :rule instantiate :premises (@p89) :args ((@list @t49 @t47 @t46 @t48))) % 0.46/0.68 (step @p91 :rule cnf_and_pos :args (@t73 0)) % 0.46/0.68 (step @p92 :rule reordering :premises (@p91) :args ((or @t72 @t76))) % 0.46/0.68 (step @p93 :rule chain_m_resolution :premises (@p92 @p77) :args (@t72 @t77 @t78)) % 0.46/0.68 (step @p94 :rule instantiate :premises (@p49) :args ((@list @t46 @t48 @t49))) % 0.46/0.68 (step @p95 :rule instantiate :premises (@p1) :args ((@list @t49))) % 0.46/0.68 (step @p96 :rule cnf_or_pos :args (@t87)) % 0.46/0.68 (step @p97 :rule reordering :premises (@p96) :args ((or @t56 @t81 @t86 (not @t87)))) % 0.46/0.68 (step @p98 :rule chain_m_resolution :premises (@p97 @p71 @p95 @p94) :args (@t86 @t67 (@list @t55 @t81 @t87))) % 0.46/0.68 (step @p99 :rule cnf_and_pos :args (@t86 1)) % 0.46/0.68 (step @p100 :rule reordering :premises (@p99) :args ((or @t83 @t88))) % 0.46/0.68 (step @p101 :rule chain_m_resolution :premises (@p100 @p98) :args (@t83 @t77 @t89)) % 0.46/0.68 (step @p102 :rule cnf_and_pos :args (@t86 0)) % 0.46/0.68 (step @p103 :rule reordering :premises (@p102) :args ((or @t85 @t88))) % 0.46/0.68 (step @p104 :rule chain_m_resolution :premises (@p103 @p98) :args (@t85 @t77 @t89)) % 0.46/0.68 (step @p105 :rule instantiate :premises (@p60) :args ((@list @t46 @t48))) % 0.46/0.68 (step @p106 :rule cnf_or_pos :args (@t91)) % 0.46/0.68 (step @p107 :rule reordering :premises (@p106) :args ((or @t56 @t90 (not @t91)))) % 0.46/0.68 (step @p108 :rule chain_m_resolution :premises (@p107 @p71 @p105) :args (@t90 (@list false false) (@list @t55 @t91))) % 0.46/0.68 (step @p109 :rule cnf_or_neg :args (@t57 2)) % 0.46/0.68 (step @p110 :rule chain_m_resolution :premises (@p109 @p29) :args ((not @t53) @t58 @t59)) % 0.46/0.68 (step @p111 :rule bool-double-not-elim :args (@t50)) % 0.46/0.68 (step @p112 :rule refl :args (@t74)) % 0.46/0.68 (step @p113 :rule refl :args (@t53)) % 0.46/0.68 (step @p114 :rule nary_cong :premises (@p113 @p112 @p111) :args ((or @t53 @t74 (not @t51)))) % 0.46/0.68 (step @p115 :rule cnf_and_neg :args (@t53)) % 0.46/0.68 (step @p116 :rule eq_resolve :premises (@p115 @p114)) % 0.46/0.68 (step @p117 :rule reordering :premises (@p116) :args ((or @t50 @t53 @t74))) % 0.46/0.68 (step @p118 :rule chain_m_resolution :premises (@p117 @p110 @p74) :args (@t50 @t65 (@list @t53 @t52))) % 0.46/0.68 (step @p119 :rule cnf_or_pos :args (@t94)) % 0.46/0.68 (step @p120 :rule reordering :premises (@p119) :args ((or @t51 @t93 @t84 @t82 @t71 @t92 (not @t94)))) % 0.46/0.68 (step @p121 :rule chain_m_resolution :premises (@p120 @p118 @p108 @p104 @p101 @p93 @p90) :args (@t92 (@list false false true true true false) (@list @t50 @t90 @t84 @t82 @t71 @t94))) % 0.46/0.68 (step @p122 :rule cnf_or_pos :args (@t96)) % 0.46/0.68 (step @p123 :rule reordering :premises (@p122) :args ((or @t54 @t95 @t69 (not @t96)))) % 0.46/0.68 (step @p124 false :rule chain_m_resolution :premises (@p123 @p121 @p80 @p37 @p31) :args (false (@list false true false true) (@list @t92 @t69 @t96 @t54))) % 0.46/0.69 ) % 0.46/0.69 % SZS output end Proof % 0.46/0.69 % cvc5 exiting %------------------------------------------------------------------------------