%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GEO191+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 : n002.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 08:16:38 AM UTC 2026 % Result : Theorem 0.38s 0.61s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO191+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 % 0.16/0.35 % Computer : n002.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 : Mon Jun 1 23:39:48 EDT 2026 % 0.16/0.35 % CPUTime : % 0.26/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.61 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.61 % SZS status Theorem % 0.38/0.61 % SZS output start Proof % 0.38/0.61 ( % 0.38/0.61 (declare-sort $$unsorted 0) % 0.38/0.61 (declare-const tptp.intersection_point (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.61 (declare-const tptp.apart_point_and_line (-> $$unsorted $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.line_connecting (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.61 (declare-const tptp.convergent_lines (-> $$unsorted $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.distinct_lines (-> $$unsorted $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.distinct_points (-> $$unsorted $$unsorted Bool)) % 0.38/0.61 (define @t1 () (@var "X" $$unsorted)) % 0.38/0.61 (define @t2 () (@list @t1)) % 0.38/0.61 (define @t3 () (@var "Z" $$unsorted)) % 0.38/0.61 (define @t4 () (@var "Y" $$unsorted)) % 0.38/0.61 (define @t5 () (tptp.distinct_points @t4 @t3)) % 0.38/0.61 (define @t6 () (tptp.distinct_points @t1 @t3)) % 0.38/0.61 (define @t7 () (or @t6 @t5)) % 0.38/0.61 (define @t8 () (tptp.distinct_points @t1 @t4)) % 0.38/0.61 (define @t9 () (@list @t1 @t4 @t3)) % 0.38/0.61 (define @t10 () (forall @t9 (=> @t8 @t7))) % 0.38/0.61 (define @t11 () (tptp.distinct_lines @t4 @t3)) % 0.38/0.61 (define @t12 () (tptp.distinct_lines @t1 @t3)) % 0.38/0.61 (define @t13 () (or @t12 @t11)) % 0.38/0.61 (define @t14 () (tptp.distinct_lines @t1 @t4)) % 0.38/0.61 (define @t15 () (forall @t9 (=> @t14 @t13))) % 0.38/0.61 (define @t16 () (tptp.convergent_lines @t1 @t4)) % 0.38/0.61 (define @t17 () (tptp.intersection_point @t1 @t4)) % 0.38/0.61 (define @t18 () (tptp.distinct_points @t3 @t17)) % 0.38/0.61 (define @t19 () (tptp.apart_point_and_line @t3 @t4)) % 0.38/0.61 (define @t20 () (tptp.apart_point_and_line @t3 @t1)) % 0.38/0.61 (define @t21 () (or @t20 @t19)) % 0.38/0.61 (define @t22 () (=> @t21 @t18)) % 0.38/0.61 (define @t23 () (forall @t9 (=> @t16 @t22))) % 0.38/0.61 (define @t24 () (@var "V" $$unsorted)) % 0.38/0.61 (define @t25 () (tptp.apart_point_and_line @t4 @t24)) % 0.38/0.61 (define @t26 () (@var "U" $$unsorted)) % 0.38/0.61 (define @t27 () (tptp.apart_point_and_line @t4 @t26)) % 0.38/0.61 (define @t28 () (tptp.apart_point_and_line @t1 @t24)) % 0.38/0.61 (define @t29 () (tptp.apart_point_and_line @t1 @t26)) % 0.38/0.61 (define @t30 () (or @t29 @t28 @t27 @t25)) % 0.38/0.61 (define @t31 () (tptp.distinct_lines @t26 @t24)) % 0.38/0.61 (define @t32 () (and @t8 @t31)) % 0.38/0.61 (define @t33 () (@list @t1 @t4 @t26 @t24)) % 0.38/0.61 (define @t34 () (forall @t33 (=> @t32 @t30))) % 0.38/0.61 (define @t35 () (tptp.apart_point_and_line @t1 @t4)) % 0.38/0.61 (define @t36 () (forall (@list @t1 @t4) (=> @t16 @t14))) % 0.38/0.61 (define @t37 () (tptp.intersection_point @t26 @t24)) % 0.38/0.61 (define @t38 () (tptp.apart_point_and_line @t37 @t4)) % 0.38/0.61 (define @t39 () (tptp.apart_point_and_line @t37 @t1)) % 0.38/0.61 (define @t40 () (or @t39 @t38)) % 0.38/0.61 (define @t41 () (tptp.apart_point_and_line @t17 @t24)) % 0.38/0.61 (define @t42 () (tptp.apart_point_and_line @t17 @t26)) % 0.38/0.61 (define @t43 () (or @t42 @t41)) % 0.38/0.61 (define @t44 () (tptp.convergent_lines @t26 @t24)) % 0.38/0.61 (define @t45 () (and @t16 @t44 @t43)) % 0.38/0.61 (define @t46 () (forall @t33 (=> @t45 @t40))) % 0.38/0.61 (define @t47 () (not @t46)) % 0.38/0.61 (define @t48 () (not @t31)) % 0.38/0.61 (define @t49 () (not @t8)) % 0.38/0.61 (define @t50 () (or @t49 @t48 @t29 @t28 @t27 @t25)) % 0.38/0.61 (define @t51 () (and (not @t42) (not @t41))) % 0.38/0.61 (define @t52 () (not @t44)) % 0.38/0.61 (define @t53 () (not @t16)) % 0.38/0.61 (define @t54 () (or @t53 @t52 @t51 @t39 @t38)) % 0.38/0.61 (define @t55 () (forall @t33 @t54)) % 0.38/0.61 (define @t56 () (@quantifiers_skolemize @t55 1)) % 0.38/0.61 (define @t57 () (@quantifiers_skolemize @t55 0)) % 0.38/0.61 (define @t58 () (tptp.intersection_point @t57 @t56)) % 0.38/0.61 (define @t59 () (@quantifiers_skolemize @t55 3)) % 0.38/0.61 (define @t60 () (@quantifiers_skolemize @t55 2)) % 0.38/0.61 (define @t61 () (tptp.intersection_point @t60 @t59)) % 0.38/0.61 (define @t62 () (and (not @t20) (not @t19))) % 0.38/0.61 (define @t63 () (not @t43)) % 0.38/0.61 (define @t64 () (or @t53 @t52 @t63)) % 0.38/0.61 (define @t65 () (tptp.apart_point_and_line @t61 @t56)) % 0.38/0.61 (define @t66 () (tptp.apart_point_and_line @t61 @t57)) % 0.38/0.61 (define @t67 () (and (not (tptp.apart_point_and_line @t58 @t60)) (not (tptp.apart_point_and_line @t58 @t59)))) % 0.38/0.61 (define @t68 () (tptp.convergent_lines @t60 @t59)) % 0.38/0.61 (define @t69 () (not @t68)) % 0.38/0.61 (define @t70 () (tptp.convergent_lines @t57 @t56)) % 0.38/0.61 (define @t71 () (not @t70)) % 0.38/0.61 (define @t72 () (or @t71 @t69 @t67 @t66 @t65)) % 0.38/0.61 (define @t73 () (@list true)) % 0.38/0.61 (define @t74 () (@list @t72)) % 0.38/0.61 (define @t75 () (tptp.distinct_points @t58 @t61)) % 0.38/0.61 (define @t76 () (or @t69 @t67 @t75)) % 0.38/0.61 (define @t77 () (@list false true false)) % 0.38/0.61 (define @t78 () (tptp.distinct_points @t61 @t58)) % 0.38/0.61 (define @t79 () (tptp.distinct_points @t58 @t58)) % 0.38/0.61 (define @t80 () (not @t75)) % 0.38/0.61 (define @t81 () (or @t80 @t79 @t78)) % 0.38/0.61 (define @t82 () (not @t14)) % 0.38/0.61 (define @t83 () (tptp.distinct_lines @t57 @t56)) % 0.38/0.61 (define @t84 () (or @t71 @t83)) % 0.38/0.61 (define @t85 () (tptp.distinct_lines @t56 @t57)) % 0.38/0.61 (define @t86 () (tptp.distinct_lines @t57 @t57)) % 0.38/0.61 (define @t87 () (not @t83)) % 0.38/0.61 (define @t88 () (or @t87 @t86 @t85)) % 0.38/0.61 (define @t89 () (tptp.apart_point_and_line @t58 @t56)) % 0.38/0.61 (define @t90 () (not @t89)) % 0.38/0.61 (define @t91 () (tptp.apart_point_and_line @t58 @t57)) % 0.38/0.61 (define @t92 () (not @t91)) % 0.38/0.61 (define @t93 () (and @t92 @t90)) % 0.38/0.61 (define @t94 () (or @t71 @t93 @t79)) % 0.38/0.61 (define @t95 () (not @t93)) % 0.38/0.61 (define @t96 () (@list false)) % 0.38/0.61 (define @t97 () (@list @t93)) % 0.38/0.61 (define @t98 () (not @t85)) % 0.38/0.61 (define @t99 () (not @t78)) % 0.38/0.61 (define @t100 () (or @t99 @t98 @t65 @t66 @t89 @t91)) % 0.38/0.61 (define @t101 () (not @t100)) % 0.38/0.61 (define @t102 () (forall @t33 @t50)) % 0.38/0.61 (assume @p1 (forall @t2 (not (tptp.distinct_points @t1 @t1)))) % 0.38/0.61 (assume @p2 (forall @t2 (not (tptp.distinct_lines @t1 @t1)))) % 0.38/0.61 (assume @p3 (forall @t2 (not (tptp.convergent_lines @t1 @t1)))) % 0.38/0.61 (assume @p4 @t10) % 0.38/0.61 (assume @p5 @t15) % 0.38/0.61 (assume @p6 (forall @t9 (=> @t16 (or (tptp.convergent_lines @t1 @t3) (tptp.convergent_lines @t4 @t3))))) % 0.38/0.61 (assume @p7 (forall @t9 (=> @t8 (=> (tptp.apart_point_and_line @t3 (tptp.line_connecting @t1 @t4)) (and (tptp.distinct_points @t3 @t1) (tptp.distinct_points @t3 @t4)))))) % 0.38/0.61 (assume @p8 @t23) % 0.38/0.61 (assume @p9 @t34) % 0.38/0.61 (assume @p10 (forall @t9 (=> @t35 (or @t6 @t19)))) % 0.38/0.61 (assume @p11 (forall @t9 (=> @t35 (or @t11 (tptp.apart_point_and_line @t1 @t3))))) % 0.38/0.61 (assume @p12 @t36) % 0.38/0.61 (assume @p13 @t47) % 0.38/0.61 (assume @p14 true) % 0.38/0.61 (step @p15 :rule aci_norm :args ((= (or (or @t49 @t48) @t30) @t50))) % 0.38/0.61 (step @p16 :rule refl :args (@t30)) % 0.38/0.61 (step @p17 :rule bool-and-de-morgan :args (@t8 @t31 true)) % 0.38/0.61 (step @p18 :rule nary_cong :premises (@p17 @p16) :args ((or (not @t32) @t30))) % 0.38/0.61 (step @p19 :rule trans :premises (@p18 @p15)) % 0.38/0.61 (step @p20 :rule bool-impl-elim :args (@t32 @t30)) % 0.38/0.61 (step @p21 :rule trans :premises (@p20 @p19)) % 0.38/0.61 (step @p22 :rule cong :premises (@p21) :args (@t34)) % 0.38/0.61 (step @p23 :rule eq_resolve :premises (@p9 @p22)) % 0.38/0.61 (step @p24 :rule aci_norm :args ((= (or @t49 @t7) (or @t49 @t6 @t5)))) % 0.38/0.61 (step @p25 :rule bool-impl-elim :args (@t8 @t7)) % 0.38/0.61 (step @p26 :rule trans :premises (@p25 @p24)) % 0.38/0.61 (step @p27 :rule cong :premises (@p26) :args (@t10)) % 0.38/0.61 (step @p28 :rule eq_resolve :premises (@p4 @p27)) % 0.38/0.61 (step @p29 :rule instantiate :premises (@p28) :args ((@list @t58 @t61 @t58))) % 0.38/0.61 (step @p30 :rule aci_norm :args ((= (or @t53 (or @t62 @t18)) (or @t53 @t62 @t18)))) % 0.38/0.61 (step @p31 :rule refl :args (@t18)) % 0.38/0.61 (step @p32 :rule bool-or-de-morgan :args (@t20 @t19 false)) % 0.38/0.61 (step @p33 :rule nary_cong :premises (@p32 @p31) :args ((or (not @t21) @t18))) % 0.38/0.61 (step @p34 :rule bool-impl-elim :args (@t21 @t18)) % 0.38/0.61 (step @p35 :rule trans :premises (@p34 @p33)) % 0.38/0.61 (step @p36 :rule refl :args (@t53)) % 0.38/0.61 (step @p37 :rule nary_cong :premises (@p36 @p35) :args ((or @t53 @t22))) % 0.38/0.61 (step @p38 :rule trans :premises (@p37 @p30)) % 0.38/0.61 (step @p39 :rule bool-impl-elim :args (@t16 @t22)) % 0.38/0.61 (step @p40 :rule trans :premises (@p39 @p38)) % 0.38/0.61 (step @p41 :rule cong :premises (@p40) :args (@t23)) % 0.38/0.61 (step @p42 :rule eq_resolve :premises (@p8 @p41)) % 0.38/0.61 (step @p43 :rule instantiate :premises (@p42) :args ((@list @t60 @t59 @t58))) % 0.38/0.61 (step @p44 :rule aci_norm :args ((= (or (or @t53 @t52 @t51) @t40) @t54))) % 0.38/0.61 (step @p45 :rule refl :args (@t40)) % 0.38/0.61 (step @p46 :rule bool-or-de-morgan :args (@t42 @t41 false)) % 0.38/0.61 (step @p47 :rule refl :args (@t52)) % 0.38/0.61 (step @p48 :rule nary_cong :premises (@p36 @p47 @p46) :args (@t64)) % 0.38/0.61 (step @p49 :rule aci_norm :args ((= (or @t53 (or @t52 @t63)) @t64))) % 0.38/0.61 (step @p50 :rule bool-and-de-morgan :args (@t44 @t43 true)) % 0.38/0.61 (step @p51 :rule nary_cong :premises (@p36 @p50) :args ((or @t53 (not (and @t44 @t43))))) % 0.38/0.61 (step @p52 :rule bool-and-de-morgan :args (@t16 @t44 (and @t43))) % 0.38/0.61 (step @p53 :rule trans :premises (@p52 @p51)) % 0.38/0.61 (step @p54 :rule trans :premises (@p53 @p49)) % 0.38/0.61 (step @p55 :rule trans :premises (@p54 @p48)) % 0.38/0.61 (step @p56 :rule nary_cong :premises (@p55 @p45) :args ((or (not @t45) @t40))) % 0.38/0.61 (step @p57 :rule trans :premises (@p56 @p44)) % 0.38/0.61 (step @p58 :rule bool-impl-elim :args (@t45 @t40)) % 0.38/0.61 (step @p59 :rule trans :premises (@p58 @p57)) % 0.38/0.61 (step @p60 :rule cong :premises (@p59) :args (@t46)) % 0.38/0.61 (step @p61 :rule cong :premises (@p60) :args (@t47)) % 0.38/0.61 (step @p62 :rule eq_resolve :premises (@p13 @p61)) % 0.38/0.61 (step @p63 :rule skolemize :premises (@p62)) % 0.38/0.61 (step @p64 :rule cnf_or_neg :args (@t72 2)) % 0.38/0.61 (step @p65 :rule chain_m_resolution :premises (@p64 @p63) :args ((not @t67) @t73 @t74)) % 0.38/0.61 (step @p66 :rule bool-double-not-elim :args (@t68)) % 0.38/0.61 (step @p67 :rule refl :args (@t72)) % 0.38/0.61 (step @p68 :rule nary_cong :premises (@p67 @p66) :args ((or @t72 (not @t69)))) % 0.38/0.61 (step @p69 :rule cnf_or_neg :args (@t72 1)) % 0.38/0.61 (step @p70 :rule eq_resolve :premises (@p69 @p68)) % 0.38/0.61 (step @p71 :rule reordering :premises (@p70) :args ((or @t68 @t72))) % 0.38/0.61 (step @p72 :rule chain_m_resolution :premises (@p71 @p63) :args (@t68 @t73 @t74)) % 0.38/0.61 (step @p73 :rule cnf_or_pos :args (@t76)) % 0.38/0.61 (step @p74 :rule reordering :premises (@p73) :args ((or @t69 @t67 @t75 (not @t76)))) % 0.38/0.61 (step @p75 :rule chain_m_resolution :premises (@p74 @p72 @p65 @p43) :args (@t75 @t77 (@list @t68 @t67 @t76))) % 0.38/0.61 (step @p76 :rule instantiate :premises (@p1) :args ((@list @t58))) % 0.38/0.61 (step @p77 :rule cnf_or_pos :args (@t81)) % 0.38/0.61 (step @p78 :rule reordering :premises (@p77) :args ((or @t79 @t80 @t78 (not @t81)))) % 0.38/0.61 (step @p79 :rule chain_m_resolution :premises (@p78 @p76 @p75 @p29) :args (@t78 (@list true false false) (@list @t79 @t75 @t81))) % 0.38/0.61 (step @p80 :rule aci_norm :args ((= (or @t82 @t13) (or @t82 @t12 @t11)))) % 0.38/0.61 (step @p81 :rule bool-impl-elim :args (@t14 @t13)) % 0.38/0.61 (step @p82 :rule trans :premises (@p81 @p80)) % 0.38/0.61 (step @p83 :rule cong :premises (@p82) :args (@t15)) % 0.38/0.61 (step @p84 :rule eq_resolve :premises (@p5 @p83)) % 0.38/0.61 (step @p85 :rule instantiate :premises (@p84) :args ((@list @t57 @t56 @t57))) % 0.38/0.61 (step @p86 :rule instantiate :premises (@p2) :args ((@list @t57))) % 0.38/0.61 (step @p87 :rule bool-impl-elim :args (@t16 @t14)) % 0.38/0.61 (step @p88 :rule cong :premises (@p87) :args (@t36)) % 0.38/0.61 (step @p89 :rule eq_resolve :premises (@p12 @p88)) % 0.38/0.61 (step @p90 :rule instantiate :premises (@p89) :args ((@list @t57 @t56))) % 0.38/0.61 (step @p91 :rule bool-double-not-elim :args (@t70)) % 0.38/0.61 (step @p92 :rule nary_cong :premises (@p67 @p91) :args ((or @t72 (not @t71)))) % 0.38/0.61 (step @p93 :rule cnf_or_neg :args (@t72 0)) % 0.38/0.61 (step @p94 :rule eq_resolve :premises (@p93 @p92)) % 0.38/0.61 (step @p95 :rule reordering :premises (@p94) :args ((or @t70 @t72))) % 0.38/0.61 (step @p96 :rule chain_m_resolution :premises (@p95 @p63) :args (@t70 @t73 @t74)) % 0.38/0.61 (step @p97 :rule cnf_or_pos :args (@t84)) % 0.38/0.61 (step @p98 :rule reordering :premises (@p97) :args ((or @t71 @t83 (not @t84)))) % 0.38/0.61 (step @p99 :rule chain_m_resolution :premises (@p98 @p96 @p90) :args (@t83 (@list false false) (@list @t70 @t84))) % 0.38/0.61 (step @p100 :rule cnf_or_pos :args (@t88)) % 0.38/0.61 (step @p101 :rule reordering :premises (@p100) :args ((or @t87 @t86 @t85 (not @t88)))) % 0.38/0.61 (step @p102 :rule chain_m_resolution :premises (@p101 @p99 @p86 @p85) :args (@t85 @t77 (@list @t83 @t86 @t88))) % 0.38/0.61 (step @p103 :rule instantiate :premises (@p42) :args ((@list @t57 @t56 @t58))) % 0.38/0.61 (step @p104 :rule cnf_or_pos :args (@t94)) % 0.38/0.61 (step @p105 :rule reordering :premises (@p104) :args ((or @t71 @t79 @t93 (not @t94)))) % 0.38/0.61 (step @p106 :rule chain_m_resolution :premises (@p105 @p96 @p76 @p103) :args (@t93 @t77 (@list @t70 @t79 @t94))) % 0.38/0.61 (step @p107 :rule cnf_and_pos :args (@t93 1)) % 0.38/0.61 (step @p108 :rule reordering :premises (@p107) :args ((or @t90 @t95))) % 0.38/0.61 (step @p109 :rule chain_m_resolution :premises (@p108 @p106) :args (@t90 @t96 @t97)) % 0.38/0.61 (step @p110 :rule cnf_and_pos :args (@t93 0)) % 0.38/0.61 (step @p111 :rule reordering :premises (@p110) :args ((or @t92 @t95))) % 0.38/0.61 (step @p112 :rule chain_m_resolution :premises (@p111 @p106) :args (@t92 @t96 @t97)) % 0.38/0.61 (step @p113 :rule cnf_or_neg :args (@t72 4)) % 0.38/0.61 (step @p114 :rule chain_m_resolution :premises (@p113 @p63) :args ((not @t65) @t73 @t74)) % 0.38/0.61 (step @p115 :rule cnf_or_neg :args (@t72 3)) % 0.38/0.61 (step @p116 :rule chain_m_resolution :premises (@p115 @p63) :args ((not @t66) @t73 @t74)) % 0.38/0.61 (step @p117 :rule cnf_or_pos :args (@t100)) % 0.38/0.61 (step @p118 :rule reordering :premises (@p117) :args ((or @t66 @t65 @t91 @t89 @t98 @t99 @t101))) % 0.38/0.61 (step @p119 :rule chain_m_resolution :premises (@p118 @p116 @p114 @p112 @p109 @p102 @p79) :args (@t101 (@list true true true true false false) (@list @t66 @t65 @t91 @t89 @t85 @t78))) % 0.38/0.62 (assume-push @p126 @t102) % 0.38/0.62 (step @p121 :rule instantiate :premises (@p23) :args ((@list @t61 @t58 @t56 @t57))) % 0.38/0.62 (step-pop @p127 :rule scope :premises (@p121)) % 0.38/0.62 (step @p122 :rule process_scope :premises (@p127) :args (@t100)) % 0.38/0.62 (step @p124 :rule implies_elim :premises (@p122)) % 0.38/0.62 (step @p125 false :rule chain_m_resolution :premises (@p124 @p119 @p23) :args (false (@list true false) (@list @t100 @t102))) % 0.38/0.62 ) % 0.38/0.62 % SZS output end Proof % 0.38/0.62 % cvc5 exiting %------------------------------------------------------------------------------