%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GEO175+3 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n014.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 08:16:33 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 : GEO175+3 : TPTP v9.2.1. Released v4.0.0. % 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 : n014.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 23:38:58 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----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 $$unsorted 0) % 0.38/0.61 (declare-const tptp.orthogonal_lines (-> $$unsorted $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.incident_point_and_line (-> $$unsorted $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.parallel_lines (-> $$unsorted $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.parallel_through_point (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.61 (declare-const tptp.equal_points (-> $$unsorted $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.orthogonal_through_point (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.61 (declare-const tptp.intersection_point (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.61 (declare-const tptp.line_connecting (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.61 (declare-const tptp.line (-> $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.apart_point_and_line (-> $$unsorted $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.unorthogonal_lines (-> $$unsorted $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.distinct_points (-> $$unsorted $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.distinct_lines (-> $$unsorted $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.point (-> $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.convergent_lines (-> $$unsorted $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.equal_lines (-> $$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 @t1 @t3)) % 0.38/0.61 (define @t6 () (tptp.distinct_points @t1 @t4)) % 0.38/0.61 (define @t7 () (@list @t1 @t4 @t3)) % 0.38/0.61 (define @t8 () (tptp.distinct_lines @t4 @t3)) % 0.38/0.61 (define @t9 () (tptp.distinct_lines @t1 @t4)) % 0.38/0.61 (define @t10 () (tptp.convergent_lines @t4 @t3)) % 0.38/0.61 (define @t11 () (tptp.convergent_lines @t1 @t3)) % 0.38/0.61 (define @t12 () (tptp.convergent_lines @t1 @t4)) % 0.38/0.61 (define @t13 () (tptp.line_connecting @t1 @t4)) % 0.38/0.61 (define @t14 () (@list @t1 @t4)) % 0.38/0.61 (define @t15 () (tptp.intersection_point @t1 @t4)) % 0.38/0.61 (define @t16 () (not (tptp.apart_point_and_line @t15 @t1))) % 0.38/0.61 (define @t17 () (forall @t14 (=> @t12 @t16))) % 0.38/0.61 (define @t18 () (not (tptp.apart_point_and_line @t15 @t4))) % 0.38/0.61 (define @t19 () (forall @t14 (=> @t12 @t18))) % 0.38/0.61 (define @t20 () (@var "V" $$unsorted)) % 0.38/0.61 (define @t21 () (tptp.apart_point_and_line @t4 @t20)) % 0.38/0.61 (define @t22 () (@var "U" $$unsorted)) % 0.38/0.61 (define @t23 () (tptp.apart_point_and_line @t4 @t22)) % 0.38/0.61 (define @t24 () (tptp.apart_point_and_line @t1 @t20)) % 0.38/0.61 (define @t25 () (tptp.apart_point_and_line @t1 @t22)) % 0.38/0.61 (define @t26 () (or @t25 @t24 @t23 @t21)) % 0.38/0.61 (define @t27 () (tptp.distinct_lines @t22 @t20)) % 0.38/0.61 (define @t28 () (and @t6 @t27)) % 0.38/0.61 (define @t29 () (@list @t1 @t4 @t22 @t20)) % 0.38/0.61 (define @t30 () (forall @t29 (=> @t28 @t26))) % 0.38/0.61 (define @t31 () (tptp.apart_point_and_line @t1 @t4)) % 0.38/0.61 (define @t32 () (tptp.apart_point_and_line @t1 @t3)) % 0.38/0.61 (define @t33 () (or @t8 @t11)) % 0.38/0.61 (define @t34 () (forall @t7 (=> @t12 @t33))) % 0.38/0.61 (define @t35 () (tptp.parallel_through_point @t4 @t1)) % 0.38/0.61 (define @t36 () (@var "M" $$unsorted)) % 0.38/0.61 (define @t37 () (@var "L" $$unsorted)) % 0.38/0.61 (define @t38 () (tptp.unorthogonal_lines @t37 @t36)) % 0.38/0.61 (define @t39 () (tptp.convergent_lines @t37 @t36)) % 0.38/0.61 (define @t40 () (@list @t37 @t36)) % 0.38/0.61 (define @t41 () (@var "N" $$unsorted)) % 0.38/0.61 (define @t42 () (tptp.unorthogonal_lines @t36 @t41)) % 0.38/0.61 (define @t43 () (tptp.convergent_lines @t36 @t41)) % 0.38/0.61 (define @t44 () (tptp.unorthogonal_lines @t37 @t41)) % 0.38/0.61 (define @t45 () (tptp.convergent_lines @t37 @t41)) % 0.38/0.61 (define @t46 () (@list @t37 @t36 @t41)) % 0.38/0.61 (define @t47 () (@var "A" $$unsorted)) % 0.38/0.61 (define @t48 () (tptp.orthogonal_through_point @t37 @t47)) % 0.38/0.61 (define @t49 () (@list @t47 @t37)) % 0.38/0.61 (define @t50 () (not @t38)) % 0.38/0.61 (define @t51 () (not @t39)) % 0.38/0.61 (define @t52 () (not @t43)) % 0.38/0.61 (define @t53 () (not @t44)) % 0.38/0.61 (define @t54 () (@var "B" $$unsorted)) % 0.38/0.61 (define @t55 () (tptp.point @t47)) % 0.38/0.61 (define @t56 () (tptp.line @t37)) % 0.38/0.61 (define @t57 () (and @t56 @t55)) % 0.38/0.61 (define @t58 () (@list @t37 @t47)) % 0.38/0.61 (define @t59 () (not @t6)) % 0.38/0.61 (define @t60 () (not @t12)) % 0.38/0.61 (define @t61 () (or @t25 @t24)) % 0.38/0.61 (define @t62 () (tptp.distinct_points @t1 (tptp.intersection_point @t22 @t20))) % 0.38/0.61 (define @t63 () (tptp.convergent_lines @t22 @t20)) % 0.38/0.61 (define @t64 () (and @t6 @t63 @t62)) % 0.38/0.61 (define @t65 () (forall @t29 (=> @t64 @t61))) % 0.38/0.61 (define @t66 () (not @t65)) % 0.38/0.61 (define @t67 () (not @t27)) % 0.38/0.61 (define @t68 () (or @t59 @t67 @t25 @t24 @t23 @t21)) % 0.38/0.61 (define @t69 () (not @t62)) % 0.38/0.61 (define @t70 () (not @t63)) % 0.38/0.61 (define @t71 () (or @t59 @t70 @t69 @t25 @t24)) % 0.38/0.61 (define @t72 () (forall @t29 @t71)) % 0.38/0.61 (define @t73 () (@quantifiers_skolemize @t72 2)) % 0.38/0.61 (define @t74 () (@quantifiers_skolemize @t72 3)) % 0.38/0.61 (define @t75 () (or @t59 @t70 @t69)) % 0.38/0.61 (define @t76 () (tptp.convergent_lines @t73 @t74)) % 0.38/0.61 (define @t77 () (@quantifiers_skolemize @t72 0)) % 0.38/0.61 (define @t78 () (tptp.apart_point_and_line @t77 @t74)) % 0.38/0.61 (define @t79 () (tptp.apart_point_and_line @t77 @t73)) % 0.38/0.61 (define @t80 () (tptp.intersection_point @t73 @t74)) % 0.38/0.61 (define @t81 () (tptp.distinct_points @t77 @t80)) % 0.38/0.61 (define @t82 () (not @t81)) % 0.38/0.61 (define @t83 () (not @t76)) % 0.38/0.61 (define @t84 () (or (not (tptp.distinct_points @t77 (@quantifiers_skolemize @t72 1))) @t83 @t82 @t79 @t78)) % 0.38/0.61 (define @t85 () (@list true)) % 0.38/0.61 (define @t86 () (@list @t84)) % 0.38/0.61 (define @t87 () (tptp.convergent_lines @t73 @t73)) % 0.38/0.61 (define @t88 () (tptp.distinct_lines @t74 @t73)) % 0.38/0.61 (define @t89 () (or @t83 @t88 @t87)) % 0.38/0.61 (define @t90 () (@list @t73 @t74)) % 0.38/0.61 (define @t91 () (tptp.apart_point_and_line @t80 @t74)) % 0.38/0.61 (define @t92 () (not @t91)) % 0.38/0.61 (define @t93 () (or @t83 @t92)) % 0.38/0.61 (define @t94 () (@list false false)) % 0.38/0.61 (define @t95 () (tptp.apart_point_and_line @t80 @t73)) % 0.38/0.61 (define @t96 () (not @t95)) % 0.38/0.61 (define @t97 () (or @t83 @t96)) % 0.38/0.61 (define @t98 () (not @t88)) % 0.38/0.61 (define @t99 () (or @t82 @t98 @t78 @t79 @t91 @t95)) % 0.38/0.61 (define @t100 () (not @t99)) % 0.38/0.61 (define @t101 () (forall @t29 @t68)) % 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 (forall @t7 (=> @t6 (or @t5 (tptp.distinct_points @t4 @t3))))) % 0.38/0.61 (assume @p5 (forall @t7 (=> @t9 (or (tptp.distinct_lines @t1 @t3) @t8)))) % 0.38/0.61 (assume @p6 (forall @t7 (=> @t12 (or @t11 @t10)))) % 0.38/0.61 (assume @p7 (forall @t14 (=> @t6 (not (tptp.apart_point_and_line @t1 @t13))))) % 0.38/0.61 (assume @p8 (forall @t14 (=> @t6 (not (tptp.apart_point_and_line @t4 @t13))))) % 0.38/0.61 (assume @p9 @t17) % 0.38/0.61 (assume @p10 @t19) % 0.38/0.61 (assume @p11 @t30) % 0.38/0.61 (assume @p12 (forall @t7 (=> @t31 (or @t5 (tptp.apart_point_and_line @t3 @t4))))) % 0.38/0.61 (assume @p13 (forall @t7 (=> @t31 (or @t8 @t32)))) % 0.38/0.61 (assume @p14 @t34) % 0.38/0.61 (assume @p15 (forall @t14 (=> @t9 @t12))) % 0.38/0.61 (assume @p16 (forall @t14 (not (tptp.convergent_lines @t35 @t4)))) % 0.38/0.61 (assume @p17 (forall @t14 (not (tptp.apart_point_and_line @t1 @t35)))) % 0.38/0.61 (assume @p18 (forall @t7 (=> @t8 (or @t31 @t32 @t10)))) % 0.38/0.61 (assume @p19 (forall @t40 (or @t39 @t38))) % 0.38/0.61 (assume @p20 (forall @t46 (=> (and @t39 @t38) (or (and @t45 @t44) (and @t43 @t42))))) % 0.38/0.61 (assume @p21 (forall @t49 (not (tptp.unorthogonal_lines @t48 @t37)))) % 0.38/0.61 (assume @p22 (forall @t49 (not (tptp.apart_point_and_line @t47 @t48)))) % 0.38/0.61 (assume @p23 (forall (@list @t47 @t37 @t36 @t41) (=> (tptp.distinct_lines @t37 @t36) (or (tptp.apart_point_and_line @t47 @t37) (tptp.apart_point_and_line @t47 @t36) @t44 @t42)))) % 0.38/0.61 (assume @p24 (forall @t40 (not (and @t51 @t50)))) % 0.38/0.61 (assume @p25 (forall @t46 (=> (and (or @t51 @t50) (or (not @t45) @t53)) (or @t52 (not @t42))))) % 0.38/0.61 (assume @p26 (forall @t46 (=> (and @t50 @t53) @t52))) % 0.38/0.61 (assume @p27 (forall (@list @t47 @t54) (=> (and @t55 (tptp.point @t54) (tptp.distinct_points @t47 @t54)) (tptp.line (tptp.line_connecting @t47 @t54))))) % 0.38/0.61 (assume @p28 (forall @t40 (=> (and @t56 (tptp.line @t36) @t39) (tptp.point (tptp.intersection_point @t37 @t36))))) % 0.38/0.61 (assume @p29 (forall @t58 (=> @t57 (tptp.line (tptp.parallel_through_point @t37 @t47))))) % 0.38/0.61 (assume @p30 (forall @t58 (=> @t57 (tptp.line @t48)))) % 0.38/0.61 (assume @p31 (forall @t14 (= (tptp.equal_points @t1 @t4) @t59))) % 0.38/0.61 (assume @p32 (forall @t14 (= (tptp.equal_lines @t1 @t4) (not @t9)))) % 0.38/0.61 (assume @p33 (forall @t14 (= (tptp.parallel_lines @t1 @t4) @t60))) % 0.38/0.61 (assume @p34 (forall @t14 (= (tptp.incident_point_and_line @t1 @t4) (not @t31)))) % 0.38/0.61 (assume @p35 (forall @t14 (= (tptp.orthogonal_lines @t1 @t4) (not (tptp.unorthogonal_lines @t1 @t4))))) % 0.38/0.61 (assume @p36 @t66) % 0.38/0.61 (assume @p37 true) % 0.38/0.61 (step @p38 :rule aci_norm :args ((= (or (or @t59 @t67) @t26) @t68))) % 0.38/0.61 (step @p39 :rule refl :args (@t26)) % 0.38/0.61 (step @p40 :rule bool-and-de-morgan :args (@t6 @t27 true)) % 0.38/0.61 (step @p41 :rule nary_cong :premises (@p40 @p39) :args ((or (not @t28) @t26))) % 0.38/0.61 (step @p42 :rule trans :premises (@p41 @p38)) % 0.38/0.61 (step @p43 :rule bool-impl-elim :args (@t28 @t26)) % 0.38/0.61 (step @p44 :rule trans :premises (@p43 @p42)) % 0.38/0.61 (step @p45 :rule cong :premises (@p44) :args (@t30)) % 0.38/0.61 (step @p46 :rule eq_resolve :premises (@p11 @p45)) % 0.38/0.61 (step @p47 :rule aci_norm :args ((= (or @t60 @t33) (or @t60 @t8 @t11)))) % 0.38/0.61 (step @p48 :rule bool-impl-elim :args (@t12 @t33)) % 0.38/0.61 (step @p49 :rule trans :premises (@p48 @p47)) % 0.38/0.61 (step @p50 :rule cong :premises (@p49) :args (@t34)) % 0.38/0.61 (step @p51 :rule eq_resolve :premises (@p14 @p50)) % 0.38/0.61 (step @p52 :rule instantiate :premises (@p51) :args ((@list @t73 @t74 @t73))) % 0.38/0.61 (step @p53 :rule instantiate :premises (@p3) :args ((@list @t73))) % 0.38/0.61 (step @p54 :rule aci_norm :args ((= (or @t75 @t61) @t71))) % 0.38/0.61 (step @p55 :rule refl :args (@t61)) % 0.38/0.61 (step @p56 :rule aci_norm :args ((= (or @t59 (or @t70 @t69)) @t75))) % 0.38/0.61 (step @p57 :rule bool-and-de-morgan :args (@t63 @t62 true)) % 0.38/0.61 (step @p58 :rule refl :args (@t59)) % 0.38/0.61 (step @p59 :rule nary_cong :premises (@p58 @p57) :args ((or @t59 (not (and @t63 @t62))))) % 0.38/0.61 (step @p60 :rule bool-and-de-morgan :args (@t6 @t63 (and @t62))) % 0.38/0.61 (step @p61 :rule trans :premises (@p60 @p59)) % 0.38/0.61 (step @p62 :rule trans :premises (@p61 @p56)) % 0.38/0.61 (step @p63 :rule nary_cong :premises (@p62 @p55) :args ((or (not @t64) @t61))) % 0.38/0.61 (step @p64 :rule trans :premises (@p63 @p54)) % 0.38/0.61 (step @p65 :rule bool-impl-elim :args (@t64 @t61)) % 0.38/0.61 (step @p66 :rule trans :premises (@p65 @p64)) % 0.38/0.61 (step @p67 :rule cong :premises (@p66) :args (@t65)) % 0.38/0.61 (step @p68 :rule cong :premises (@p67) :args (@t66)) % 0.38/0.61 (step @p69 :rule eq_resolve :premises (@p36 @p68)) % 0.38/0.61 (step @p70 :rule skolemize :premises (@p69)) % 0.38/0.61 (step @p71 :rule bool-double-not-elim :args (@t76)) % 0.38/0.61 (step @p72 :rule refl :args (@t84)) % 0.38/0.61 (step @p73 :rule nary_cong :premises (@p72 @p71) :args ((or @t84 (not @t83)))) % 0.38/0.61 (step @p74 :rule cnf_or_neg :args (@t84 1)) % 0.38/0.61 (step @p75 :rule eq_resolve :premises (@p74 @p73)) % 0.38/0.61 (step @p76 :rule reordering :premises (@p75) :args ((or @t76 @t84))) % 0.38/0.61 (step @p77 :rule chain_m_resolution :premises (@p76 @p70) :args (@t76 @t85 @t86)) % 0.38/0.61 (step @p78 :rule cnf_or_pos :args (@t89)) % 0.38/0.61 (step @p79 :rule reordering :premises (@p78) :args ((or @t83 @t87 @t88 (not @t89)))) % 0.38/0.61 (step @p80 :rule chain_m_resolution :premises (@p79 @p77 @p53 @p52) :args (@t88 (@list false true false) (@list @t76 @t87 @t89))) % 0.38/0.61 (step @p81 :rule bool-impl-elim :args (@t12 @t18)) % 0.38/0.61 (step @p82 :rule cong :premises (@p81) :args (@t19)) % 0.38/0.61 (step @p83 :rule eq_resolve :premises (@p10 @p82)) % 0.38/0.61 (step @p84 :rule instantiate :premises (@p83) :args (@t90)) % 0.38/0.61 (step @p85 :rule cnf_or_pos :args (@t93)) % 0.38/0.61 (step @p86 :rule reordering :premises (@p85) :args ((or @t83 @t92 (not @t93)))) % 0.38/0.61 (step @p87 :rule chain_m_resolution :premises (@p86 @p77 @p84) :args (@t92 @t94 (@list @t76 @t93))) % 0.38/0.61 (step @p88 :rule bool-impl-elim :args (@t12 @t16)) % 0.38/0.61 (step @p89 :rule cong :premises (@p88) :args (@t17)) % 0.38/0.61 (step @p90 :rule eq_resolve :premises (@p9 @p89)) % 0.38/0.61 (step @p91 :rule instantiate :premises (@p90) :args (@t90)) % 0.38/0.61 (step @p92 :rule cnf_or_pos :args (@t97)) % 0.38/0.61 (step @p93 :rule reordering :premises (@p92) :args ((or @t83 @t96 (not @t97)))) % 0.38/0.61 (step @p94 :rule chain_m_resolution :premises (@p93 @p77 @p91) :args (@t96 @t94 (@list @t76 @t97))) % 0.38/0.61 (step @p95 :rule cnf_or_neg :args (@t84 4)) % 0.38/0.61 (step @p96 :rule chain_m_resolution :premises (@p95 @p70) :args ((not @t78) @t85 @t86)) % 0.38/0.61 (step @p97 :rule cnf_or_neg :args (@t84 3)) % 0.38/0.61 (step @p98 :rule chain_m_resolution :premises (@p97 @p70) :args ((not @t79) @t85 @t86)) % 0.38/0.61 (step @p99 :rule bool-double-not-elim :args (@t81)) % 0.38/0.61 (step @p100 :rule nary_cong :premises (@p72 @p99) :args ((or @t84 (not @t82)))) % 0.38/0.61 (step @p101 :rule cnf_or_neg :args (@t84 2)) % 0.38/0.61 (step @p102 :rule eq_resolve :premises (@p101 @p100)) % 0.38/0.61 (step @p103 :rule reordering :premises (@p102) :args ((or @t81 @t84))) % 0.38/0.61 (step @p104 :rule chain_m_resolution :premises (@p103 @p70) :args (@t81 @t85 @t86)) % 0.38/0.61 (step @p105 :rule cnf_or_pos :args (@t99)) % 0.38/0.61 (step @p106 :rule reordering :premises (@p105) :args ((or @t82 @t79 @t78 @t95 @t91 @t98 @t100))) % 0.38/0.61 (step @p107 :rule chain_m_resolution :premises (@p106 @p104 @p98 @p96 @p94 @p87 @p80) :args (@t100 (@list false true true true true false) (@list @t81 @t79 @t78 @t95 @t91 @t88))) % 0.38/0.61 (assume-push @p114 @t101) % 0.38/0.61 (step @p109 :rule instantiate :premises (@p46) :args ((@list @t77 @t80 @t74 @t73))) % 0.38/0.61 (step-pop @p115 :rule scope :premises (@p109)) % 0.38/0.61 (step @p110 :rule process_scope :premises (@p115) :args (@t99)) % 0.38/0.61 (step @p112 :rule implies_elim :premises (@p110)) % 0.38/0.61 (step @p113 false :rule chain_m_resolution :premises (@p112 @p107 @p46) :args (false (@list true false) (@list @t99 @t101))) % 0.38/0.61 ) % 0.38/0.61 % SZS output end Proof % 0.38/0.61 % cvc5 exiting %------------------------------------------------------------------------------