%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GEO174+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 : n023.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 08:16:32 AM UTC 2026 % Result : Theorem 0.37s 0.58s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO174+3 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n023.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 23:39:13 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.58 % SZS status Theorem % 0.37/0.58 % SZS output start Proof % 0.37/0.58 ( % 0.37/0.58 (declare-sort $$unsorted 0) % 0.37/0.58 (declare-const tptp.orthogonal_lines (-> $$unsorted $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.incident_point_and_line (-> $$unsorted $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.parallel_lines (-> $$unsorted $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.parallel_through_point (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.equal_points (-> $$unsorted $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.orthogonal_through_point (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.intersection_point (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.line_connecting (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.line (-> $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.apart_point_and_line (-> $$unsorted $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.unorthogonal_lines (-> $$unsorted $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.distinct_points (-> $$unsorted $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.distinct_lines (-> $$unsorted $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.point (-> $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.convergent_lines (-> $$unsorted $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.equal_lines (-> $$unsorted $$unsorted Bool)) % 0.37/0.58 (define @t1 () (@var "X" $$unsorted)) % 0.37/0.58 (define @t2 () (@list @t1)) % 0.37/0.58 (define @t3 () (@var "Z" $$unsorted)) % 0.37/0.58 (define @t4 () (@var "Y" $$unsorted)) % 0.37/0.58 (define @t5 () (tptp.distinct_points @t1 @t3)) % 0.37/0.58 (define @t6 () (tptp.distinct_points @t1 @t4)) % 0.37/0.58 (define @t7 () (@list @t1 @t4 @t3)) % 0.37/0.58 (define @t8 () (tptp.distinct_lines @t4 @t3)) % 0.37/0.58 (define @t9 () (tptp.distinct_lines @t1 @t4)) % 0.37/0.58 (define @t10 () (tptp.convergent_lines @t4 @t3)) % 0.37/0.58 (define @t11 () (tptp.convergent_lines @t1 @t3)) % 0.37/0.58 (define @t12 () (tptp.convergent_lines @t1 @t4)) % 0.37/0.58 (define @t13 () (tptp.line_connecting @t1 @t4)) % 0.37/0.58 (define @t14 () (not (tptp.apart_point_and_line @t1 @t13))) % 0.37/0.58 (define @t15 () (@list @t1 @t4)) % 0.37/0.58 (define @t16 () (forall @t15 (=> @t6 @t14))) % 0.37/0.58 (define @t17 () (not (tptp.apart_point_and_line @t4 @t13))) % 0.37/0.58 (define @t18 () (forall @t15 (=> @t6 @t17))) % 0.37/0.58 (define @t19 () (tptp.intersection_point @t1 @t4)) % 0.37/0.58 (define @t20 () (@var "V" $$unsorted)) % 0.37/0.58 (define @t21 () (@var "U" $$unsorted)) % 0.37/0.58 (define @t22 () (tptp.apart_point_and_line @t4 @t21)) % 0.37/0.58 (define @t23 () (tptp.apart_point_and_line @t1 @t21)) % 0.37/0.58 (define @t24 () (@list @t1 @t4 @t21 @t20)) % 0.37/0.58 (define @t25 () (tptp.apart_point_and_line @t1 @t4)) % 0.37/0.58 (define @t26 () (tptp.apart_point_and_line @t1 @t3)) % 0.37/0.58 (define @t27 () (or @t8 @t26)) % 0.37/0.58 (define @t28 () (forall @t7 (=> @t25 @t27))) % 0.37/0.58 (define @t29 () (tptp.parallel_through_point @t4 @t1)) % 0.37/0.58 (define @t30 () (@var "M" $$unsorted)) % 0.37/0.58 (define @t31 () (@var "L" $$unsorted)) % 0.37/0.58 (define @t32 () (tptp.unorthogonal_lines @t31 @t30)) % 0.37/0.58 (define @t33 () (tptp.convergent_lines @t31 @t30)) % 0.37/0.58 (define @t34 () (@list @t31 @t30)) % 0.37/0.58 (define @t35 () (@var "N" $$unsorted)) % 0.37/0.58 (define @t36 () (tptp.unorthogonal_lines @t30 @t35)) % 0.37/0.58 (define @t37 () (tptp.convergent_lines @t30 @t35)) % 0.37/0.58 (define @t38 () (tptp.unorthogonal_lines @t31 @t35)) % 0.37/0.58 (define @t39 () (tptp.convergent_lines @t31 @t35)) % 0.37/0.58 (define @t40 () (@list @t31 @t30 @t35)) % 0.37/0.58 (define @t41 () (@var "A" $$unsorted)) % 0.37/0.58 (define @t42 () (tptp.orthogonal_through_point @t31 @t41)) % 0.37/0.58 (define @t43 () (@list @t41 @t31)) % 0.37/0.58 (define @t44 () (not @t32)) % 0.37/0.58 (define @t45 () (not @t33)) % 0.37/0.58 (define @t46 () (not @t37)) % 0.37/0.58 (define @t47 () (not @t38)) % 0.37/0.58 (define @t48 () (@var "B" $$unsorted)) % 0.37/0.58 (define @t49 () (tptp.point @t41)) % 0.37/0.58 (define @t50 () (tptp.line @t31)) % 0.37/0.58 (define @t51 () (and @t50 @t49)) % 0.37/0.58 (define @t52 () (@list @t31 @t41)) % 0.37/0.58 (define @t53 () (not @t6)) % 0.37/0.58 (define @t54 () (not @t25)) % 0.37/0.58 (define @t55 () (tptp.distinct_lines @t21 @t13)) % 0.37/0.58 (define @t56 () (or @t23 @t22)) % 0.37/0.58 (define @t57 () (tptp.convergent_lines @t21 @t20)) % 0.37/0.58 (define @t58 () (and @t6 @t57 @t56)) % 0.37/0.58 (define @t59 () (forall @t24 (=> @t58 @t55))) % 0.37/0.58 (define @t60 () (not @t59)) % 0.37/0.58 (define @t61 () (or @t54 @t8 @t26)) % 0.37/0.58 (define @t62 () (and (not @t23) (not @t22))) % 0.37/0.58 (define @t63 () (not @t57)) % 0.37/0.58 (define @t64 () (or @t53 @t63 @t62 @t55)) % 0.37/0.58 (define @t65 () (forall @t24 @t64)) % 0.37/0.58 (define @t66 () (@quantifiers_skolemize @t65 1)) % 0.37/0.58 (define @t67 () (@quantifiers_skolemize @t65 0)) % 0.37/0.58 (define @t68 () (@list @t67 @t66)) % 0.37/0.58 (define @t69 () (not @t56)) % 0.37/0.58 (define @t70 () (or @t53 @t63 @t69)) % 0.37/0.58 (define @t71 () (tptp.distinct_points @t67 @t66)) % 0.37/0.58 (define @t72 () (tptp.line_connecting @t67 @t66)) % 0.37/0.58 (define @t73 () (@quantifiers_skolemize @t65 2)) % 0.37/0.58 (define @t74 () (tptp.distinct_lines @t73 @t72)) % 0.37/0.58 (define @t75 () (tptp.apart_point_and_line @t66 @t73)) % 0.37/0.58 (define @t76 () (not @t75)) % 0.37/0.58 (define @t77 () (tptp.apart_point_and_line @t67 @t73)) % 0.37/0.58 (define @t78 () (not @t77)) % 0.37/0.58 (define @t79 () (and @t78 @t76)) % 0.37/0.58 (define @t80 () (not @t71)) % 0.37/0.58 (define @t81 () (or @t80 (not (tptp.convergent_lines @t73 (@quantifiers_skolemize @t65 3))) @t79 @t74)) % 0.37/0.58 (define @t82 () (@list true)) % 0.37/0.58 (define @t83 () (@list @t81)) % 0.37/0.58 (define @t84 () (tptp.apart_point_and_line @t67 @t72)) % 0.37/0.58 (define @t85 () (not @t84)) % 0.37/0.58 (define @t86 () (or @t80 @t85)) % 0.37/0.58 (define @t87 () (@list false false)) % 0.37/0.58 (define @t88 () (tptp.apart_point_and_line @t66 @t72)) % 0.37/0.58 (define @t89 () (not @t88)) % 0.37/0.58 (define @t90 () (or @t80 @t89)) % 0.37/0.58 (define @t91 () (or @t76 @t74 @t88)) % 0.37/0.58 (define @t92 () (or @t78 @t74 @t84)) % 0.37/0.58 (define @t93 () (not @t92)) % 0.37/0.58 (define @t94 () (forall @t7 @t61)) % 0.37/0.58 (assume @p1 (forall @t2 (not (tptp.distinct_points @t1 @t1)))) % 0.37/0.58 (assume @p2 (forall @t2 (not (tptp.distinct_lines @t1 @t1)))) % 0.37/0.58 (assume @p3 (forall @t2 (not (tptp.convergent_lines @t1 @t1)))) % 0.37/0.58 (assume @p4 (forall @t7 (=> @t6 (or @t5 (tptp.distinct_points @t4 @t3))))) % 0.37/0.58 (assume @p5 (forall @t7 (=> @t9 (or (tptp.distinct_lines @t1 @t3) @t8)))) % 0.37/0.58 (assume @p6 (forall @t7 (=> @t12 (or @t11 @t10)))) % 0.37/0.58 (assume @p7 @t16) % 0.37/0.58 (assume @p8 @t18) % 0.37/0.58 (assume @p9 (forall @t15 (=> @t12 (not (tptp.apart_point_and_line @t19 @t1))))) % 0.37/0.58 (assume @p10 (forall @t15 (=> @t12 (not (tptp.apart_point_and_line @t19 @t4))))) % 0.37/0.58 (assume @p11 (forall @t24 (=> (and @t6 (tptp.distinct_lines @t21 @t20)) (or @t23 (tptp.apart_point_and_line @t1 @t20) @t22 (tptp.apart_point_and_line @t4 @t20))))) % 0.37/0.58 (assume @p12 (forall @t7 (=> @t25 (or @t5 (tptp.apart_point_and_line @t3 @t4))))) % 0.37/0.58 (assume @p13 @t28) % 0.37/0.58 (assume @p14 (forall @t7 (=> @t12 (or @t8 @t11)))) % 0.37/0.58 (assume @p15 (forall @t15 (=> @t9 @t12))) % 0.37/0.58 (assume @p16 (forall @t15 (not (tptp.convergent_lines @t29 @t4)))) % 0.37/0.58 (assume @p17 (forall @t15 (not (tptp.apart_point_and_line @t1 @t29)))) % 0.37/0.58 (assume @p18 (forall @t7 (=> @t8 (or @t25 @t26 @t10)))) % 0.37/0.58 (assume @p19 (forall @t34 (or @t33 @t32))) % 0.37/0.58 (assume @p20 (forall @t40 (=> (and @t33 @t32) (or (and @t39 @t38) (and @t37 @t36))))) % 0.37/0.58 (assume @p21 (forall @t43 (not (tptp.unorthogonal_lines @t42 @t31)))) % 0.37/0.58 (assume @p22 (forall @t43 (not (tptp.apart_point_and_line @t41 @t42)))) % 0.37/0.58 (assume @p23 (forall (@list @t41 @t31 @t30 @t35) (=> (tptp.distinct_lines @t31 @t30) (or (tptp.apart_point_and_line @t41 @t31) (tptp.apart_point_and_line @t41 @t30) @t38 @t36)))) % 0.37/0.58 (assume @p24 (forall @t34 (not (and @t45 @t44)))) % 0.37/0.58 (assume @p25 (forall @t40 (=> (and (or @t45 @t44) (or (not @t39) @t47)) (or @t46 (not @t36))))) % 0.37/0.58 (assume @p26 (forall @t40 (=> (and @t44 @t47) @t46))) % 0.37/0.58 (assume @p27 (forall (@list @t41 @t48) (=> (and @t49 (tptp.point @t48) (tptp.distinct_points @t41 @t48)) (tptp.line (tptp.line_connecting @t41 @t48))))) % 0.37/0.58 (assume @p28 (forall @t34 (=> (and @t50 (tptp.line @t30) @t33) (tptp.point (tptp.intersection_point @t31 @t30))))) % 0.37/0.58 (assume @p29 (forall @t52 (=> @t51 (tptp.line (tptp.parallel_through_point @t31 @t41))))) % 0.37/0.58 (assume @p30 (forall @t52 (=> @t51 (tptp.line @t42)))) % 0.37/0.58 (assume @p31 (forall @t15 (= (tptp.equal_points @t1 @t4) @t53))) % 0.37/0.58 (assume @p32 (forall @t15 (= (tptp.equal_lines @t1 @t4) (not @t9)))) % 0.37/0.58 (assume @p33 (forall @t15 (= (tptp.parallel_lines @t1 @t4) (not @t12)))) % 0.37/0.58 (assume @p34 (forall @t15 (= (tptp.incident_point_and_line @t1 @t4) @t54))) % 0.37/0.58 (assume @p35 (forall @t15 (= (tptp.orthogonal_lines @t1 @t4) (not (tptp.unorthogonal_lines @t1 @t4))))) % 0.37/0.58 (assume @p36 @t60) % 0.37/0.58 (assume @p37 true) % 0.37/0.58 (step @p38 :rule aci_norm :args ((= (or @t54 @t27) @t61))) % 0.37/0.58 (step @p39 :rule bool-impl-elim :args (@t25 @t27)) % 0.37/0.58 (step @p40 :rule trans :premises (@p39 @p38)) % 0.37/0.58 (step @p41 :rule cong :premises (@p40) :args (@t28)) % 0.37/0.58 (step @p42 :rule eq_resolve :premises (@p13 @p41)) % 0.37/0.58 (step @p43 :rule bool-impl-elim :args (@t6 @t14)) % 0.37/0.58 (step @p44 :rule cong :premises (@p43) :args (@t16)) % 0.37/0.58 (step @p45 :rule eq_resolve :premises (@p7 @p44)) % 0.37/0.58 (step @p46 :rule instantiate :premises (@p45) :args (@t68)) % 0.37/0.58 (step @p47 :rule aci_norm :args ((= (or (or @t53 @t63 @t62) @t55) @t64))) % 0.37/0.58 (step @p48 :rule refl :args (@t55)) % 0.37/0.58 (step @p49 :rule bool-or-de-morgan :args (@t23 @t22 false)) % 0.37/0.58 (step @p50 :rule refl :args (@t63)) % 0.37/0.58 (step @p51 :rule refl :args (@t53)) % 0.37/0.58 (step @p52 :rule nary_cong :premises (@p51 @p50 @p49) :args (@t70)) % 0.37/0.58 (step @p53 :rule aci_norm :args ((= (or @t53 (or @t63 @t69)) @t70))) % 0.37/0.58 (step @p54 :rule bool-and-de-morgan :args (@t57 @t56 true)) % 0.37/0.58 (step @p55 :rule nary_cong :premises (@p51 @p54) :args ((or @t53 (not (and @t57 @t56))))) % 0.37/0.58 (step @p56 :rule bool-and-de-morgan :args (@t6 @t57 (and @t56))) % 0.37/0.58 (step @p57 :rule trans :premises (@p56 @p55)) % 0.37/0.58 (step @p58 :rule trans :premises (@p57 @p53)) % 0.37/0.58 (step @p59 :rule trans :premises (@p58 @p52)) % 0.37/0.58 (step @p60 :rule nary_cong :premises (@p59 @p48) :args ((or (not @t58) @t55))) % 0.37/0.58 (step @p61 :rule trans :premises (@p60 @p47)) % 0.37/0.58 (step @p62 :rule bool-impl-elim :args (@t58 @t55)) % 0.37/0.58 (step @p63 :rule trans :premises (@p62 @p61)) % 0.37/0.58 (step @p64 :rule cong :premises (@p63) :args (@t59)) % 0.37/0.58 (step @p65 :rule cong :premises (@p64) :args (@t60)) % 0.37/0.58 (step @p66 :rule eq_resolve :premises (@p36 @p65)) % 0.37/0.58 (step @p67 :rule skolemize :premises (@p66)) % 0.37/0.58 (step @p68 :rule bool-double-not-elim :args (@t71)) % 0.37/0.58 (step @p69 :rule refl :args (@t81)) % 0.37/0.58 (step @p70 :rule nary_cong :premises (@p69 @p68) :args ((or @t81 (not @t80)))) % 0.37/0.58 (step @p71 :rule cnf_or_neg :args (@t81 0)) % 0.37/0.58 (step @p72 :rule eq_resolve :premises (@p71 @p70)) % 0.37/0.58 (step @p73 :rule reordering :premises (@p72) :args ((or @t71 @t81))) % 0.37/0.58 (step @p74 :rule chain_m_resolution :premises (@p73 @p67) :args (@t71 @t82 @t83)) % 0.37/0.58 (step @p75 :rule cnf_or_pos :args (@t86)) % 0.37/0.58 (step @p76 :rule reordering :premises (@p75) :args ((or @t80 @t85 (not @t86)))) % 0.37/0.58 (step @p77 :rule chain_m_resolution :premises (@p76 @p74 @p46) :args (@t85 @t87 (@list @t71 @t86))) % 0.37/0.58 (step @p78 :rule cnf_or_neg :args (@t81 3)) % 0.37/0.58 (step @p79 :rule chain_m_resolution :premises (@p78 @p67) :args ((not @t74) @t82 @t83)) % 0.37/0.58 (step @p80 :rule cnf_or_neg :args (@t81 2)) % 0.37/0.58 (step @p81 :rule chain_m_resolution :premises (@p80 @p67) :args ((not @t79) @t82 @t83)) % 0.37/0.58 (step @p82 :rule instantiate :premises (@p42) :args ((@list @t66 @t73 @t72))) % 0.37/0.58 (step @p83 :rule bool-impl-elim :args (@t6 @t17)) % 0.37/0.58 (step @p84 :rule cong :premises (@p83) :args (@t18)) % 0.37/0.58 (step @p85 :rule eq_resolve :premises (@p8 @p84)) % 0.37/0.58 (step @p86 :rule instantiate :premises (@p85) :args (@t68)) % 0.37/0.58 (step @p87 :rule cnf_or_pos :args (@t90)) % 0.37/0.58 (step @p88 :rule reordering :premises (@p87) :args ((or @t80 @t89 (not @t90)))) % 0.37/0.58 (step @p89 :rule chain_m_resolution :premises (@p88 @p74 @p86) :args (@t89 @t87 (@list @t71 @t90))) % 0.37/0.58 (step @p90 :rule cnf_or_pos :args (@t91)) % 0.37/0.58 (step @p91 :rule reordering :premises (@p90) :args ((or @t76 @t74 @t88 (not @t91)))) % 0.37/0.58 (step @p92 :rule chain_m_resolution :premises (@p91 @p79 @p89 @p82) :args (@t76 (@list true true false) (@list @t74 @t88 @t91))) % 0.37/0.58 (step @p93 :rule bool-double-not-elim :args (@t75)) % 0.37/0.58 (step @p94 :rule bool-double-not-elim :args (@t77)) % 0.37/0.58 (step @p95 :rule refl :args (@t79)) % 0.37/0.58 (step @p96 :rule nary_cong :premises (@p95 @p94 @p93) :args ((or @t79 (not @t78) (not @t76)))) % 0.37/0.58 (step @p97 :rule cnf_and_neg :args (@t79)) % 0.37/0.58 (step @p98 :rule eq_resolve :premises (@p97 @p96)) % 0.37/0.58 (step @p99 :rule reordering :premises (@p98) :args ((or @t77 @t75 @t79))) % 0.37/0.58 (step @p100 :rule chain_m_resolution :premises (@p99 @p92 @p81) :args (@t77 (@list true true) (@list @t75 @t79))) % 0.37/0.58 (step @p101 :rule cnf_or_pos :args (@t92)) % 0.37/0.58 (step @p102 :rule reordering :premises (@p101) :args ((or @t78 @t74 @t84 @t93))) % 0.37/0.58 (step @p103 :rule chain_m_resolution :premises (@p102 @p100 @p79 @p77) :args (@t93 (@list false true true) (@list @t77 @t74 @t84))) % 0.37/0.58 (assume-push @p110 @t94) % 0.37/0.58 (step @p105 :rule instantiate :premises (@p42) :args ((@list @t67 @t73 @t72))) % 0.37/0.58 (step-pop @p111 :rule scope :premises (@p105)) % 0.37/0.58 (step @p106 :rule process_scope :premises (@p111) :args (@t92)) % 0.37/0.58 (step @p108 :rule implies_elim :premises (@p106)) % 0.37/0.58 (step @p109 false :rule chain_m_resolution :premises (@p108 @p103 @p42) :args (false (@list true false) (@list @t92 @t94))) % 0.37/0.58 ) % 0.37/0.58 % SZS output end Proof % 0.37/0.58 % cvc5 exiting %------------------------------------------------------------------------------