%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GEO213+1 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n010.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 08:16:46 AM UTC 2026 % Result : Theorem 0.39s 0.60s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO213+1 : TPTP v9.2.1. Released v3.3.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n010.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 % 0.17/0.34 % CPUTime : % 0.34/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.39/0.60 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.39/0.60 % SZS status Theorem % 0.39/0.60 % SZS output start Proof % 0.39/0.60 ( % 0.39/0.60 (declare-sort $$unsorted 0) % 0.39/0.60 (declare-const tptp.unorthogonal_lines (-> $$unsorted $$unsorted Bool)) % 0.39/0.60 (declare-const tptp.parallel_through_point (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.60 (declare-const tptp.orthogonal_through_point (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.60 (declare-const tptp.intersection_point (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.60 (declare-const tptp.apart_point_and_line (-> $$unsorted $$unsorted Bool)) % 0.39/0.60 (declare-const tptp.line_connecting (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.60 (declare-const tptp.convergent_lines (-> $$unsorted $$unsorted Bool)) % 0.39/0.60 (declare-const tptp.distinct_lines (-> $$unsorted $$unsorted Bool)) % 0.39/0.60 (declare-const tptp.distinct_points (-> $$unsorted $$unsorted Bool)) % 0.39/0.60 (define @t1 () (@var "X" $$unsorted)) % 0.39/0.60 (define @t2 () (@list @t1)) % 0.39/0.60 (define @t3 () (forall @t2 (not (tptp.convergent_lines @t1 @t1)))) % 0.39/0.60 (define @t4 () (@var "Z" $$unsorted)) % 0.39/0.60 (define @t5 () (@var "Y" $$unsorted)) % 0.39/0.60 (define @t6 () (tptp.distinct_points @t1 @t4)) % 0.39/0.60 (define @t7 () (tptp.distinct_points @t1 @t5)) % 0.39/0.60 (define @t8 () (@list @t1 @t5 @t4)) % 0.39/0.60 (define @t9 () (tptp.distinct_lines @t5 @t4)) % 0.39/0.60 (define @t10 () (tptp.distinct_lines @t1 @t4)) % 0.39/0.60 (define @t11 () (or @t10 @t9)) % 0.39/0.60 (define @t12 () (tptp.distinct_lines @t1 @t5)) % 0.39/0.60 (define @t13 () (forall @t8 (=> @t12 @t11))) % 0.39/0.60 (define @t14 () (tptp.convergent_lines @t5 @t4)) % 0.39/0.60 (define @t15 () (tptp.convergent_lines @t1 @t4)) % 0.39/0.60 (define @t16 () (or @t15 @t14)) % 0.39/0.60 (define @t17 () (tptp.convergent_lines @t1 @t5)) % 0.39/0.60 (define @t18 () (forall @t8 (=> @t17 @t16))) % 0.39/0.60 (define @t19 () (tptp.line_connecting @t1 @t5)) % 0.39/0.60 (define @t20 () (@list @t1 @t5)) % 0.39/0.60 (define @t21 () (tptp.intersection_point @t1 @t5)) % 0.39/0.60 (define @t22 () (@var "V" $$unsorted)) % 0.39/0.60 (define @t23 () (@var "U" $$unsorted)) % 0.39/0.60 (define @t24 () (tptp.apart_point_and_line @t1 @t5)) % 0.39/0.60 (define @t25 () (tptp.apart_point_and_line @t1 @t4)) % 0.39/0.60 (define @t26 () (or @t9 @t15)) % 0.39/0.60 (define @t27 () (forall @t8 (=> @t17 @t26))) % 0.39/0.60 (define @t28 () (tptp.parallel_through_point @t5 @t1)) % 0.39/0.60 (define @t29 () (@var "M" $$unsorted)) % 0.39/0.60 (define @t30 () (@var "L" $$unsorted)) % 0.39/0.60 (define @t31 () (tptp.unorthogonal_lines @t30 @t29)) % 0.39/0.60 (define @t32 () (tptp.convergent_lines @t30 @t29)) % 0.39/0.60 (define @t33 () (@var "N" $$unsorted)) % 0.39/0.60 (define @t34 () (tptp.unorthogonal_lines @t29 @t33)) % 0.39/0.60 (define @t35 () (and (tptp.convergent_lines @t29 @t33) @t34)) % 0.39/0.60 (define @t36 () (tptp.unorthogonal_lines @t30 @t33)) % 0.39/0.60 (define @t37 () (and (tptp.convergent_lines @t30 @t33) @t36)) % 0.39/0.60 (define @t38 () (or @t37 @t35)) % 0.39/0.60 (define @t39 () (and @t32 @t31)) % 0.39/0.60 (define @t40 () (@list @t30 @t29 @t33)) % 0.39/0.60 (define @t41 () (forall @t40 (=> @t39 @t38))) % 0.39/0.60 (define @t42 () (@var "A" $$unsorted)) % 0.39/0.60 (define @t43 () (tptp.orthogonal_through_point @t30 @t42)) % 0.39/0.60 (define @t44 () (@list @t42 @t30)) % 0.39/0.60 (define @t45 () (tptp.distinct_lines @t30 @t33)) % 0.39/0.60 (define @t46 () (or @t45 @t34)) % 0.39/0.60 (define @t47 () (forall @t40 (=> @t31 @t46))) % 0.39/0.60 (define @t48 () (not @t47)) % 0.39/0.60 (define @t49 () (not @t17)) % 0.39/0.60 (define @t50 () (not @t31)) % 0.39/0.60 (define @t51 () (or @t50 @t45 @t34)) % 0.39/0.60 (define @t52 () (forall @t40 @t51)) % 0.39/0.60 (define @t53 () (@quantifiers_skolemize @t52 2)) % 0.39/0.60 (define @t54 () (@quantifiers_skolemize @t52 0)) % 0.39/0.60 (define @t55 () (@list @t53 @t54 @t53)) % 0.39/0.60 (define @t56 () (not @t32)) % 0.39/0.60 (define @t57 () (tptp.convergent_lines @t54 @t54)) % 0.39/0.60 (define @t58 () (and @t57 (tptp.unorthogonal_lines @t54 @t54))) % 0.39/0.60 (define @t59 () (not @t58)) % 0.39/0.60 (define @t60 () (@list true)) % 0.39/0.60 (define @t61 () (@quantifiers_skolemize @t52 1)) % 0.39/0.60 (define @t62 () (not @t12)) % 0.39/0.60 (define @t63 () (@list @t53)) % 0.39/0.60 (define @t64 () (tptp.unorthogonal_lines @t61 @t53)) % 0.39/0.60 (define @t65 () (tptp.distinct_lines @t54 @t53)) % 0.39/0.60 (define @t66 () (tptp.unorthogonal_lines @t54 @t61)) % 0.39/0.60 (define @t67 () (not @t66)) % 0.39/0.60 (define @t68 () (or @t67 @t65 @t64)) % 0.39/0.60 (define @t69 () (@list @t68)) % 0.39/0.60 (define @t70 () (tptp.distinct_lines @t53 @t53)) % 0.39/0.60 (define @t71 () (tptp.distinct_lines @t53 @t54)) % 0.39/0.60 (define @t72 () (not @t71)) % 0.39/0.60 (define @t73 () (or @t72 @t70 @t65)) % 0.39/0.60 (define @t74 () (tptp.convergent_lines @t61 @t53)) % 0.39/0.60 (define @t75 () (or @t74 @t64)) % 0.39/0.60 (define @t76 () (tptp.convergent_lines @t61 @t54)) % 0.39/0.60 (define @t77 () (not @t74)) % 0.39/0.60 (define @t78 () (or @t77 @t71 @t76)) % 0.39/0.60 (define @t79 () (tptp.convergent_lines @t54 @t61)) % 0.39/0.60 (define @t80 () (tptp.convergent_lines @t61 @t61)) % 0.39/0.60 (define @t81 () (not @t76)) % 0.39/0.60 (define @t82 () (or @t81 @t80 @t79)) % 0.39/0.60 (define @t83 () (@list true false false)) % 0.39/0.60 (define @t84 () (and @t74 @t64)) % 0.39/0.60 (define @t85 () (not @t84)) % 0.39/0.60 (define @t86 () (tptp.unorthogonal_lines @t54 @t53)) % 0.39/0.60 (define @t87 () (tptp.convergent_lines @t54 @t53)) % 0.39/0.60 (define @t88 () (and @t87 @t86)) % 0.39/0.60 (define @t89 () (not @t79)) % 0.39/0.60 (define @t90 () (or @t89 @t67 @t88 @t84)) % 0.39/0.60 (define @t91 () (not @t88)) % 0.39/0.60 (define @t92 () (@list false)) % 0.39/0.60 (define @t93 () (@list @t88)) % 0.39/0.60 (define @t94 () (tptp.convergent_lines @t53 @t54)) % 0.39/0.60 (define @t95 () (and @t94 (tptp.unorthogonal_lines @t53 @t54))) % 0.39/0.60 (define @t96 () (not @t86)) % 0.39/0.60 (define @t97 () (not @t87)) % 0.39/0.60 (define @t98 () (or @t97 @t96 @t58 @t95)) % 0.39/0.60 (define @t99 () (tptp.convergent_lines @t53 @t53)) % 0.39/0.60 (define @t100 () (not @t94)) % 0.39/0.60 (define @t101 () (or @t100 @t65 @t99)) % 0.39/0.60 (assume @p1 (forall @t2 (not (tptp.distinct_points @t1 @t1)))) % 0.39/0.60 (assume @p2 (forall @t2 (not (tptp.distinct_lines @t1 @t1)))) % 0.39/0.60 (assume @p3 @t3) % 0.39/0.60 (assume @p4 (forall @t8 (=> @t7 (or @t6 (tptp.distinct_points @t5 @t4))))) % 0.39/0.60 (assume @p5 @t13) % 0.39/0.60 (assume @p6 @t18) % 0.39/0.60 (assume @p7 (forall @t20 (=> @t7 (not (tptp.apart_point_and_line @t1 @t19))))) % 0.39/0.60 (assume @p8 (forall @t20 (=> @t7 (not (tptp.apart_point_and_line @t5 @t19))))) % 0.39/0.60 (assume @p9 (forall @t20 (=> @t17 (not (tptp.apart_point_and_line @t21 @t1))))) % 0.39/0.60 (assume @p10 (forall @t20 (=> @t17 (not (tptp.apart_point_and_line @t21 @t5))))) % 0.39/0.60 (assume @p11 (forall (@list @t1 @t5 @t23 @t22) (=> (and @t7 (tptp.distinct_lines @t23 @t22)) (or (tptp.apart_point_and_line @t1 @t23) (tptp.apart_point_and_line @t1 @t22) (tptp.apart_point_and_line @t5 @t23) (tptp.apart_point_and_line @t5 @t22))))) % 0.39/0.60 (assume @p12 (forall @t8 (=> @t24 (or @t6 (tptp.apart_point_and_line @t4 @t5))))) % 0.39/0.60 (assume @p13 (forall @t8 (=> @t24 (or @t9 @t25)))) % 0.39/0.60 (assume @p14 @t27) % 0.39/0.60 (assume @p15 (forall @t20 (not (tptp.convergent_lines @t28 @t5)))) % 0.39/0.60 (assume @p16 (forall @t20 (not (tptp.apart_point_and_line @t1 @t28)))) % 0.39/0.60 (assume @p17 (forall @t8 (=> @t9 (or @t24 @t25 @t14)))) % 0.39/0.60 (assume @p18 (forall (@list @t30 @t29) (or @t32 @t31))) % 0.39/0.60 (assume @p19 @t41) % 0.39/0.60 (assume @p20 (forall @t44 (not (tptp.unorthogonal_lines @t43 @t30)))) % 0.39/0.60 (assume @p21 (forall @t44 (not (tptp.apart_point_and_line @t42 @t43)))) % 0.39/0.60 (assume @p22 (forall (@list @t42 @t30 @t29 @t33) (=> (tptp.distinct_lines @t30 @t29) (or (tptp.apart_point_and_line @t42 @t30) (tptp.apart_point_and_line @t42 @t29) @t36 @t34)))) % 0.39/0.60 (assume @p23 @t48) % 0.39/0.60 (assume @p24 true) % 0.39/0.60 (step @p25 :rule aci_norm :args ((= (or @t49 @t26) (or @t49 @t9 @t15)))) % 0.39/0.60 (step @p26 :rule bool-impl-elim :args (@t17 @t26)) % 0.39/0.60 (step @p27 :rule trans :premises (@p26 @p25)) % 0.39/0.60 (step @p28 :rule cong :premises (@p27) :args (@t27)) % 0.39/0.60 (step @p29 :rule eq_resolve :premises (@p14 @p28)) % 0.39/0.60 (step @p30 :rule instantiate :premises (@p29) :args (@t55)) % 0.39/0.60 (step @p31 :rule aci_norm :args ((= (or (or @t56 @t50) @t38) (or @t56 @t50 @t37 @t35)))) % 0.39/0.60 (step @p32 :rule refl :args (@t38)) % 0.39/0.60 (step @p33 :rule bool-and-de-morgan :args (@t32 @t31 true)) % 0.39/0.60 (step @p34 :rule nary_cong :premises (@p33 @p32) :args ((or (not @t39) @t38))) % 0.39/0.60 (step @p35 :rule trans :premises (@p34 @p31)) % 0.39/0.60 (step @p36 :rule bool-impl-elim :args (@t39 @t38)) % 0.39/0.60 (step @p37 :rule trans :premises (@p36 @p35)) % 0.39/0.60 (step @p38 :rule cong :premises (@p37) :args (@t41)) % 0.39/0.60 (step @p39 :rule eq_resolve :premises (@p19 @p38)) % 0.39/0.60 (step @p40 :rule instantiate :premises (@p39) :args ((@list @t54 @t53 @t54))) % 0.39/0.60 (step @p41 :rule instantiate :premises (@p3) :args ((@list @t54))) % 0.39/0.60 (step @p42 :rule cnf_and_pos :args (@t58 0)) % 0.39/0.60 (step @p43 :rule reordering :premises (@p42) :args ((or @t57 @t59))) % 0.39/0.60 (step @p44 :rule chain_m_resolution :premises (@p43 @p41) :args (@t59 @t60 (@list @t57))) % 0.39/0.60 (step @p45 :rule instantiate :premises (@p39) :args ((@list @t54 @t61 @t53))) % 0.39/0.60 (step @p46 :rule aci_norm :args ((= (or @t49 @t16) (or @t49 @t15 @t14)))) % 0.39/0.60 (step @p47 :rule bool-impl-elim :args (@t17 @t16)) % 0.39/0.60 (step @p48 :rule trans :premises (@p47 @p46)) % 0.39/0.60 (step @p49 :rule cong :premises (@p48) :args (@t18)) % 0.39/0.60 (step @p50 :rule eq_resolve :premises (@p6 @p49)) % 0.39/0.60 (step @p51 :rule instantiate :premises (@p50) :args ((@list @t61 @t54 @t61))) % 0.39/0.60 (step @p52 :rule instantiate :premises (@p29) :args ((@list @t61 @t53 @t54))) % 0.39/0.60 (step @p53 :rule aci_norm :args ((= (or @t62 @t11) (or @t62 @t10 @t9)))) % 0.39/0.60 (step @p54 :rule bool-impl-elim :args (@t12 @t11)) % 0.39/0.60 (step @p55 :rule trans :premises (@p54 @p53)) % 0.39/0.60 (step @p56 :rule cong :premises (@p55) :args (@t13)) % 0.39/0.60 (step @p57 :rule eq_resolve :premises (@p5 @p56)) % 0.39/0.60 (step @p58 :rule instantiate :premises (@p57) :args (@t55)) % 0.39/0.60 (step @p59 :rule instantiate :premises (@p2) :args (@t63)) % 0.39/0.60 (step @p60 :rule aci_norm :args ((= (or @t50 @t46) @t51))) % 0.39/0.60 (step @p61 :rule bool-impl-elim :args (@t31 @t46)) % 0.39/0.60 (step @p62 :rule trans :premises (@p61 @p60)) % 0.39/0.60 (step @p63 :rule cong :premises (@p62) :args (@t47)) % 0.39/0.60 (step @p64 :rule cong :premises (@p63) :args (@t48)) % 0.39/0.60 (step @p65 :rule eq_resolve :premises (@p23 @p64)) % 0.39/0.60 (step @p66 :rule skolemize :premises (@p65)) % 0.39/0.60 (step @p67 :rule cnf_or_neg :args (@t68 1)) % 0.39/0.60 (step @p68 :rule chain_m_resolution :premises (@p67 @p66) :args ((not @t65) @t60 @t69)) % 0.39/0.60 (step @p69 :rule cnf_or_pos :args (@t73)) % 0.39/0.60 (step @p70 :rule reordering :premises (@p69) :args ((or @t65 @t70 @t72 (not @t73)))) % 0.39/0.60 (step @p71 :rule chain_m_resolution :premises (@p70 @p68 @p59 @p58) :args (@t72 (@list true true false) (@list @t65 @t70 @t73))) % 0.39/0.60 (step @p72 :rule instantiate :premises (@p18) :args ((@list @t61 @t53))) % 0.39/0.60 (step @p73 :rule cnf_or_neg :args (@t68 2)) % 0.39/0.60 (step @p74 :rule chain_m_resolution :premises (@p73 @p66) :args ((not @t64) @t60 @t69)) % 0.39/0.60 (step @p75 :rule cnf_or_pos :args (@t75)) % 0.39/0.60 (step @p76 :rule reordering :premises (@p75) :args ((or @t64 @t74 (not @t75)))) % 0.39/0.60 (step @p77 :rule chain_m_resolution :premises (@p76 @p74 @p72) :args (@t74 (@list true false) (@list @t64 @t75))) % 0.39/0.60 (step @p78 :rule cnf_or_pos :args (@t78)) % 0.39/0.60 (step @p79 :rule reordering :premises (@p78) :args ((or @t77 @t76 @t71 (not @t78)))) % 0.39/0.60 (step @p80 :rule chain_m_resolution :premises (@p79 @p77 @p71 @p52) :args (@t76 (@list false true false) (@list @t74 @t71 @t78))) % 0.39/0.60 (step @p81 :rule instantiate :premises (@p3) :args ((@list @t61))) % 0.39/0.60 (step @p82 :rule cnf_or_pos :args (@t82)) % 0.39/0.60 (step @p83 :rule reordering :premises (@p82) :args ((or @t80 @t81 @t79 (not @t82)))) % 0.39/0.60 (step @p84 :rule chain_m_resolution :premises (@p83 @p81 @p80 @p51) :args (@t79 @t83 (@list @t80 @t76 @t82))) % 0.39/0.60 (step @p85 :rule cnf_and_pos :args (@t84 1)) % 0.39/0.60 (step @p86 :rule reordering :premises (@p85) :args ((or @t64 @t85))) % 0.39/0.60 (step @p87 :rule chain_m_resolution :premises (@p86 @p74) :args (@t85 @t60 (@list @t64))) % 0.39/0.60 (step @p88 :rule bool-double-not-elim :args (@t66)) % 0.39/0.60 (step @p89 :rule refl :args (@t68)) % 0.39/0.60 (step @p90 :rule nary_cong :premises (@p89 @p88) :args ((or @t68 (not @t67)))) % 0.39/0.60 (step @p91 :rule cnf_or_neg :args (@t68 0)) % 0.39/0.60 (step @p92 :rule eq_resolve :premises (@p91 @p90)) % 0.39/0.60 (step @p93 :rule reordering :premises (@p92) :args ((or @t66 @t68))) % 0.39/0.60 (step @p94 :rule chain_m_resolution :premises (@p93 @p66) :args (@t66 @t60 @t69)) % 0.39/0.60 (step @p95 :rule cnf_or_pos :args (@t90)) % 0.39/0.60 (step @p96 :rule reordering :premises (@p95) :args ((or @t67 @t84 @t89 @t88 (not @t90)))) % 0.39/0.60 (step @p97 :rule chain_m_resolution :premises (@p96 @p94 @p87 @p84 @p45) :args (@t88 (@list false true false false) (@list @t66 @t84 @t79 @t90))) % 0.39/0.60 (step @p98 :rule cnf_and_pos :args (@t88 1)) % 0.39/0.60 (step @p99 :rule reordering :premises (@p98) :args ((or @t86 @t91))) % 0.39/0.60 (step @p100 :rule chain_m_resolution :premises (@p99 @p97) :args (@t86 @t92 @t93)) % 0.39/0.60 (step @p101 :rule cnf_and_pos :args (@t88 0)) % 0.39/0.60 (step @p102 :rule reordering :premises (@p101) :args ((or @t87 @t91))) % 0.39/0.60 (step @p103 :rule chain_m_resolution :premises (@p102 @p97) :args (@t87 @t92 @t93)) % 0.39/0.60 (step @p104 :rule cnf_or_pos :args (@t98)) % 0.39/0.60 (step @p105 :rule reordering :premises (@p104) :args ((or @t97 @t96 @t58 @t95 (not @t98)))) % 0.39/0.60 (step @p106 :rule chain_m_resolution :premises (@p105 @p103 @p100 @p44 @p40) :args (@t95 (@list false false true false) (@list @t87 @t86 @t58 @t98))) % 0.39/0.60 (step @p107 :rule cnf_and_pos :args (@t95 0)) % 0.39/0.60 (step @p108 :rule reordering :premises (@p107) :args ((or @t94 (not @t95)))) % 0.39/0.60 (step @p109 :rule chain_m_resolution :premises (@p108 @p106) :args (@t94 @t92 (@list @t95))) % 0.39/0.60 (step @p110 :rule cnf_or_pos :args (@t101)) % 0.39/0.60 (step @p111 :rule reordering :premises (@p110) :args ((or @t65 @t99 @t100 (not @t101)))) % 0.39/0.60 (step @p112 :rule chain_m_resolution :premises (@p111 @p68 @p109 @p30) :args (@t99 @t83 (@list @t65 @t94 @t101))) % 0.39/0.60 (assume-push @p119 @t3) % 0.39/0.60 (step @p114 :rule instantiate :premises (@p3) :args (@t63)) % 0.39/0.60 (step-pop @p120 :rule scope :premises (@p114)) % 0.39/0.60 (step @p115 :rule process_scope :premises (@p120) :args ((not @t99))) % 0.39/0.60 (step @p117 :rule implies_elim :premises (@p115)) % 0.39/0.60 (step @p118 false :rule chain_m_resolution :premises (@p117 @p112 @p3) :args (false (@list false false) (@list @t99 @t3))) % 0.39/0.60 ) % 0.39/0.60 % SZS output end Proof % 0.39/0.60 % cvc5 exiting %------------------------------------------------------------------------------