%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GEO213+2 : 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 : n019.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 0.44s 0.65s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO213+2 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n019.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Mon Jun 1 23:40:34 EDT 2026 % 0.17/0.35 % CPUTime : % 0.32/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.44/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.44/0.65 % SZS status Theorem % 0.44/0.65 % SZS output start Proof % 0.44/0.65 ( % 0.44/0.65 (declare-sort $$unsorted 0) % 0.44/0.65 (declare-const tptp.parallel_through_point (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.intersection_point (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.unorthogonal_lines (-> $$unsorted $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.apart_point_and_line (-> $$unsorted $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.line_connecting (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.convergent_lines (-> $$unsorted $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.distinct_lines (-> $$unsorted $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.orthogonal_through_point (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.distinct_points (-> $$unsorted $$unsorted Bool)) % 0.44/0.65 (define @t1 () (@var "X" $$unsorted)) % 0.44/0.65 (define @t2 () (@list @t1)) % 0.44/0.65 (define @t3 () (forall @t2 (not (tptp.distinct_lines @t1 @t1)))) % 0.44/0.65 (define @t4 () (@var "Z" $$unsorted)) % 0.44/0.65 (define @t5 () (@var "Y" $$unsorted)) % 0.44/0.65 (define @t6 () (tptp.distinct_points @t1 @t4)) % 0.44/0.65 (define @t7 () (tptp.distinct_points @t1 @t5)) % 0.44/0.65 (define @t8 () (@list @t1 @t5 @t4)) % 0.44/0.65 (define @t9 () (tptp.distinct_lines @t5 @t4)) % 0.44/0.65 (define @t10 () (tptp.distinct_lines @t1 @t4)) % 0.44/0.65 (define @t11 () (or @t10 @t9)) % 0.44/0.65 (define @t12 () (tptp.distinct_lines @t1 @t5)) % 0.44/0.65 (define @t13 () (forall @t8 (=> @t12 @t11))) % 0.44/0.65 (define @t14 () (tptp.convergent_lines @t5 @t4)) % 0.44/0.65 (define @t15 () (tptp.convergent_lines @t1 @t4)) % 0.44/0.65 (define @t16 () (or @t15 @t14)) % 0.44/0.65 (define @t17 () (tptp.convergent_lines @t1 @t5)) % 0.44/0.65 (define @t18 () (forall @t8 (=> @t17 @t16))) % 0.44/0.65 (define @t19 () (tptp.apart_point_and_line @t4 @t5)) % 0.44/0.65 (define @t20 () (@var "V" $$unsorted)) % 0.44/0.65 (define @t21 () (@var "U" $$unsorted)) % 0.44/0.65 (define @t22 () (tptp.apart_point_and_line @t1 @t5)) % 0.44/0.65 (define @t23 () (tptp.apart_point_and_line @t1 @t4)) % 0.44/0.65 (define @t24 () (@list @t1 @t5)) % 0.44/0.65 (define @t25 () (forall @t24 (=> @t17 @t12))) % 0.44/0.65 (define @t26 () (tptp.parallel_through_point @t5 @t1)) % 0.44/0.65 (define @t27 () (@var "M" $$unsorted)) % 0.44/0.65 (define @t28 () (@var "L" $$unsorted)) % 0.44/0.65 (define @t29 () (tptp.unorthogonal_lines @t28 @t27)) % 0.44/0.65 (define @t30 () (tptp.convergent_lines @t28 @t27)) % 0.44/0.65 (define @t31 () (@var "N" $$unsorted)) % 0.44/0.65 (define @t32 () (tptp.unorthogonal_lines @t27 @t31)) % 0.44/0.65 (define @t33 () (and (tptp.convergent_lines @t27 @t31) @t32)) % 0.44/0.65 (define @t34 () (tptp.unorthogonal_lines @t28 @t31)) % 0.44/0.65 (define @t35 () (and (tptp.convergent_lines @t28 @t31) @t34)) % 0.44/0.65 (define @t36 () (or @t35 @t33)) % 0.44/0.65 (define @t37 () (and @t30 @t29)) % 0.44/0.65 (define @t38 () (@list @t28 @t27 @t31)) % 0.44/0.65 (define @t39 () (forall @t38 (=> @t37 @t36))) % 0.44/0.65 (define @t40 () (@var "A" $$unsorted)) % 0.44/0.65 (define @t41 () (tptp.orthogonal_through_point @t28 @t40)) % 0.44/0.65 (define @t42 () (@list @t40 @t28)) % 0.44/0.65 (define @t43 () (tptp.distinct_lines @t28 @t31)) % 0.44/0.65 (define @t44 () (or @t43 @t32)) % 0.44/0.65 (define @t45 () (forall @t38 (=> @t29 @t44))) % 0.44/0.65 (define @t46 () (not @t45)) % 0.44/0.65 (define @t47 () (not @t12)) % 0.44/0.65 (define @t48 () (not @t29)) % 0.44/0.65 (define @t49 () (or @t48 @t43 @t32)) % 0.44/0.65 (define @t50 () (forall @t38 @t49)) % 0.44/0.65 (define @t51 () (@quantifiers_skolemize @t50 2)) % 0.44/0.65 (define @t52 () (@quantifiers_skolemize @t50 0)) % 0.44/0.65 (define @t53 () (not @t17)) % 0.44/0.65 (define @t54 () (@quantifiers_skolemize @t50 1)) % 0.44/0.65 (define @t55 () (not @t30)) % 0.44/0.65 (define @t56 () (tptp.unorthogonal_lines @t54 @t51)) % 0.44/0.65 (define @t57 () (tptp.distinct_lines @t52 @t51)) % 0.44/0.65 (define @t58 () (tptp.unorthogonal_lines @t52 @t54)) % 0.44/0.65 (define @t59 () (not @t58)) % 0.44/0.65 (define @t60 () (or @t59 @t57 @t56)) % 0.44/0.65 (define @t61 () (@list true)) % 0.44/0.65 (define @t62 () (@list @t60)) % 0.44/0.65 (define @t63 () (tptp.convergent_lines @t54 @t51)) % 0.44/0.65 (define @t64 () (and @t63 @t56)) % 0.44/0.65 (define @t65 () (not @t64)) % 0.44/0.65 (define @t66 () (tptp.convergent_lines @t52 @t51)) % 0.44/0.65 (define @t67 () (not @t66)) % 0.44/0.65 (define @t68 () (or @t67 @t57)) % 0.44/0.65 (define @t69 () (@list true false)) % 0.44/0.65 (define @t70 () (and @t66 (tptp.unorthogonal_lines @t52 @t51))) % 0.44/0.65 (define @t71 () (not @t70)) % 0.44/0.65 (define @t72 () (tptp.convergent_lines @t52 @t54)) % 0.44/0.65 (define @t73 () (not @t72)) % 0.44/0.65 (define @t74 () (or @t73 @t59 @t70 @t64)) % 0.44/0.65 (define @t75 () (tptp.convergent_lines @t54 @t54)) % 0.44/0.65 (define @t76 () (tptp.convergent_lines @t54 @t52)) % 0.44/0.65 (define @t77 () (not @t76)) % 0.44/0.65 (define @t78 () (or @t77 @t75 @t72)) % 0.44/0.65 (define @t79 () (or @t63 @t56)) % 0.44/0.65 (define @t80 () (tptp.convergent_lines @t51 @t52)) % 0.44/0.65 (define @t81 () (not @t63)) % 0.44/0.65 (define @t82 () (or @t81 @t76 @t80)) % 0.44/0.65 (define @t83 () (tptp.distinct_lines @t51 @t52)) % 0.44/0.65 (define @t84 () (not @t80)) % 0.44/0.65 (define @t85 () (or @t84 @t83)) % 0.44/0.65 (define @t86 () (@list false false)) % 0.44/0.65 (define @t87 () (tptp.distinct_lines @t51 @t51)) % 0.44/0.65 (define @t88 () (not @t83)) % 0.44/0.65 (define @t89 () (or @t88 @t87 @t57)) % 0.44/0.65 (assume @p1 (forall @t2 (not (tptp.distinct_points @t1 @t1)))) % 0.44/0.65 (assume @p2 @t3) % 0.44/0.65 (assume @p3 (forall @t2 (not (tptp.convergent_lines @t1 @t1)))) % 0.44/0.65 (assume @p4 (forall @t8 (=> @t7 (or @t6 (tptp.distinct_points @t5 @t4))))) % 0.44/0.65 (assume @p5 @t13) % 0.44/0.65 (assume @p6 @t18) % 0.44/0.65 (assume @p7 (forall @t8 (=> @t7 (=> (tptp.apart_point_and_line @t4 (tptp.line_connecting @t1 @t5)) (and (tptp.distinct_points @t4 @t1) (tptp.distinct_points @t4 @t5)))))) % 0.44/0.65 (assume @p8 (forall @t8 (=> @t17 (=> (or (tptp.apart_point_and_line @t4 @t1) @t19) (tptp.distinct_points @t4 (tptp.intersection_point @t1 @t5)))))) % 0.44/0.65 (assume @p9 (forall (@list @t1 @t5 @t21 @t20) (=> (and @t7 (tptp.distinct_lines @t21 @t20)) (or (tptp.apart_point_and_line @t1 @t21) (tptp.apart_point_and_line @t1 @t20) (tptp.apart_point_and_line @t5 @t21) (tptp.apart_point_and_line @t5 @t20))))) % 0.44/0.65 (assume @p10 (forall @t8 (=> @t22 (or @t6 @t19)))) % 0.44/0.65 (assume @p11 (forall @t8 (=> @t22 (or @t9 @t23)))) % 0.44/0.65 (assume @p12 @t25) % 0.44/0.65 (assume @p13 (forall @t24 (not (tptp.convergent_lines @t26 @t5)))) % 0.44/0.65 (assume @p14 (forall @t24 (not (tptp.apart_point_and_line @t1 @t26)))) % 0.44/0.65 (assume @p15 (forall @t8 (=> @t9 (or @t22 @t23 @t14)))) % 0.44/0.65 (assume @p16 (forall (@list @t28 @t27) (or @t30 @t29))) % 0.44/0.65 (assume @p17 @t39) % 0.44/0.65 (assume @p18 (forall @t42 (not (tptp.unorthogonal_lines @t41 @t28)))) % 0.44/0.65 (assume @p19 (forall @t42 (not (tptp.apart_point_and_line @t40 @t41)))) % 0.44/0.65 (assume @p20 (forall (@list @t40 @t28 @t27 @t31) (=> (tptp.distinct_lines @t28 @t27) (or (tptp.apart_point_and_line @t40 @t28) (tptp.apart_point_and_line @t40 @t27) @t34 @t32)))) % 0.44/0.65 (assume @p21 @t46) % 0.44/0.65 (assume @p22 true) % 0.44/0.65 (step @p23 :rule aci_norm :args ((= (or @t47 @t11) (or @t47 @t10 @t9)))) % 0.44/0.65 (step @p24 :rule bool-impl-elim :args (@t12 @t11)) % 0.44/0.65 (step @p25 :rule trans :premises (@p24 @p23)) % 0.44/0.65 (step @p26 :rule cong :premises (@p25) :args (@t13)) % 0.44/0.65 (step @p27 :rule eq_resolve :premises (@p5 @p26)) % 0.44/0.65 (step @p28 :rule instantiate :premises (@p27) :args ((@list @t51 @t52 @t51))) % 0.44/0.65 (step @p29 :rule bool-impl-elim :args (@t17 @t12)) % 0.44/0.65 (step @p30 :rule cong :premises (@p29) :args (@t25)) % 0.44/0.65 (step @p31 :rule eq_resolve :premises (@p12 @p30)) % 0.44/0.65 (step @p32 :rule instantiate :premises (@p31) :args ((@list @t51 @t52))) % 0.44/0.65 (step @p33 :rule aci_norm :args ((= (or @t53 @t16) (or @t53 @t15 @t14)))) % 0.44/0.65 (step @p34 :rule bool-impl-elim :args (@t17 @t16)) % 0.44/0.65 (step @p35 :rule trans :premises (@p34 @p33)) % 0.44/0.65 (step @p36 :rule cong :premises (@p35) :args (@t18)) % 0.44/0.65 (step @p37 :rule eq_resolve :premises (@p6 @p36)) % 0.44/0.65 (step @p38 :rule instantiate :premises (@p37) :args ((@list @t54 @t51 @t52))) % 0.44/0.65 (step @p39 :rule instantiate :premises (@p37) :args ((@list @t54 @t52 @t54))) % 0.44/0.65 (step @p40 :rule aci_norm :args ((= (or (or @t55 @t48) @t36) (or @t55 @t48 @t35 @t33)))) % 0.44/0.65 (step @p41 :rule refl :args (@t36)) % 0.44/0.65 (step @p42 :rule bool-and-de-morgan :args (@t30 @t29 true)) % 0.44/0.65 (step @p43 :rule nary_cong :premises (@p42 @p41) :args ((or (not @t37) @t36))) % 0.44/0.65 (step @p44 :rule trans :premises (@p43 @p40)) % 0.44/0.65 (step @p45 :rule bool-impl-elim :args (@t37 @t36)) % 0.44/0.65 (step @p46 :rule trans :premises (@p45 @p44)) % 0.44/0.65 (step @p47 :rule cong :premises (@p46) :args (@t39)) % 0.44/0.65 (step @p48 :rule eq_resolve :premises (@p17 @p47)) % 0.44/0.65 (step @p49 :rule instantiate :premises (@p48) :args ((@list @t52 @t54 @t51))) % 0.44/0.65 (step @p50 :rule aci_norm :args ((= (or @t48 @t44) @t49))) % 0.44/0.65 (step @p51 :rule bool-impl-elim :args (@t29 @t44)) % 0.44/0.65 (step @p52 :rule trans :premises (@p51 @p50)) % 0.44/0.65 (step @p53 :rule cong :premises (@p52) :args (@t45)) % 0.44/0.65 (step @p54 :rule cong :premises (@p53) :args (@t46)) % 0.44/0.65 (step @p55 :rule eq_resolve :premises (@p21 @p54)) % 0.44/0.65 (step @p56 :rule skolemize :premises (@p55)) % 0.44/0.65 (step @p57 :rule cnf_or_neg :args (@t60 2)) % 0.44/0.65 (step @p58 :rule chain_m_resolution :premises (@p57 @p56) :args ((not @t56) @t61 @t62)) % 0.44/0.66 (step @p59 :rule cnf_and_pos :args (@t64 1)) % 0.44/0.66 (step @p60 :rule reordering :premises (@p59) :args ((or @t56 @t65))) % 0.44/0.66 (step @p61 :rule chain_m_resolution :premises (@p60 @p58) :args (@t65 @t61 (@list @t56))) % 0.44/0.66 (step @p62 :rule instantiate :premises (@p31) :args ((@list @t52 @t51))) % 0.44/0.66 (step @p63 :rule cnf_or_neg :args (@t60 1)) % 0.44/0.66 (step @p64 :rule chain_m_resolution :premises (@p63 @p56) :args ((not @t57) @t61 @t62)) % 0.44/0.66 (step @p65 :rule cnf_or_pos :args (@t68)) % 0.44/0.66 (step @p66 :rule reordering :premises (@p65) :args ((or @t57 @t67 (not @t68)))) % 0.44/0.66 (step @p67 :rule chain_m_resolution :premises (@p66 @p64 @p62) :args (@t67 @t69 (@list @t57 @t68))) % 0.44/0.66 (step @p68 :rule cnf_and_pos :args (@t70 0)) % 0.44/0.66 (step @p69 :rule reordering :premises (@p68) :args ((or @t66 @t71))) % 0.44/0.66 (step @p70 :rule chain_m_resolution :premises (@p69 @p67) :args (@t71 @t61 (@list @t66))) % 0.44/0.66 (step @p71 :rule bool-double-not-elim :args (@t58)) % 0.44/0.66 (step @p72 :rule refl :args (@t60)) % 0.44/0.66 (step @p73 :rule nary_cong :premises (@p72 @p71) :args ((or @t60 (not @t59)))) % 0.44/0.66 (step @p74 :rule cnf_or_neg :args (@t60 0)) % 0.44/0.66 (step @p75 :rule eq_resolve :premises (@p74 @p73)) % 0.44/0.66 (step @p76 :rule reordering :premises (@p75) :args ((or @t58 @t60))) % 0.44/0.66 (step @p77 :rule chain_m_resolution :premises (@p76 @p56) :args (@t58 @t61 @t62)) % 0.44/0.66 (step @p78 :rule cnf_or_pos :args (@t74)) % 0.44/0.66 (step @p79 :rule reordering :premises (@p78) :args ((or @t59 @t70 @t64 @t73 (not @t74)))) % 0.44/0.66 (step @p80 :rule chain_m_resolution :premises (@p79 @p77 @p70 @p61 @p49) :args (@t73 (@list false true true false) (@list @t58 @t70 @t64 @t74))) % 0.44/0.66 (step @p81 :rule instantiate :premises (@p3) :args ((@list @t54))) % 0.44/0.66 (step @p82 :rule cnf_or_pos :args (@t78)) % 0.44/0.66 (step @p83 :rule reordering :premises (@p82) :args ((or @t75 @t72 @t77 (not @t78)))) % 0.44/0.66 (step @p84 :rule chain_m_resolution :premises (@p83 @p81 @p80 @p39) :args (@t77 (@list true true false) (@list @t75 @t72 @t78))) % 0.44/0.66 (step @p85 :rule instantiate :premises (@p16) :args ((@list @t54 @t51))) % 0.44/0.66 (step @p86 :rule cnf_or_pos :args (@t79)) % 0.44/0.66 (step @p87 :rule reordering :premises (@p86) :args ((or @t56 @t63 (not @t79)))) % 0.44/0.66 (step @p88 :rule chain_m_resolution :premises (@p87 @p58 @p85) :args (@t63 @t69 (@list @t56 @t79))) % 0.44/0.66 (step @p89 :rule cnf_or_pos :args (@t82)) % 0.44/0.66 (step @p90 :rule reordering :premises (@p89) :args ((or @t81 @t76 @t80 (not @t82)))) % 0.44/0.66 (step @p91 :rule chain_m_resolution :premises (@p90 @p88 @p84 @p38) :args (@t80 (@list false true false) (@list @t63 @t76 @t82))) % 0.44/0.66 (step @p92 :rule cnf_or_pos :args (@t85)) % 0.44/0.66 (step @p93 :rule reordering :premises (@p92) :args ((or @t84 @t83 (not @t85)))) % 0.44/0.66 (step @p94 :rule chain_m_resolution :premises (@p93 @p91 @p32) :args (@t83 @t86 (@list @t80 @t85))) % 0.44/0.66 (step @p95 :rule cnf_or_pos :args (@t89)) % 0.44/0.66 (step @p96 :rule reordering :premises (@p95) :args ((or @t57 @t88 @t87 (not @t89)))) % 0.44/0.66 (step @p97 :rule chain_m_resolution :premises (@p96 @p64 @p94 @p28) :args (@t87 (@list true false false) (@list @t57 @t83 @t89))) % 0.44/0.66 (assume-push @p104 @t3) % 0.44/0.66 (step @p99 :rule instantiate :premises (@p2) :args ((@list @t51))) % 0.44/0.66 (step-pop @p105 :rule scope :premises (@p99)) % 0.44/0.66 (step @p100 :rule process_scope :premises (@p105) :args ((not @t87))) % 0.44/0.66 (step @p102 :rule implies_elim :premises (@p100)) % 0.44/0.66 (step @p103 false :rule chain_m_resolution :premises (@p102 @p97 @p2) :args (false @t86 (@list @t87 @t3))) % 0.44/0.66 ) % 0.44/0.66 % SZS output end Proof % 0.44/0.66 % cvc5 exiting %------------------------------------------------------------------------------