%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO084-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:17:01 AM UTC 2026
% Result : Unsatisfiable 9.14s 1.64s
% Output : CNFRefutation 9.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 21 unt; 0 def)
% Number of atoms : 68 ( 12 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 29 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 1 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c3_37,axiom,
! [VAR_0] : inner_point(ax0_sk8(VAR_0),VAR_0),
file('theBenchmark.p',c3_37) ).
cnf(c_4,plain,
inner_point(ax0_sk8(A),A),
inference(clausify,[status(thm)],[c3_37]) ).
fof(c4_38,axiom,
! [VAR_0,VAR_1] :
( meet(VAR_0,ax0_sk9(VAR_0,VAR_1),ax0_sk10(VAR_0,VAR_1))
| ~ inner_point(VAR_0,VAR_1) ),
file('theBenchmark.p',c4_38) ).
cnf(c_5,plain,
( meet(A,ax0_sk9(A,B),ax0_sk10(A,B))
| ~ inner_point(A,B) ),
inference(clausify,[status(thm)],[c4_38]) ).
fof(c4_39,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = sum(ax0_sk9(VAR_0,VAR_1),ax0_sk10(VAR_0,VAR_1))
| ~ inner_point(VAR_0,VAR_1) ),
file('theBenchmark.p',c4_39) ).
cnf(c_6,plain,
( B = sum(ax0_sk9(A,B),ax0_sk10(A,B))
| ~ inner_point(A,B) ),
inference(clausify,[status(thm)],[c4_39]) ).
cnf(c_17,plain,
A = sum(ax0_sk9(ax0_sk8(A),A),ax0_sk10(ax0_sk8(A),A)),
inference(resolve,[status(thm)],[c_6,c_4]) ).
cnf(c_18,plain,
sum(ax0_sk9(ax0_sk8(A),A),ax0_sk10(ax0_sk8(A),A)) = A,
inference(copy,[status(thm)],[c_17]) ).
cnf(c_20,plain,
meet(ax0_sk8(A),ax0_sk9(ax0_sk8(A),A),ax0_sk10(ax0_sk8(A),A)),
inference(resolve,[status(thm)],[c_5,c_4]) ).
fof(corollary_2_6_2_70,axiom,
~ part_of(sum(sk14,sk15),sk16),
file('theBenchmark.p',corollary_2_6_2_70) ).
cnf(c_23,plain,
~ part_of(sum(sk14,sk15),sk16),
inference(clausify,[status(thm)],[corollary_2_6_2_70]) ).
fof(corollary_2_6_2_68,axiom,
part_of(sk15,sk16),
file('theBenchmark.p',corollary_2_6_2_68) ).
cnf(c_25,plain,
part_of(sk15,sk16),
inference(clausify,[status(thm)],[corollary_2_6_2_68]) ).
fof(corollary_2_6_2_67,axiom,
part_of(sk14,sk16),
file('theBenchmark.p',corollary_2_6_2_67) ).
cnf(c_26,plain,
part_of(sk14,sk16),
inference(clausify,[status(thm)],[corollary_2_6_2_67]) ).
fof(c8_44,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ax0_sk12(VAR_2,VAR_1) = sum(VAR_1,VAR_2)
| ~ meet(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',c8_44) ).
cnf(c_29,plain,
( ax0_sk12(C,B) = sum(B,C)
| ~ meet(A,B,C) ),
inference(clausify,[status(thm)],[c8_44]) ).
fof(sum_defn_4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( incident_c(VAR_3,VAR_2)
| incident_c(VAR_3,VAR_1)
| ~ incident_c(VAR_3,VAR_0)
| VAR_0 != sum(VAR_1,VAR_2) ),
file('theBenchmark.p',sum_defn_4) ).
cnf(c_63,plain,
( incident_c(D,C)
| incident_c(D,B)
| ~ incident_c(D,A)
| A != sum(B,C) ),
inference(clausify,[status(thm)],[sum_defn_4]) ).
cnf(c_64,plain,
( incident_c(D,B)
| incident_c(D,A)
| ~ incident_c(D,C)
| sum(A,B) != C ),
inference(copy,[status(thm)],[c_63]) ).
fof(part_of_defn_3,axiom,
! [VAR_0,VAR_1] :
( part_of(VAR_0,VAR_1)
| ~ incident_c(ax0_sk1(VAR_0,VAR_1),VAR_1) ),
file('theBenchmark.p',part_of_defn_3) ).
cnf(c_65,plain,
( part_of(A,B)
| ~ incident_c(ax0_sk1(A,B),B) ),
inference(clausify,[status(thm)],[part_of_defn_3]) ).
fof(part_of_defn_2,axiom,
! [VAR_0,VAR_1] :
( part_of(VAR_0,VAR_1)
| incident_c(ax0_sk1(VAR_0,VAR_1),VAR_0) ),
file('theBenchmark.p',part_of_defn_2) ).
cnf(c_66,plain,
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ),
inference(clausify,[status(thm)],[part_of_defn_2]) ).
fof(part_of_defn_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( incident_c(VAR_2,VAR_1)
| ~ incident_c(VAR_2,VAR_0)
| ~ part_of(VAR_0,VAR_1) ),
file('theBenchmark.p',part_of_defn_1) ).
cnf(c_67,plain,
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
inference(clausify,[status(thm)],[part_of_defn_1]) ).
cnf(c_4602,plain,
ax0_sk12(ax0_sk10(ax0_sk8(A),A),ax0_sk9(ax0_sk8(A),A)) = sum(ax0_sk9(ax0_sk8(A),A),ax0_sk10(ax0_sk8(A),A)),
inference(resolve,[status(thm)],[c_29,c_20]) ).
cnf(c_91,plain,
ax0_sk12(ax0_sk10(ax0_sk8(A),A),ax0_sk9(ax0_sk8(A),A)) = A,
inference(paramod,[status(thm)],[c_18,c_4602]) ).
cnf(c_298,plain,
~ incident_c(ax0_sk1(sum(sk14,sk15),sk16),sk16),
inference(resolve,[status(thm)],[c_65,c_23]) ).
cnf(c_303,plain,
incident_c(ax0_sk1(sum(sk14,sk15),sk16),sum(sk14,sk15)),
inference(resolve,[status(thm)],[c_66,c_23]) ).
cnf(c_306,plain,
( incident_c(A,sk16)
| ~ incident_c(A,sk14) ),
inference(resolve,[status(thm)],[c_67,c_26]) ).
cnf(c_307,plain,
( incident_c(A,sk16)
| ~ incident_c(A,sk15) ),
inference(resolve,[status(thm)],[c_67,c_25]) ).
cnf(c_1879,plain,
~ incident_c(ax0_sk1(sum(sk14,sk15),sk16),sk15),
inference(resolve,[status(thm)],[c_307,c_298]) ).
cnf(c_1880,plain,
~ incident_c(ax0_sk1(sum(sk14,sk15),sk16),sk14),
inference(resolve,[status(thm)],[c_306,c_298]) ).
cnf(c_4603,plain,
A = ax0_sk12(ax0_sk10(ax0_sk8(A),A),ax0_sk9(ax0_sk8(A),A)),
inference(copy,[status(thm)],[c_91]) ).
cnf(c_4604,plain,
( incident_c(A,C)
| incident_c(A,B)
| ~ incident_c(A,ax0_sk12(ax0_sk10(ax0_sk8(sum(B,C)),sum(B,C)),ax0_sk9(ax0_sk8(sum(B,C)),sum(B,C)))) ),
inference(resolve,[status(thm)],[c_64,c_4603]) ).
cnf(c_4605,plain,
( incident_c(ax0_sk1(sum(sk14,sk15),sk16),A)
| ~ incident_c(ax0_sk1(sum(sk14,sk15),sk16),ax0_sk12(ax0_sk10(ax0_sk8(sum(sk14,A)),sum(sk14,A)),ax0_sk9(ax0_sk8(sum(sk14,A)),sum(sk14,A)))) ),
inference(resolve,[status(thm)],[c_4604,c_1880]) ).
cnf(c_4606,plain,
~ incident_c(ax0_sk1(sum(sk14,sk15),sk16),ax0_sk12(ax0_sk10(ax0_sk8(sum(sk14,sk15)),sum(sk14,sk15)),ax0_sk9(ax0_sk8(sum(sk14,sk15)),sum(sk14,sk15)))),
inference(resolve,[status(thm)],[c_4605,c_1879]) ).
cnf(c_4607,plain,
~ incident_c(ax0_sk1(sum(sk14,sk15),sk16),sum(sk14,sk15)),
inference(paramod,[status(thm)],[c_91,c_4606]) ).
cnf(c_4601,plain,
$false,
inference(resolve,[status(thm)],[c_303,c_4607]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO084-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n020.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Fri Sep 25 12:42:18 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 2947898 was started by sandbox2 on n020,
% 0.16/0.44 % Fri Sep 25 12:42:18 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 9.14/1.64
% 9.14/1.64 % given #500 (T,wt=8): 2728 incident_c(ax0_sk5(sk16,sk16,ax0_sk13(sk16,sk15)),sk16). [resolve(2724,a,115,a)].
% 9.14/1.64
% 9.14/1.64 % SZS status Unsatisfiable for theBenchmark
% 9.14/1.64
% 9.14/1.64 % Proof 1 at 1.05 (+ 0.11) seconds.
% 9.14/1.64 % Length of proof is 23.
% 9.14/1.64 % Level of proof is 4.
% 9.14/1.64 % Maximum clause weight is 14.000.
% 9.14/1.64 % Given clauses 552.
% 9.14/1.64
% 9.14/1.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------