%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO083-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 214.78s 28.64s
% Output : CNFRefutation 214.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 18 unt; 0 def)
% Number of atoms : 84 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 80 ( 39 ~; 41 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 80 ( 6 sgn 22 !; 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_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]) ).
fof(corollary_2_6_1_70,axiom,
~ part_of(sum(sk14,sk15),sum(sk14,sk16)),
file('theBenchmark.p',corollary_2_6_1_70) ).
cnf(c_23,plain,
~ part_of(sum(sk14,sk15),sum(sk14,sk16)),
inference(clausify,[status(thm)],[corollary_2_6_1_70]) ).
fof(corollary_2_6_1_67,axiom,
part_of(sk15,sk16),
file('theBenchmark.p',corollary_2_6_1_67) ).
cnf(c_26,plain,
part_of(sk15,sk16),
inference(clausify,[status(thm)],[corollary_2_6_1_67]) ).
fof(sum_defn_6,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( incident_c(VAR_3,VAR_0)
| ~ incident_c(VAR_3,VAR_2)
| VAR_0 != sum(VAR_1,VAR_2) ),
file('theBenchmark.p',sum_defn_6) ).
cnf(c_59,plain,
( incident_c(D,A)
| ~ incident_c(D,C)
| A != sum(B,C) ),
inference(clausify,[status(thm)],[sum_defn_6]) ).
cnf(c_60,plain,
( incident_c(D,C)
| ~ incident_c(D,B)
| sum(A,B) != C ),
inference(copy,[status(thm)],[c_59]) ).
fof(sum_defn_5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( incident_c(VAR_3,VAR_0)
| ~ incident_c(VAR_3,VAR_1)
| VAR_0 != sum(VAR_1,VAR_2) ),
file('theBenchmark.p',sum_defn_5) ).
cnf(c_61,plain,
( incident_c(D,A)
| ~ incident_c(D,B)
| A != sum(B,C) ),
inference(clausify,[status(thm)],[sum_defn_5]) ).
cnf(c_62,plain,
( incident_c(D,C)
| ~ incident_c(D,A)
| sum(A,B) != C ),
inference(copy,[status(thm)],[c_61]) ).
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_9790,plain,
A = sum(ax0_sk9(ax0_sk8(A),A),ax0_sk10(ax0_sk8(A),A)),
inference(copy,[status(thm)],[c_18]) ).
cnf(c_9791,plain,
( incident_c(A,sum(ax0_sk9(ax0_sk8(sum(C,B)),sum(C,B)),ax0_sk10(ax0_sk8(sum(C,B)),sum(C,B))))
| ~ incident_c(A,B) ),
inference(resolve,[status(thm)],[c_60,c_9790]) ).
cnf(c_119,plain,
( incident_c(A,sum(C,B))
| ~ incident_c(A,B) ),
inference(paramod,[status(thm)],[c_18,c_9791]) ).
cnf(c_9792,plain,
A = sum(ax0_sk9(ax0_sk8(A),A),ax0_sk10(ax0_sk8(A),A)),
inference(copy,[status(thm)],[c_18]) ).
cnf(c_9793,plain,
( incident_c(A,sum(ax0_sk9(ax0_sk8(sum(B,C)),sum(B,C)),ax0_sk10(ax0_sk8(sum(B,C)),sum(B,C))))
| ~ incident_c(A,B) ),
inference(resolve,[status(thm)],[c_62,c_9792]) ).
cnf(c_126,plain,
( incident_c(A,sum(B,C))
| ~ incident_c(A,B) ),
inference(paramod,[status(thm)],[c_18,c_9793]) ).
cnf(c_9794,plain,
A = sum(ax0_sk9(ax0_sk8(A),A),ax0_sk10(ax0_sk8(A),A)),
inference(copy,[status(thm)],[c_18]) ).
cnf(c_9795,plain,
( incident_c(A,C)
| incident_c(A,B)
| ~ incident_c(A,sum(ax0_sk9(ax0_sk8(sum(B,C)),sum(B,C)),ax0_sk10(ax0_sk8(sum(B,C)),sum(B,C)))) ),
inference(resolve,[status(thm)],[c_64,c_9794]) ).
cnf(c_133,plain,
( incident_c(A,C)
| incident_c(A,B)
| ~ incident_c(A,sum(B,C)) ),
inference(paramod,[status(thm)],[c_18,c_9795]) ).
cnf(c_137,plain,
~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk16)),
inference(resolve,[status(thm)],[c_65,c_23]) ).
cnf(c_138,plain,
incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sum(sk14,sk15)),
inference(resolve,[status(thm)],[c_66,c_23]) ).
cnf(c_141,plain,
( incident_c(A,sk16)
| ~ incident_c(A,sk15) ),
inference(resolve,[status(thm)],[c_67,c_26]) ).
cnf(c_2701,plain,
~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk14),
inference(resolve,[status(thm)],[c_126,c_137]) ).
cnf(c_2702,plain,
~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk16),
inference(resolve,[status(thm)],[c_119,c_137]) ).
cnf(c_9796,plain,
( incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15)
| incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk14) ),
inference(resolve,[status(thm)],[c_138,c_133]) ).
cnf(c_2792,plain,
incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15),
inference(resolve,[status(thm)],[c_2701,c_9796]) ).
cnf(c_9797,plain,
~ incident_c(ax0_sk1(sum(sk14,sk15),sum(sk14,sk16)),sk15),
inference(resolve,[status(thm)],[c_141,c_2702]) ).
cnf(c_9789,plain,
$false,
inference(resolve,[status(thm)],[c_2792,c_9797]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO083-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n010.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 12:40:46 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 763276 was started by sandbox on n010,
% 0.08/0.35 % Fri Sep 25 12:40:46 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 214.78/28.64
% 214.78/28.64 % given #500 (T,wt=18): 2039 incident_c(ax0_sk2(sk15,sk14,sk15),sum(sk14,A)). [resolve(126,a,1205,a)].
% 214.78/28.64
% 214.78/28.64 % given #1000 (A,wt=28): 316 -incident_c(ax0_sk13(sk14,A),sk15) | end_point(ax0_sk13(sk14,A),sk15) | incident_c(ax0_sk13(sk14,A),A) | sk14 = A. [resolve(87,a,28,b),flip(d)].
% 214.78/28.64
% 214.78/28.64 % given #1500 (T,wt=22): 529 -meet(A,B,sk14) | -incident_c(ax0_sk7(sk14),B) | end_point(ax0_sk7(sk14),B). [resolve(447,a,39,c)].
% 214.78/28.64
% 214.78/28.64 % given #2000 (W,wt=23): 4865 incident_c(sk17,A) | -part_of(sum(sk15,B),C) | incident_c(ax0_sk1(sk15,A),C). [resolve(2586,b,67,b)].
% 214.78/28.64
% 214.78/28.64 % SZS status Unsatisfiable for theBenchmark
% 214.78/28.64
% 214.78/28.64 % Proof 1 at 3.23 (+ 0.79) seconds.
% 214.78/28.64 % Length of proof is 25.
% 214.78/28.64 % Level of proof is 6.
% 214.78/28.64 % Maximum clause weight is 31.000.
% 214.78/28.64 % Given clauses 2079.
% 214.78/28.64
% 214.78/28.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------