%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO124-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 : Fri Sep 25 01:17:06 PM UTC 2026
% Result : Unsatisfiable 47.48s 6.69s
% Output : Proof 47.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 15 unt; 0 def)
% Number of atoms : 90 ( 26 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 87 ( 41 ~; 46 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 74 ( 6 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f77,axiom,
( between_c(ax2_sk4(A,D,C,B),B,C,D)
| ~ between_o(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o3_24) ).
fof(f77_nnf,plain,
! [A,B,C,D] :
( between_c(ax2_sk4(A,D,C,B),B,C,D)
| ~ between_o(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f77]) ).
fof(f77_sk,plain,
! [A,B,C,D] :
( between_c(ax2_sk4(A,D,C,B),B,C,D)
| ~ between_o(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f77_nnf]) ).
cnf(c77,plain,
( between_c(ax2_sk4(X0,X3,X2,X1),X1,X2,X3)
| ~ between_o(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f77_sk]) ).
cnf(f61,axiom,
( ordered_by(B,A,C)
| ~ incident_o(C,B)
| A = C
| ~ start_point(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',start_point_defn_8) ).
fof(f61_nnf,plain,
! [A,B,C] :
( ordered_by(B,A,C)
| ~ incident_o(C,B)
| A = C
| ~ start_point(A,B) ),
inference(nnf_transformation,[status(thm)],[f61]) ).
fof(f61_sk,plain,
! [A,B,C] :
( ordered_by(B,A,C)
| ~ incident_o(C,B)
| A = C
| ~ start_point(A,B) ),
inference(skolemisation,[status(esa)],[f61_nnf]) ).
cnf(c61,plain,
( ordered_by(X1,X0,X2)
| ~ incident_o(X2,X1)
| X0 = X2
| ~ start_point(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f61_sk]) ).
cnf(f96,negated_conjecture,
start_point(sk26,sk25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_4_10_1_133) ).
fof(f96_nnf,plain,
start_point(sk26,sk25),
inference(nnf_transformation,[status(thm)],[f96]) ).
cnf(c96,plain,
start_point(sk26,sk25),
inference(cnf_transformation,[status(esa)],[f96_nnf]) ).
cnf(p1557,plain,
( ordered_by(sk25,sk26,X0)
| ~ incident_o(X0,sk25)
| sk26 = X0 ),
inference(resolution,[status(thm)],[c61,c96]) ).
cnf(f60,axiom,
( incident_o(A,B)
| ~ start_point(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',start_point_defn_7) ).
fof(f60_nnf,plain,
! [A,B] :
( incident_o(A,B)
| ~ start_point(A,B) ),
inference(nnf_transformation,[status(thm)],[f60]) ).
fof(f60_sk,plain,
! [A,B] :
( incident_o(A,B)
| ~ start_point(A,B) ),
inference(skolemisation,[status(esa)],[f60_nnf]) ).
cnf(c60,plain,
( incident_o(X0,X1)
| ~ start_point(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f60_sk]) ).
cnf(f97,negated_conjecture,
start_point(sk27,sk25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_4_10_1_134) ).
fof(f97_nnf,plain,
start_point(sk27,sk25),
inference(nnf_transformation,[status(thm)],[f97]) ).
cnf(c97,plain,
start_point(sk27,sk25),
inference(cnf_transformation,[status(esa)],[f97_nnf]) ).
cnf(p110,plain,
incident_o(sk27,sk25),
inference(resolution,[status(thm)],[c60,c97]) ).
cnf(p1560,plain,
( ordered_by(sk25,sk26,sk27)
| sk26 = sk27 ),
inference(resolution,[status(thm)],[p1557,p110]) ).
cnf(f58,axiom,
( between_o(A,B,C,D)
| ~ ordered_by(A,C,D)
| ~ ordered_by(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_o_defn_5) ).
fof(f58_nnf,plain,
! [A,B,C,D] :
( between_o(A,B,C,D)
| ~ ordered_by(A,C,D)
| ~ ordered_by(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f58]) ).
fof(f58_sk,plain,
! [A,B,C,D] :
( between_o(A,B,C,D)
| ~ ordered_by(A,C,D)
| ~ ordered_by(A,B,C) ),
inference(skolemisation,[status(esa)],[f58_nnf]) ).
cnf(c58,plain,
( between_o(X0,X1,X2,X3)
| ~ ordered_by(X0,X2,X3)
| ~ ordered_by(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
cnf(p1577,plain,
( between_o(sk25,sk26,sk27,X0)
| ~ ordered_by(sk25,sk27,X0)
| sk26 = sk27 ),
inference(resolution,[status(thm)],[p1560,c58]) ).
cnf(p1558,plain,
( ordered_by(sk25,sk27,X0)
| ~ incident_o(X0,sk25)
| sk27 = X0 ),
inference(resolution,[status(thm)],[c61,c97]) ).
cnf(p109,plain,
incident_o(sk26,sk25),
inference(resolution,[status(thm)],[c60,c96]) ).
cnf(p1581,plain,
( ordered_by(sk25,sk27,sk26)
| sk27 = sk26 ),
inference(resolution,[status(thm)],[p1558,p109]) ).
cnf(p1640,plain,
( sk27 = sk26
| between_o(sk25,sk26,sk27,sk26)
| sk26 = sk27 ),
inference(resolution,[status(thm)],[p1577,p1581]) ).
cnf(p1857,plain,
( sk27 = sk26
| sk26 = sk27
| between_c(ax2_sk4(sk25,sk26,sk27,sk26),sk26,sk27,sk26) ),
inference(resolution,[status(thm)],[c77,p1640]) ).
cnf(f48,axiom,
( B != D
| ~ between_c(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_c_defn_1) ).
fof(f48_nnf,plain,
! [A,B,C,D] :
( B != D
| ~ between_c(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f48]) ).
fof(f48_sk,plain,
! [A,B,C,D] :
( B != D
| ~ between_c(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f48_nnf]) ).
cnf(c48,plain,
( X1 != X3
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
cnf(p135,plain,
~ between_c(X0,X1,X2,X1),
inference(equality_resolution,[status(thm)],[c48]) ).
cnf(p1928,plain,
( sk27 = sk26
| sk26 = sk27 ),
inference(resolution,[status(thm)],[p1857,p135]) ).
cnf(f98,negated_conjecture,
sk26 != sk27,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_4_10_1_135) ).
fof(f98_nnf,plain,
sk26 != sk27,
inference(nnf_transformation,[status(thm)],[f98]) ).
fof(f98_sk,plain,
sk26 != sk27,
inference(skolemisation,[status(esa)],[f98_nnf]) ).
cnf(c98,plain,
sk26 != sk27,
inference(cnf_transformation,[status(esa)],[f98_sk]) ).
cnf(p1929,plain,
( sk26 != sk26
| sk26 = sk27 ),
inference(superposition,[status(thm)],[p1928,c98]) ).
cnf(p2055,plain,
sk26 = sk27,
inference(equality_resolution,[status(thm)],[p1929]) ).
cnf(p2056,plain,
$false,
inference(resolution,[status(thm)],[p2055,c98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO124-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 10:55:59 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 47.48/6.69 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 47.48/6.69 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------