%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO117-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 : Fri Sep 25 01:17:05 PM UTC 2026
% Result : Unsatisfiable 7.06s 1.49s
% Output : Proof 7.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 50 ( 18 unt; 0 def)
% Number of atoms : 86 ( 22 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 90 ( 54 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 122 ( 6 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f59,axiom,
( between_o(A,D,C,B)
| ~ ordered_by(A,C,D)
| ~ ordered_by(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_o_defn_6) ).
fof(f59_nnf,plain,
! [A,B,C,D] :
( between_o(A,D,C,B)
| ~ ordered_by(A,C,D)
| ~ ordered_by(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f59]) ).
fof(f59_sk,plain,
! [A,B,C,D] :
( between_o(A,D,C,B)
| ~ ordered_by(A,C,D)
| ~ ordered_by(A,B,C) ),
inference(skolemisation,[status(esa)],[f59_nnf]) ).
cnf(c59,plain,
( between_o(X0,X3,X2,X1)
| ~ ordered_by(X0,X2,X3)
| ~ ordered_by(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f59_sk]) ).
cnf(hi50,axiom,
ifeq(ordered_by(X0,X1,X2),true,ifeq(ordered_by(X0,X2,X3),true,between_o(X0,X3,X2,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c59]) ).
cnf(f96,negated_conjecture,
ordered_by(sk25,sk26,sk26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_4_133) ).
fof(f96_nnf,plain,
ordered_by(sk25,sk26,sk26),
inference(nnf_transformation,[status(thm)],[f96]) ).
cnf(c96,plain,
ordered_by(sk25,sk26,sk26),
inference(cnf_transformation,[status(esa)],[f96_nnf]) ).
cnf(hi81,negated_conjecture,
ordered_by(sk25,sk26,sk26) = true,
inference(equality_encoding,[status(esa)],[c96]) ).
cnf(h6,plain,
between_o(sk25,sk26,sk26,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi50,hi81,hi81]) ).
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(hi68,axiom,
ifeq(between_o(X0,X1,X2,X3),true,between_c(ax2_sk4(X0,X3,X2,X1),X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c77]) ).
cnf(h60,plain,
between_c(ax2_sk4(sk25,sk26,sk26,sk26),sk26,sk26,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi68,h6]) ).
cnf(f51,axiom,
( end_point(D,ax1_sk1(D,C,B,A))
| ~ between_c(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_c_defn_4) ).
fof(f51_nnf,plain,
! [A,B,C,D] :
( end_point(D,ax1_sk1(D,C,B,A))
| ~ between_c(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f51]) ).
fof(f51_sk,plain,
! [A,B,C,D] :
( end_point(D,ax1_sk1(D,C,B,A))
| ~ between_c(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f51_nnf]) ).
cnf(c51,plain,
( end_point(X3,ax1_sk1(X3,X2,X1,X0))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(hi42,axiom,
ifeq(between_c(X0,X1,X2,X3),true,end_point(X3,ax1_sk1(X3,X2,X1,X0)),true) = true,
inference(equality_encoding,[status(esa)],[c51]) ).
cnf(h978,plain,
end_point(sk26,ax1_sk1(sk26,sk26,sk26,ax2_sk4(sk25,sk26,sk26,sk26))) = true,
inference(hyper_resolution,[status(thm)],[hi42,h60]) ).
cnf(f52,axiom,
( inner_point(C,ax1_sk1(D,C,B,A))
| ~ between_c(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_c_defn_5) ).
fof(f52_nnf,plain,
! [A,B,C,D] :
( inner_point(C,ax1_sk1(D,C,B,A))
| ~ between_c(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f52]) ).
fof(f52_sk,plain,
! [A,B,C,D] :
( inner_point(C,ax1_sk1(D,C,B,A))
| ~ between_c(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c52,plain,
( inner_point(X2,ax1_sk1(X3,X2,X1,X0))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi43,axiom,
ifeq(between_c(X0,X1,X2,X3),true,inner_point(X2,ax1_sk1(X3,X2,X1,X0)),true) = true,
inference(equality_encoding,[status(esa)],[c52]) ).
cnf(h977,plain,
inner_point(sk26,ax1_sk1(sk26,sk26,sk26,ax2_sk4(sk25,sk26,sk26,sk26))) = true,
inference(hyper_resolution,[status(thm)],[hi43,h60]) ).
cnf(f21,axiom,
( ~ end_point(A,B)
| ~ inner_point(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_point_defn_22) ).
fof(f21_nnf,plain,
! [A,B] :
( ~ end_point(A,B)
| ~ inner_point(A,B) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B] :
( ~ end_point(A,B)
| ~ inner_point(A,B) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( ~ end_point(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi82,axiom,
ifeq(inner_point(X0,X1),true,ifeq(end_point(X0,X1),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi82,h977,h978]) ).
cnf(t331,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(f30,axiom,
( ~ end_point(B,A)
| ~ closed(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed_defn_31) ).
fof(f30_nnf,plain,
! [A,B] :
( ~ end_point(B,A)
| ~ closed(A) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [A,B] :
( ~ end_point(B,A)
| ~ closed(A) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
( ~ end_point(X1,X0)
| ~ closed(X0) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(f41,axiom,
( A != ax0_sk11(A,B)
| ~ end_point(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c6_42) ).
fof(f41_nnf,plain,
! [A,B] :
( A != ax0_sk11(A,B)
| ~ end_point(A,B) ),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
! [A,B] :
( A != ax0_sk11(A,B)
| ~ end_point(A,B) ),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c41,plain,
( X0 != ax0_sk11(X0,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c21,c30,c41,c48]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t331]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO117-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n020.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 10:59:05 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.06/1.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.06/1.49 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------