%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO002-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 01:16:27 PM UTC 2026
% Result : Unsatisfiable 4.19s 1.06s
% Output : Proof 4.19s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t58,axiom,
sF1 = ifeq(between(a,a,b),true,false,true),
introduced(definition) ).
cnf(f46,negated_conjecture,
~ between(a,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_between_a_and_b) ).
fof(f46_nnf,plain,
~ between(a,a,b),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
~ between(a,a,b),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c46,plain,
~ between(a,a,b),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(t6,plain,
between(a,a,b) = false,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t65,plain,
between(a,a,b) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t57,axiom,
sF0 = between(a,a,b),
introduced(definition) ).
cnf(t161,plain,
sF0 = false,
inference(step,[status(thm)],[t57,t65]) ).
cnf(t70,plain,
false = sF0,
inference(orient,[status(thm)],[t161]) ).
cnf(t164,plain,
between(a,a,b) = sF0,
inference(step,[status(thm)],[t65,t70]) ).
cnf(t73,plain,
between(a,a,b) = sF0,
inference(orient,[status(thm)],[t164]) ).
cnf(t176,plain,
sF1 = ifeq(sF0,true,false,true),
inference(step,[status(thm)],[t58,t73]) ).
cnf(t177,plain,
sF1 = ifeq(sF0,true,sF0,true),
inference(step,[status(thm)],[t176,t70]) ).
cnf(t20,plain,
ifeq(between(a,a,b),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t174,plain,
ifeq(sF0,true,false,true) = true,
inference(step,[status(thm)],[t20,t73]) ).
cnf(t175,plain,
ifeq(sF0,true,sF0,true) = true,
inference(step,[status(thm)],[t174,t70]) ).
cnf(t94,plain,
ifeq(sF0,true,sF0,true) = true,
inference(orient,[status(thm)],[t175]) ).
cnf(t178,plain,
sF1 = true,
inference(step,[status(thm)],[t177,t94]) ).
cnf(t95,plain,
true = sF1,
inference(orient,[status(thm)],[t178]) ).
cnf(f45,axiom,
( between(W,V,U)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
fof(f45_nnf,plain,
! [U,V,W] :
( between(W,V,U)
| ~ between(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
! [U,V,W] :
( between(W,V,U)
| ~ between(U,V,W) ),
inference(skolemisation,[status(esa)],[f45_nnf]) ).
cnf(c45,plain,
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(t28,plain,
ifeq(between(X1,X2,X3),true,between(X3,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
cnf(t200,plain,
ifeq(between(X1,X2,X3),sF1,between(X3,X2,X1),true) = true,
inference(step,[status(thm)],[t28,t95]) ).
cnf(t201,plain,
ifeq(between(X1,X2,X3),sF1,between(X3,X2,X1),sF1) = true,
inference(step,[status(thm)],[t200,t95]) ).
cnf(t202,plain,
ifeq(between(X1,X2,X3),sF1,between(X3,X2,X1),sF1) = sF1,
inference(step,[status(thm)],[t201,t95]) ).
cnf(t124,plain,
ifeq(between(X1,X2,X3),sF1,between(X3,X2,X1),sF1) = sF1,
inference(orient,[status(thm)],[t202]) ).
cnf(t128,plain,
sF1 = ifeq(between(b,a,a),sF1,sF0,sF1),
inference(cp,[status(thm)],[t124,t73]) ).
cnf(f43,axiom,
between(U,V,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3) ).
fof(f43_nnf,plain,
! [U,V] : between(U,V,V),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [U,V] : between(U,V,V),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c43,plain,
between(X0,X1,X1),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(t5,plain,
between(X1,X2,X2) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t64,plain,
between(X1,X2,X2) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t181,plain,
between(X1,X2,X2) = sF1,
inference(step,[status(thm)],[t64,t95]) ).
cnf(t100,plain,
between(X1,X2,X2) = sF1,
inference(orient,[status(thm)],[t181]) ).
cnf(t203,plain,
sF1 = ifeq(sF1,sF1,sF0,sF1),
inference(step,[status(thm)],[t128,t100]) ).
cnf(t15,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t88,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t15]) ).
cnf(t204,plain,
sF1 = sF0,
inference(step,[status(thm)],[t203,t88]) ).
cnf(t137,plain,
sF1 = sF0,
inference(orient,[status(thm)],[t204]) ).
cnf(t217,plain,
true = sF0,
inference(step,[status(thm)],[t95,t137]) ).
cnf(t150,plain,
true = sF0,
inference(orient,[status(thm)],[t217]) ).
cnf(f9,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension1) ).
fof(f9_nnf,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(f10,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension2) ).
fof(f10_nnf,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(f11,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension3) ).
fof(f11_nnf,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c9,c10,c11,c46]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t150]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t70]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO002-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n019.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
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Wed Sep 23 10:18:34 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.19/1.06 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.19/1.06 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------