%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO001-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 01:16:25 PM UTC 2026
% Result : Unsatisfiable 6.53s 1.29s
% Output : Proof 6.53s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t58,axiom,
sF1 = ifeq(between(c,b,a),true,false,true),
introduced(definition) ).
cnf(f46,negated_conjecture,
~ between(c,b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_between_c_and_a) ).
fof(f46_nnf,plain,
~ between(c,b,a),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
~ between(c,b,a),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c46,plain,
~ between(c,b,a),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(t7,plain,
between(c,b,a) = false,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t66,plain,
between(c,b,a) = false,
inference(orient,[status(thm)],[t7]) ).
cnf(t57,axiom,
sF0 = between(c,b,a),
introduced(definition) ).
cnf(t974,plain,
sF0 = false,
inference(step,[status(thm)],[t57,t66]) ).
cnf(t70,plain,
false = sF0,
inference(orient,[status(thm)],[t974]) ).
cnf(t977,plain,
between(c,b,a) = sF0,
inference(step,[status(thm)],[t66,t70]) ).
cnf(t73,plain,
between(c,b,a) = sF0,
inference(orient,[status(thm)],[t977]) ).
cnf(t989,plain,
sF1 = ifeq(sF0,true,false,true),
inference(step,[status(thm)],[t58,t73]) ).
cnf(t990,plain,
sF1 = ifeq(sF0,true,sF0,true),
inference(step,[status(thm)],[t989,t70]) ).
cnf(t21,plain,
ifeq(between(c,b,a),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t987,plain,
ifeq(sF0,true,false,true) = true,
inference(step,[status(thm)],[t21,t73]) ).
cnf(t988,plain,
ifeq(sF0,true,sF0,true) = true,
inference(step,[status(thm)],[t987,t70]) ).
cnf(t95,plain,
ifeq(sF0,true,sF0,true) = true,
inference(orient,[status(thm)],[t988]) ).
cnf(t991,plain,
sF1 = true,
inference(step,[status(thm)],[t990,t95]) ).
cnf(t96,plain,
true = sF1,
inference(orient,[status(thm)],[t991]) ).
cnf(f8,axiom,
( between(X,inner_pasch(U,V,W,X,Y),U)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch2) ).
fof(f8_nnf,plain,
! [U,V,W,Y,X] :
( between(X,inner_pasch(U,V,W,X,Y),U)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [U,V,W,Y,X] :
( between(X,inner_pasch(U,V,W,X,Y),U)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( between(X4,inner_pasch(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t46,plain,
ifeq(between(X1,X2,X3),true,ifeq(between(X4,X5,X3),true,between(X5,inner_pasch(X1,X2,X3,X5,X4),X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t1105,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),true,between(X5,inner_pasch(X1,X2,X3,X5,X4),X1),true),true) = true,
inference(step,[status(thm)],[t46,t96]) ).
cnf(t1106,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),sF1,between(X5,inner_pasch(X1,X2,X3,X5,X4),X1),true),true) = true,
inference(step,[status(thm)],[t1105,t96]) ).
cnf(t1107,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),sF1,between(X5,inner_pasch(X1,X2,X3,X5,X4),X1),sF1),true) = true,
inference(step,[status(thm)],[t1106,t96]) ).
cnf(t1108,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),sF1,between(X5,inner_pasch(X1,X2,X3,X5,X4),X1),sF1),sF1) = true,
inference(step,[status(thm)],[t1107,t96]) ).
cnf(t1109,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),sF1,between(X5,inner_pasch(X1,X2,X3,X5,X4),X1),sF1),sF1) = sF1,
inference(step,[status(thm)],[t1108,t96]) ).
cnf(t415,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),sF1,between(X5,inner_pasch(X1,X2,X3,X5,X4),X1),sF1),sF1) = sF1,
inference(orient,[status(thm)],[t1109]) ).
cnf(f6,axiom,
( X = Y
| ~ between(X,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_betweeness) ).
fof(f6_nnf,plain,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t20,plain,
ifeq(between(X1,X2,X1),true,X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t94,plain,
ifeq(between(X1,X2,X1),true,X1,X2) = X2,
inference(orient,[status(thm)],[t20]) ).
cnf(t1007,plain,
ifeq(between(X1,X2,X1),sF1,X1,X2) = X2,
inference(step,[status(thm)],[t94,t96]) ).
cnf(t114,plain,
ifeq(between(X1,X2,X1),sF1,X1,X2) = X2,
inference(rw,[status(thm)],[t1007]) ).
cnf(t121,plain,
ifeq(between(X1,X2,X1),sF1,X1,X2) = X2,
inference(orient,[status(thm)],[t114]) ).
cnf(f7,axiom,
( between(V,inner_pasch(U,V,W,X,Y),Y)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch1) ).
fof(f7_nnf,plain,
! [U,V,W,Y,X] :
( between(V,inner_pasch(U,V,W,X,Y),Y)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [U,V,W,Y,X] :
( between(V,inner_pasch(U,V,W,X,Y),Y)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( between(X1,inner_pasch(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t45,plain,
ifeq(between(X1,X2,X3),true,ifeq(between(X4,X5,X3),true,between(X2,inner_pasch(X1,X2,X3,X5,X4),X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t1091,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),true,between(X2,inner_pasch(X1,X2,X3,X5,X4),X4),true),true) = true,
inference(step,[status(thm)],[t45,t96]) ).
cnf(t1092,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),sF1,between(X2,inner_pasch(X1,X2,X3,X5,X4),X4),true),true) = true,
inference(step,[status(thm)],[t1091,t96]) ).
cnf(t1093,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),sF1,between(X2,inner_pasch(X1,X2,X3,X5,X4),X4),sF1),true) = true,
inference(step,[status(thm)],[t1092,t96]) ).
cnf(t1094,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),sF1,between(X2,inner_pasch(X1,X2,X3,X5,X4),X4),sF1),sF1) = true,
inference(step,[status(thm)],[t1093,t96]) ).
cnf(t1095,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),sF1,between(X2,inner_pasch(X1,X2,X3,X5,X4),X4),sF1),sF1) = sF1,
inference(step,[status(thm)],[t1094,t96]) ).
cnf(t348,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X4,X5,X3),sF1,between(X2,inner_pasch(X1,X2,X3,X5,X4),X4),sF1),sF1) = sF1,
inference(orient,[status(thm)],[t1095]) ).
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(t994,plain,
between(X1,X2,X2) = sF1,
inference(step,[status(thm)],[t64,t96]) ).
cnf(t101,plain,
between(X1,X2,X2) = sF1,
inference(orient,[status(thm)],[t994]) ).
cnf(t350,plain,
sF1 = ifeq(between(X1,X2,X3),sF1,ifeq(sF1,sF1,between(X2,inner_pasch(X1,X2,X3,X3,X4),X4),sF1),sF1),
inference(cp,[status(thm)],[t348,t101]) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t89,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(t1167,plain,
sF1 = ifeq(between(X1,X2,X3),sF1,between(X2,inner_pasch(X1,X2,X3,X3,X4),X4),sF1),
inference(step,[status(thm)],[t350,t89]) ).
cnf(t738,plain,
ifeq(between(X1,X2,X3),sF1,between(X2,inner_pasch(X1,X2,X3,X3,X4),X4),sF1) = sF1,
inference(orient,[status(thm)],[t1167]) ).
cnf(f45,hypothesis,
between(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_between_a_and_c) ).
fof(f45_nnf,plain,
between(a,b,c),
inference(nnf_transformation,[status(thm)],[f45]) ).
cnf(c45,plain,
between(a,b,c),
inference(cnf_transformation,[status(esa)],[f45_nnf]) ).
cnf(t6,plain,
between(a,b,c) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
cnf(t65,plain,
between(a,b,c) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t996,plain,
between(a,b,c) = sF1,
inference(step,[status(thm)],[t65,t96]) ).
cnf(t103,plain,
between(a,b,c) = sF1,
inference(orient,[status(thm)],[t996]) ).
cnf(t739,plain,
sF1 = ifeq(sF1,sF1,between(b,inner_pasch(a,b,c,c,X1),X1),sF1),
inference(cp,[status(thm)],[t738,t103]) ).
cnf(t1168,plain,
sF1 = between(b,inner_pasch(a,b,c,c,X1),X1),
inference(step,[status(thm)],[t739,t89]) ).
cnf(t753,plain,
between(b,inner_pasch(a,b,c,c,X1),X1) = sF1,
inference(orient,[status(thm)],[t1168]) ).
cnf(t754,plain,
inner_pasch(a,b,c,c,b) = ifeq(sF1,sF1,b,inner_pasch(a,b,c,c,b)),
inference(cp,[status(thm)],[t121,t753]) ).
cnf(t1169,plain,
inner_pasch(a,b,c,c,b) = b,
inference(step,[status(thm)],[t754,t89]) ).
cnf(t770,plain,
inner_pasch(a,b,c,c,b) = b,
inference(orient,[status(thm)],[t1169]) ).
cnf(t771,plain,
sF1 = ifeq(between(a,b,c),sF1,ifeq(between(b,c,c),sF1,between(c,b,a),sF1),sF1),
inference(cp,[status(thm)],[t415,t770]) ).
cnf(t1170,plain,
sF1 = ifeq(sF1,sF1,ifeq(between(b,c,c),sF1,between(c,b,a),sF1),sF1),
inference(step,[status(thm)],[t771,t103]) ).
cnf(t1171,plain,
sF1 = ifeq(between(b,c,c),sF1,between(c,b,a),sF1),
inference(step,[status(thm)],[t1170,t89]) ).
cnf(t1172,plain,
sF1 = ifeq(sF1,sF1,between(c,b,a),sF1),
inference(step,[status(thm)],[t1171,t101]) ).
cnf(t1173,plain,
sF1 = between(c,b,a),
inference(step,[status(thm)],[t1172,t89]) ).
cnf(t1174,plain,
sF1 = sF0,
inference(step,[status(thm)],[t1173,t73]) ).
cnf(t772,plain,
sF1 = sF0,
inference(orient,[status(thm)],[t1174]) ).
cnf(t1189,plain,
true = sF0,
inference(step,[status(thm)],[t96,t772]) ).
cnf(t787,plain,
true = sF0,
inference(orient,[status(thm)],[t1189]) ).
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,t787]) ).
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 : GEO001-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 10:12:29 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.53/1.29 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.53/1.29 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------