%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO047-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 01:16:46 PM UTC 2026
% Result : Unsatisfiable 8.93s 1.70s
% Output : Proof 8.93s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t69,axiom,
sF1 = ifeq(between(u,v,x),true,false,true),
introduced(definition) ).
cnf(f58,negated_conjecture,
~ between(u,v,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v_between_u_and_x) ).
fof(f58_nnf,plain,
~ between(u,v,x),
inference(nnf_transformation,[status(thm)],[f58]) ).
fof(f58_sk,plain,
~ between(u,v,x),
inference(skolemisation,[status(esa)],[f58_nnf]) ).
cnf(c58,plain,
~ between(u,v,x),
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
cnf(t11,plain,
between(u,v,x) = false,
inference(equality_encoding,[status(esa)],[c58]) ).
cnf(t81,plain,
between(u,v,x) = false,
inference(orient,[status(thm)],[t11]) ).
cnf(t68,axiom,
sF0 = between(u,v,x),
introduced(definition) ).
cnf(t1097,plain,
sF0 = false,
inference(step,[status(thm)],[t68,t81]) ).
cnf(t83,plain,
false = sF0,
inference(orient,[status(thm)],[t1097]) ).
cnf(t1106,plain,
between(u,v,x) = sF0,
inference(step,[status(thm)],[t81,t83]) ).
cnf(t92,plain,
between(u,v,x) = sF0,
inference(orient,[status(thm)],[t1106]) ).
cnf(t1112,plain,
sF1 = ifeq(sF0,true,false,true),
inference(step,[status(thm)],[t69,t92]) ).
cnf(t1113,plain,
sF1 = ifeq(sF0,true,sF0,true),
inference(step,[status(thm)],[t1112,t83]) ).
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(t23,plain,
ifeq(between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t7,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = false,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t77,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = false,
inference(orient,[status(thm)],[t7]) ).
cnf(t1100,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = sF0,
inference(step,[status(thm)],[t77,t83]) ).
cnf(t86,plain,
between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = sF0,
inference(orient,[status(thm)],[t1100]) ).
cnf(t1110,plain,
ifeq(sF0,true,false,true) = true,
inference(step,[status(thm)],[t23,t86]) ).
cnf(t1111,plain,
ifeq(sF0,true,sF0,true) = true,
inference(step,[status(thm)],[t1110,t83]) ).
cnf(t108,plain,
ifeq(sF0,true,sF0,true) = true,
inference(orient,[status(thm)],[t1111]) ).
cnf(t1114,plain,
sF1 = true,
inference(step,[status(thm)],[t1113,t108]) ).
cnf(t110,plain,
true = sF1,
inference(orient,[status(thm)],[t1114]) ).
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(t31,plain,
ifeq(between(X1,X2,X3),true,between(X3,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
cnf(t1143,plain,
ifeq(between(X1,X2,X3),sF1,between(X3,X2,X1),true) = true,
inference(step,[status(thm)],[t31,t110]) ).
cnf(t1144,plain,
ifeq(between(X1,X2,X3),sF1,between(X3,X2,X1),sF1) = true,
inference(step,[status(thm)],[t1143,t110]) ).
cnf(t1145,plain,
ifeq(between(X1,X2,X3),sF1,between(X3,X2,X1),sF1) = sF1,
inference(step,[status(thm)],[t1144,t110]) ).
cnf(t145,plain,
ifeq(between(X1,X2,X3),sF1,between(X3,X2,X1),sF1) = sF1,
inference(orient,[status(thm)],[t1145]) ).
cnf(f55,axiom,
( between(U,W,X)
| ~ between(V,W,X)
| ~ between(U,V,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b8) ).
fof(f55_nnf,plain,
! [U,V,X,W] :
( between(U,W,X)
| ~ between(V,W,X)
| ~ between(U,V,X) ),
inference(nnf_transformation,[status(thm)],[f55]) ).
fof(f55_sk,plain,
! [U,V,X,W] :
( between(U,W,X)
| ~ between(V,W,X)
| ~ between(U,V,X) ),
inference(skolemisation,[status(esa)],[f55_nnf]) ).
cnf(c55,plain,
( between(X0,X3,X2)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(t48,plain,
ifeq(between(X1,X2,X3),true,ifeq(between(X2,X4,X3),true,between(X1,X4,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c55]) ).
cnf(t1236,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X2,X4,X3),true,between(X1,X4,X3),true),true) = true,
inference(step,[status(thm)],[t48,t110]) ).
cnf(t1237,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X2,X4,X3),sF1,between(X1,X4,X3),true),true) = true,
inference(step,[status(thm)],[t1236,t110]) ).
cnf(t1238,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X2,X4,X3),sF1,between(X1,X4,X3),sF1),true) = true,
inference(step,[status(thm)],[t1237,t110]) ).
cnf(t1239,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X2,X4,X3),sF1,between(X1,X4,X3),sF1),sF1) = true,
inference(step,[status(thm)],[t1238,t110]) ).
cnf(t1240,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X2,X4,X3),sF1,between(X1,X4,X3),sF1),sF1) = sF1,
inference(step,[status(thm)],[t1239,t110]) ).
cnf(t423,plain,
ifeq(between(X1,X2,X3),sF1,ifeq(between(X2,X4,X3),sF1,between(X1,X4,X3),sF1),sF1) = sF1,
inference(orient,[status(thm)],[t1240]) ).
cnf(f56,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f56_nnf,plain,
between(u,v,w),
inference(nnf_transformation,[status(thm)],[f56]) ).
cnf(c56,plain,
between(u,v,w),
inference(cnf_transformation,[status(esa)],[f56_nnf]) ).
cnf(t10,plain,
between(u,v,w) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(t80,plain,
between(u,v,w) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t1121,plain,
between(u,v,w) = sF1,
inference(step,[status(thm)],[t80,t110]) ).
cnf(t119,plain,
between(u,v,w) = sF1,
inference(orient,[status(thm)],[t1121]) ).
cnf(t152,plain,
sF1 = ifeq(sF1,sF1,between(w,v,u),sF1),
inference(cp,[status(thm)],[t145,t119]) ).
cnf(t18,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t102,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t18]) ).
cnf(t1146,plain,
sF1 = between(w,v,u),
inference(step,[status(thm)],[t152,t102]) ).
cnf(t160,plain,
between(w,v,u) = sF1,
inference(orient,[status(thm)],[t1146]) ).
cnf(t443,plain,
sF1 = ifeq(between(X1,w,u),sF1,ifeq(sF1,sF1,between(X1,v,u),sF1),sF1),
inference(cp,[status(thm)],[t423,t160]) ).
cnf(t1301,plain,
sF1 = ifeq(between(X1,w,u),sF1,between(X1,v,u),sF1),
inference(step,[status(thm)],[t443,t102]) ).
cnf(t868,plain,
ifeq(between(X1,w,u),sF1,between(X1,v,u),sF1) = sF1,
inference(orient,[status(thm)],[t1301]) ).
cnf(f57,hypothesis,
between(u,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_between_u_and_x) ).
fof(f57_nnf,plain,
between(u,w,x),
inference(nnf_transformation,[status(thm)],[f57]) ).
cnf(c57,plain,
between(u,w,x),
inference(cnf_transformation,[status(esa)],[f57_nnf]) ).
cnf(t12,plain,
between(u,w,x) = true,
inference(equality_encoding,[status(esa)],[c57]) ).
cnf(t82,plain,
between(u,w,x) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t1123,plain,
between(u,w,x) = sF1,
inference(step,[status(thm)],[t82,t110]) ).
cnf(t121,plain,
between(u,w,x) = sF1,
inference(orient,[status(thm)],[t1123]) ).
cnf(t156,plain,
sF1 = ifeq(sF1,sF1,between(x,w,u),sF1),
inference(cp,[status(thm)],[t145,t121]) ).
cnf(t1147,plain,
sF1 = between(x,w,u),
inference(step,[status(thm)],[t156,t102]) ).
cnf(t161,plain,
between(x,w,u) = sF1,
inference(orient,[status(thm)],[t1147]) ).
cnf(t869,plain,
sF1 = ifeq(sF1,sF1,between(x,v,u),sF1),
inference(cp,[status(thm)],[t868,t161]) ).
cnf(t1302,plain,
sF1 = between(x,v,u),
inference(step,[status(thm)],[t869,t102]) ).
cnf(t871,plain,
between(x,v,u) = sF1,
inference(orient,[status(thm)],[t1302]) ).
cnf(t874,plain,
sF1 = ifeq(sF1,sF1,between(u,v,x),sF1),
inference(cp,[status(thm)],[t145,t871]) ).
cnf(t1303,plain,
sF1 = between(u,v,x),
inference(step,[status(thm)],[t874,t102]) ).
cnf(t1304,plain,
sF1 = sF0,
inference(step,[status(thm)],[t1303,t92]) ).
cnf(t889,plain,
sF1 = sF0,
inference(orient,[status(thm)],[t1304]) ).
cnf(t1323,plain,
true = sF0,
inference(step,[status(thm)],[t110,t889]) ).
cnf(t908,plain,
true = sF0,
inference(orient,[status(thm)],[t1323]) ).
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,c58]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t908]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t83]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO047-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.38 % Computer : n018.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Wed Sep 23 10:36:01 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.93/1.70 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.93/1.70 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------