%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO048-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 01:16:48 PM UTC 2026
% Result : Unsatisfiable 6.56s 11.36s
% Output : Proof 6.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 96 ( 88 unt; 0 def)
% Number of atoms : 108 ( 58 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 50 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 13 con; 0-5 aty)
% Number of variables : 62 ( 4 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t71,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(t1503,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(orient,[status(thm)],[t71]) ).
cnf(t83,axiom,
sF1 = inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),
introduced(definition) ).
cnf(t82,axiom,
sF0 = inner_pasch(u,x,u1,v1,w),
introduced(definition) ).
cnf(t114,plain,
inner_pasch(u,x,u1,v1,w) = sF0,
inference(orient,[status(thm)],[t82]) ).
cnf(t1742,plain,
sF1 = inner_pasch(v1,sF0,u,v,w),
inference(step,[status(thm)],[t83,t114]) ).
cnf(t196,plain,
inner_pasch(v1,sF0,u,v,w) = sF1,
inference(orient,[status(thm)],[t1742]) ).
cnf(t1531,plain,
true = ifeq(between(v1,sF0,u),true,ifeq(between(w,v,u),true,between(v,sF1,v1),true),true),
inference(cp,[status(thm)],[t1503,t196]) ).
cnf(t1520,plain,
true = ifeq(between(u,x,u1),true,ifeq(between(w,v1,u1),true,between(v1,sF0,u),true),true),
inference(cp,[status(thm)],[t1503,t114]) ).
cnf(f65,hypothesis,
between(u,x,u1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_between_u_and_u1) ).
fof(f65_nnf,plain,
between(u,x,u1),
inference(nnf_transformation,[status(thm)],[f65]) ).
cnf(c65,plain,
between(u,x,u1),
inference(cnf_transformation,[status(esa)],[f65_nnf]) ).
cnf(t14,plain,
between(u,x,u1) = true,
inference(equality_encoding,[status(esa)],[c65]) ).
cnf(t102,plain,
between(u,x,u1) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t1898,plain,
true = ifeq(true,true,ifeq(between(w,v1,u1),true,between(v1,sF0,u),true),true),
inference(step,[status(thm)],[t1520,t102]) ).
cnf(t21,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t110,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t21]) ).
cnf(t1899,plain,
true = ifeq(between(w,v1,u1),true,between(v1,sF0,u),true),
inference(step,[status(thm)],[t1898,t110]) ).
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(t39,plain,
ifeq(between(X1,X2,X3),true,between(X3,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
cnf(t137,plain,
ifeq(between(X1,X2,X3),true,between(X3,X2,X1),true) = true,
inference(orient,[status(thm)],[t39]) ).
cnf(f64,hypothesis,
between(u1,v1,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1_between_u1_and_w) ).
fof(f64_nnf,plain,
between(u1,v1,w),
inference(nnf_transformation,[status(thm)],[f64]) ).
cnf(c64,plain,
between(u1,v1,w),
inference(cnf_transformation,[status(esa)],[f64_nnf]) ).
cnf(t15,plain,
between(u1,v1,w) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(t103,plain,
between(u1,v1,w) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(t148,plain,
true = ifeq(true,true,between(w,v1,u1),true),
inference(cp,[status(thm)],[t137,t103]) ).
cnf(t1739,plain,
true = between(w,v1,u1),
inference(step,[status(thm)],[t148,t110]) ).
cnf(t154,plain,
between(w,v1,u1) = true,
inference(orient,[status(thm)],[t1739]) ).
cnf(t1900,plain,
true = ifeq(true,true,between(v1,sF0,u),true),
inference(step,[status(thm)],[t1899,t154]) ).
cnf(t1901,plain,
true = between(v1,sF0,u),
inference(step,[status(thm)],[t1900,t110]) ).
cnf(t1588,plain,
between(v1,sF0,u) = true,
inference(orient,[status(thm)],[t1901]) ).
cnf(t1905,plain,
true = ifeq(true,true,ifeq(between(w,v,u),true,between(v,sF1,v1),true),true),
inference(step,[status(thm)],[t1531,t1588]) ).
cnf(t1906,plain,
true = ifeq(between(w,v,u),true,between(v,sF1,v1),true),
inference(step,[status(thm)],[t1905,t110]) ).
cnf(f63,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f63_nnf,plain,
between(u,v,w),
inference(nnf_transformation,[status(thm)],[f63]) ).
cnf(c63,plain,
between(u,v,w),
inference(cnf_transformation,[status(esa)],[f63_nnf]) ).
cnf(t13,plain,
between(u,v,w) = true,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(t101,plain,
between(u,v,w) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t144,plain,
true = ifeq(true,true,between(w,v,u),true),
inference(cp,[status(thm)],[t137,t101]) ).
cnf(t1737,plain,
true = between(w,v,u),
inference(step,[status(thm)],[t144,t110]) ).
cnf(t152,plain,
between(w,v,u) = true,
inference(orient,[status(thm)],[t1737]) ).
cnf(t1907,plain,
true = ifeq(true,true,between(v,sF1,v1),true),
inference(step,[status(thm)],[t1906,t152]) ).
cnf(t1908,plain,
true = between(v,sF1,v1),
inference(step,[status(thm)],[t1907,t110]) ).
cnf(f67,negated_conjecture,
~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_conclusion2) ).
fof(f67_nnf,plain,
~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1),
inference(nnf_transformation,[status(thm)],[f67]) ).
fof(f67_sk,plain,
~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1),
inference(skolemisation,[status(esa)],[f67_nnf]) ).
cnf(c67,plain,
~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
cnf(t51,plain,
between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1) = false,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(t1757,plain,
between(v,inner_pasch(v1,sF0,u,v,w),v1) = false,
inference(step,[status(thm)],[t51,t114]) ).
cnf(t1758,plain,
between(v,sF1,v1) = false,
inference(step,[status(thm)],[t1757,t196]) ).
cnf(t232,plain,
between(v,sF1,v1) = false,
inference(orient,[status(thm)],[t1758]) ).
cnf(t1909,plain,
true = false,
inference(step,[status(thm)],[t1908,t232]) ).
cnf(t1641,plain,
false = true,
inference(orient,[status(thm)],[t1909]) ).
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(f57,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_1) ).
fof(f57_nnf,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(nnf_transformation,[status(thm)],[f57]) ).
fof(f57_sk,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(skolemisation,[status(esa)],[f57_nnf]) ).
cnf(c57,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(cnf_transformation,[status(esa)],[f57_sk]) ).
cnf(f58,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_2) ).
fof(f58_nnf,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(nnf_transformation,[status(thm)],[f58]) ).
fof(f58_sk,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(skolemisation,[status(esa)],[f58_nnf]) ).
cnf(c58,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
cnf(f59,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_3) ).
fof(f59_nnf,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(nnf_transformation,[status(thm)],[f59]) ).
fof(f59_sk,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(skolemisation,[status(esa)],[f59_nnf]) ).
cnf(c59,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(cnf_transformation,[status(esa)],[f59_sk]) ).
cnf(f60,axiom,
V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_1) ).
fof(f60_nnf,plain,
! [V,U] : V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2),
inference(nnf_transformation,[status(thm)],[f60]) ).
fof(f60_sk,plain,
! [V,U] : V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2),
inference(skolemisation,[status(esa)],[f60_nnf]) ).
cnf(c60,plain,
X0 != extension(X1,X0,lower_dimension_point_1,lower_dimension_point_2),
inference(cnf_transformation,[status(esa)],[f60_sk]) ).
cnf(f66,negated_conjecture,
~ between(x,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_conclusion1) ).
fof(f66_nnf,plain,
~ between(x,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),w),
inference(nnf_transformation,[status(thm)],[f66]) ).
fof(f66_sk,plain,
~ between(x,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),w),
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c66,plain,
~ between(x,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),w),
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c9,c10,c11,c57,c58,c59,c60,c66,c67]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1641]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO048-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/10.39 % Computer : n016.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Wed Sep 23 10:39:37 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.56/11.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.56/11.36 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------