%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO062-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 01:16:51 PM UTC 2026
% Result : Unsatisfiable 6.14s 1.25s
% Output : Proof 6.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 83 ( 83 unt; 0 def)
% Number of atoms : 83 ( 70 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 35 ( 35 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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; 12 con; 0-4 aty)
% Number of variables : 36 ( 4 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t90,axiom,
sF3 = ifeq(v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v),false,true),
introduced(definition) ).
cnf(t87,axiom,
sF0 = extension(w,u,lower_dimension_point_1,lower_dimension_point_2),
introduced(definition) ).
cnf(t115,plain,
extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = sF0,
inference(orient,[status(thm)],[t87]) ).
cnf(t2152,plain,
sF3 = ifeq(v,extension(sF0,u,u,v),false,true),
inference(step,[status(thm)],[t90,t115]) ).
cnf(t88,axiom,
sF1 = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v),
introduced(definition) ).
cnf(t2052,plain,
sF1 = extension(sF0,u,u,v),
inference(step,[status(thm)],[t88,t115]) ).
cnf(t147,plain,
extension(sF0,u,u,v) = sF1,
inference(orient,[status(thm)],[t2052]) ).
cnf(t2153,plain,
sF3 = ifeq(v,sF1,false,true),
inference(step,[status(thm)],[t2152,t147]) ).
cnf(t89,axiom,
sF2 = eq(v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v)),
introduced(definition) ).
cnf(t2059,plain,
sF2 = eq(v,extension(sF0,u,u,v)),
inference(step,[status(thm)],[t89,t115]) ).
cnf(t2060,plain,
sF2 = eq(v,sF1),
inference(step,[status(thm)],[t2059,t147]) ).
cnf(f74,negated_conjecture,
v != insertion(u,w,u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_equals_insertion) ).
fof(f74_nnf,plain,
v != insertion(u,w,u,v),
inference(nnf_transformation,[status(thm)],[f74]) ).
fof(f74_sk,plain,
v != insertion(u,w,u,v),
inference(skolemisation,[status(esa)],[f74_nnf]) ).
cnf(c74,plain,
v != insertion(u,w,u,v),
inference(cnf_transformation,[status(esa)],[f74_sk]) ).
cnf(u11,axiom,
eq(v,insertion(u,w,u,v)) = false,
inference(equality_encoding,[status(esa)],[c74]) ).
cnf(f19,axiom,
insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',insertion) ).
fof(f19_nnf,plain,
! [U1,W1,U,V] : insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [U1,W1,U,V] : insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
insertion(X0,X1,X2,X3) = extension(extension(X1,X0,lower_dimension_point_1,lower_dimension_point_2),X0,X2,X3),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(d1,axiom,
insertion(X0,X1,X2,X3) = extension(extension(X1,X0,lower_dimension_point_1,lower_dimension_point_2),X0,X2,X3),
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t37,plain,
eq(v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v)) = false,
inference(definition_unfolding,[status(thm)],[u11,d1]) ).
cnf(t2053,plain,
eq(v,extension(sF0,u,u,v)) = false,
inference(step,[status(thm)],[t37,t115]) ).
cnf(t2054,plain,
eq(v,sF1) = false,
inference(step,[status(thm)],[t2053,t147]) ).
cnf(t153,plain,
eq(v,sF1) = false,
inference(orient,[status(thm)],[t2054]) ).
cnf(t2061,plain,
sF2 = false,
inference(step,[status(thm)],[t2060,t153]) ).
cnf(t220,plain,
false = sF2,
inference(orient,[status(thm)],[t2061]) ).
cnf(t2154,plain,
sF3 = ifeq(v,sF1,sF2,true),
inference(step,[status(thm)],[t2153,t220]) ).
cnf(u10,axiom,
ifeq(v,insertion(u,w,u,v),false,true) = true,
inference(equality_encoding,[status(esa)],[c74]) ).
cnf(t51,plain,
ifeq(v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v),false,true) = true,
inference(definition_unfolding,[status(thm)],[u10,d1]) ).
cnf(t2149,plain,
ifeq(v,extension(sF0,u,u,v),false,true) = true,
inference(step,[status(thm)],[t51,t115]) ).
cnf(t2150,plain,
ifeq(v,sF1,false,true) = true,
inference(step,[status(thm)],[t2149,t147]) ).
cnf(t2151,plain,
ifeq(v,sF1,sF2,true) = true,
inference(step,[status(thm)],[t2150,t220]) ).
cnf(t387,plain,
ifeq(v,sF1,sF2,true) = true,
inference(orient,[status(thm)],[t2151]) ).
cnf(t2155,plain,
sF3 = true,
inference(step,[status(thm)],[t2154,t387]) ).
cnf(t388,plain,
true = sF3,
inference(orient,[status(thm)],[t2155]) ).
cnf(f61,axiom,
V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e3_1) ).
fof(f61_nnf,plain,
! [V,U] : V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2),
inference(nnf_transformation,[status(thm)],[f61]) ).
fof(f61_sk,plain,
! [V,U] : V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2),
inference(skolemisation,[status(esa)],[f61_nnf]) ).
cnf(c61,plain,
X0 != extension(X1,X0,lower_dimension_point_1,lower_dimension_point_2),
inference(cnf_transformation,[status(esa)],[f61_sk]) ).
cnf(t23,plain,
eq(X1,extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2)) = false,
inference(equality_encoding,[status(esa)],[c61]) ).
cnf(t116,plain,
eq(X1,extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2)) = false,
inference(orient,[status(thm)],[t23]) ).
cnf(t117,plain,
false = eq(u,sF0),
inference(cp,[status(thm)],[t116,t115]) ).
cnf(t118,plain,
eq(u,sF0) = false,
inference(orient,[status(thm)],[t117]) ).
cnf(t2081,plain,
eq(u,sF0) = sF2,
inference(step,[status(thm)],[t118,t220]) ).
cnf(t240,plain,
eq(u,sF0) = sF2,
inference(orient,[status(thm)],[t2081]) ).
cnf(t1810,plain,
eq(sF0,sF0) = sF2,
inference(rw,[status(thm)],[t240]) ).
cnf(t0,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t91,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t2156,plain,
eq(X1,X1) = sF3,
inference(step,[status(thm)],[t91,t388]) ).
cnf(t389,plain,
eq(X1,X1) = sF3,
inference(orient,[status(thm)],[t2156]) ).
cnf(t2539,plain,
sF3 = sF2,
inference(step,[status(thm)],[t1810,t389]) ).
cnf(t1929,plain,
sF3 = sF2,
inference(orient,[status(thm)],[t2539]) ).
cnf(t2574,plain,
true = sF2,
inference(step,[status(thm)],[t388,t1929]) ).
cnf(t1964,plain,
true = sF2,
inference(orient,[status(thm)],[t2574]) ).
cnf(f9,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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(f58,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_1) ).
fof(f58_nnf,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(nnf_transformation,[status(thm)],[f58]) ).
fof(f58_sk,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(skolemisation,[status(esa)],[f58_nnf]) ).
cnf(c58,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
cnf(f59,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_2) ).
fof(f59_nnf,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(nnf_transformation,[status(thm)],[f59]) ).
fof(f59_sk,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(skolemisation,[status(esa)],[f59_nnf]) ).
cnf(c59,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(cnf_transformation,[status(esa)],[f59_sk]) ).
cnf(f60,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_3) ).
fof(f60_nnf,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(nnf_transformation,[status(thm)],[f60]) ).
fof(f60_sk,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(skolemisation,[status(esa)],[f60_nnf]) ).
cnf(c60,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(cnf_transformation,[status(esa)],[f60_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c9,c10,c11,c58,c59,c60,c61,c74]) ).
cnf(g0_0,plain,
sF2 != false,
inference(rw,[status(thm)],[goal_0,t1964]) ).
cnf(g0_1,plain,
sF2 != sF2,
inference(rw,[status(thm)],[g0_0,t220]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO062-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 10:42:09 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.14/1.25 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.14/1.25 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------