%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO057-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 01:16:50 PM UTC 2026
% Result : Unsatisfiable 0.07s 15.93s
% Output : Proof 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 42 unt; 0 def)
% Number of atoms : 42 ( 29 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 18 ( 18 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-4 aty)
% Number of variables : 30 ( 4 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f32,negated_conjecture,
u != reflection(u,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_null_extension_by_reflection) ).
fof(f32_nnf,plain,
u != reflection(u,u),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
u != reflection(u,u),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c32,plain,
u != reflection(u,u),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(u3,axiom,
eq(u,reflection(u,u)) = false,
inference(equality_encoding,[status(esa)],[c32]) ).
cnf(f18,axiom,
reflection(U,V) = extension(U,V,U,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
fof(f18_nnf,plain,
! [U,V] : reflection(U,V) = extension(U,V,U,V),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [U,V] : reflection(U,V) = extension(U,V,U,V),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
reflection(X0,X1) = extension(X0,X1,X0,X1),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(d0,axiom,
reflection(X0,X1) = extension(X0,X1,X0,X1),
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t12,plain,
eq(u,extension(u,u,u,u)) = false,
inference(definition_unfolding,[status(thm)],[u3,d0]) ).
cnf(t43,axiom,
sF0 = extension(u,u,u,u),
introduced(definition) ).
cnf(f28,axiom,
V = extension(U,V,W,W),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
fof(f28_nnf,plain,
! [V,U,W] : V = extension(U,V,W,W),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [V,U,W] : V = extension(U,V,W,W),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
X0 = extension(X1,X0,X2,X2),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(t10,plain,
extension(X1,X2,X3,X3) = X2,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(t56,plain,
extension(X1,X2,X3,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t68,plain,
sF0 = u,
inference(step,[status(thm)],[t43,t56]) ).
cnf(t58,plain,
u = sF0,
inference(orient,[status(thm)],[t68]) ).
cnf(t69,plain,
eq(sF0,extension(u,u,u,u)) = false,
inference(step,[status(thm)],[t12,t58]) ).
cnf(t70,plain,
eq(sF0,u) = false,
inference(step,[status(thm)],[t69,t56]) ).
cnf(t71,plain,
eq(sF0,sF0) = false,
inference(step,[status(thm)],[t70,t58]) ).
cnf(t0,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t46,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t72,plain,
true = false,
inference(step,[status(thm)],[t71,t46]) ).
cnf(t59,plain,
false = true,
inference(orient,[status(thm)],[t72]) ).
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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c9,c10,c11,c32]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t59]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO057-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.04/15.53 % Computer : n012.cluster.edu
% 0.04/15.53 % Model : x86_64 x86_64
% 0.04/15.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/15.53 % Memory : 8046.5625MB
% 0.04/15.53 % OS : Linux 6.8.0-71-generic
% 0.04/15.53 % CPULimit : 300
% 0.04/15.53 % WCLimit : 300
% 0.04/15.53 % DateTime : Wed Sep 23 10:37:30 UTC 2026
% 0.04/15.53 % CPUTime :
% 0.04/15.53 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/15.93 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/15.93 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------