%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO056-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 01:16:49 PM UTC 2026
% Result : Unsatisfiable 3.88s 1.01s
% Output : Proof 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 54 unt; 0 def)
% Number of atoms : 54 ( 41 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 : 11 ( 11 usr; 8 con; 0-4 aty)
% Number of variables : 30 ( 4 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f33,negated_conjecture,
v != reflection(u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_equals_reflection) ).
fof(f33_nnf,plain,
v != reflection(u,v),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
v != reflection(u,v),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c33,plain,
v != reflection(u,v),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(u3,axiom,
eq(v,reflection(u,v)) = false,
inference(equality_encoding,[status(esa)],[c33]) ).
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(t13,plain,
eq(v,extension(u,v,u,v)) = false,
inference(definition_unfolding,[status(thm)],[u3,d0]) ).
cnf(t44,axiom,
sF0 = extension(u,v,u,v),
introduced(definition) ).
cnf(f32,hypothesis,
u = v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_equals_v) ).
fof(f32_nnf,plain,
u = v,
inference(nnf_transformation,[status(thm)],[f32]) ).
cnf(c32,plain,
u = v,
inference(cnf_transformation,[status(esa)],[f32_nnf]) ).
cnf(t0,plain,
v = u,
inference(equality_encoding,[status(esa)],[c32]) ).
cnf(t47,plain,
u = v,
inference(orient,[status(thm)],[t0]) ).
cnf(t72,plain,
sF0 = extension(v,v,u,v),
inference(step,[status(thm)],[t44,t47]) ).
cnf(t73,plain,
sF0 = extension(v,v,v,v),
inference(step,[status(thm)],[t72,t47]) ).
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(t11,plain,
extension(X1,X2,X3,X3) = X2,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(t58,plain,
extension(X1,X2,X3,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t74,plain,
sF0 = v,
inference(step,[status(thm)],[t73,t58]) ).
cnf(t60,plain,
v = sF0,
inference(orient,[status(thm)],[t74]) ).
cnf(t77,plain,
eq(sF0,extension(u,v,u,v)) = false,
inference(step,[status(thm)],[t13,t60]) ).
cnf(t75,plain,
u = sF0,
inference(step,[status(thm)],[t47,t60]) ).
cnf(t61,plain,
u = sF0,
inference(orient,[status(thm)],[t75]) ).
cnf(t78,plain,
eq(sF0,extension(sF0,v,u,v)) = false,
inference(step,[status(thm)],[t77,t61]) ).
cnf(t79,plain,
eq(sF0,extension(sF0,sF0,u,v)) = false,
inference(step,[status(thm)],[t78,t60]) ).
cnf(t80,plain,
eq(sF0,extension(sF0,sF0,sF0,v)) = false,
inference(step,[status(thm)],[t79,t61]) ).
cnf(t81,plain,
eq(sF0,extension(sF0,sF0,sF0,sF0)) = false,
inference(step,[status(thm)],[t80,t60]) ).
cnf(t82,plain,
eq(sF0,sF0) = false,
inference(step,[status(thm)],[t81,t58]) ).
cnf(t1,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t48,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t83,plain,
true = false,
inference(step,[status(thm)],[t82,t48]) ).
cnf(t63,plain,
false = true,
inference(orient,[status(thm)],[t83]) ).
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,c33]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t63]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO056-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 10:37:56 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.88/1.01 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.88/1.01 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------