%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO056-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 4.53s 1.06s
% Output : Proof 4.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 53 unt; 0 def)
% Number of atoms : 53 ( 40 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 19 ( 19 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-4 aty)
% Number of variables : 12 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f20,negated_conjecture,
v != reflection(u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v_equals_reflection) ).
fof(f20_nnf,plain,
v != reflection(u,v),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
v != reflection(u,v),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
v != reflection(u,v),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(u1,axiom,
eq(v,reflection(u,v)) = false,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(f18,axiom,
reflection(U,V) = extension(U,V,U,V),
file('/export/starexec/sandbox/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(t11,plain,
eq(v,extension(u,v,u,v)) = false,
inference(definition_unfolding,[status(thm)],[u1,d0]) ).
cnf(f19,hypothesis,
u = v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_equals_v) ).
fof(f19_nnf,plain,
u = v,
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
u = v,
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(t0,plain,
v = u,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t34,plain,
u = v,
inference(orient,[status(thm)],[t0]) ).
cnf(t101,plain,
eq(v,extension(v,v,u,v)) = false,
inference(step,[status(thm)],[t11,t34]) ).
cnf(t102,plain,
eq(v,extension(v,v,v,v)) = false,
inference(step,[status(thm)],[t101,t34]) ).
cnf(t31,axiom,
sF0 = extension(u,v,u,v),
introduced(definition) ).
cnf(t99,plain,
sF0 = extension(v,v,u,v),
inference(step,[status(thm)],[t31,t34]) ).
cnf(t100,plain,
sF0 = extension(v,v,v,v),
inference(step,[status(thm)],[t99,t34]) ).
cnf(t45,plain,
extension(v,v,v,v) = sF0,
inference(orient,[status(thm)],[t100]) ).
cnf(t103,plain,
eq(v,sF0) = false,
inference(step,[status(thm)],[t102,t45]) ).
cnf(t46,plain,
eq(v,sF0) = false,
inference(orient,[status(thm)],[t103]) ).
cnf(t32,axiom,
sF1 = eq(v,extension(u,v,u,v)),
introduced(definition) ).
cnf(t104,plain,
sF1 = eq(v,extension(v,v,u,v)),
inference(step,[status(thm)],[t32,t34]) ).
cnf(t105,plain,
sF1 = eq(v,extension(v,v,v,v)),
inference(step,[status(thm)],[t104,t34]) ).
cnf(t106,plain,
sF1 = eq(v,sF0),
inference(step,[status(thm)],[t105,t45]) ).
cnf(t107,plain,
sF1 = false,
inference(step,[status(thm)],[t106,t46]) ).
cnf(t50,plain,
false = sF1,
inference(orient,[status(thm)],[t107]) ).
cnf(t116,plain,
eq(v,sF0) = sF1,
inference(step,[status(thm)],[t46,t50]) ).
cnf(t59,plain,
eq(v,sF0) = sF1,
inference(orient,[status(thm)],[t116]) ).
cnf(t80,plain,
eq(sF0,sF0) = sF1,
inference(rw,[status(thm)],[t59]) ).
cnf(t1,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t35,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t131,plain,
true = sF1,
inference(step,[status(thm)],[t80,t35]) ).
cnf(t84,plain,
true = sF1,
inference(orient,[status(thm)],[t131]) ).
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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c9,c10,c11,c20]) ).
cnf(g0_0,plain,
sF1 != false,
inference(rw,[status(thm)],[goal_0,t84]) ).
cnf(g0_1,plain,
sF1 != sF1,
inference(rw,[status(thm)],[g0_0,t50]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO056-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 10:38:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.53/1.06 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.53/1.06 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------