%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO053-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 14.90s 2.33s
% Output : Proof 14.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 59 unt; 0 def)
% Number of atoms : 59 ( 46 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 35 ( 35 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 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 ( 2 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t98,axiom,
sF1 = ifeq(v,w,false,true),
introduced(definition) ).
cnf(t97,axiom,
sF0 = eq(v,w),
introduced(definition) ).
cnf(f84,negated_conjecture,
v != w,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v_equals_w) ).
fof(f84_nnf,plain,
v != w,
inference(nnf_transformation,[status(thm)],[f84]) ).
fof(f84_sk,plain,
v != w,
inference(skolemisation,[status(esa)],[f84_nnf]) ).
cnf(c84,plain,
v != w,
inference(cnf_transformation,[status(esa)],[f84_sk]) ).
cnf(t4,plain,
eq(v,w) = false,
inference(equality_encoding,[status(esa)],[c84]) ).
cnf(t103,plain,
eq(v,w) = false,
inference(orient,[status(thm)],[t4]) ).
cnf(t5099,plain,
sF0 = false,
inference(step,[status(thm)],[t97,t103]) ).
cnf(t108,plain,
false = sF0,
inference(orient,[status(thm)],[t5099]) ).
cnf(t5118,plain,
sF1 = ifeq(v,w,sF0,true),
inference(step,[status(thm)],[t98,t108]) ).
cnf(t25,plain,
ifeq(v,w,false,true) = true,
inference(equality_encoding,[status(esa)],[c84]) ).
cnf(t5117,plain,
ifeq(v,w,sF0,true) = true,
inference(step,[status(thm)],[t25,t108]) ).
cnf(t138,plain,
ifeq(v,w,sF0,true) = true,
inference(orient,[status(thm)],[t5117]) ).
cnf(t5119,plain,
sF1 = true,
inference(step,[status(thm)],[t5118,t138]) ).
cnf(t139,plain,
true = sF1,
inference(orient,[status(thm)],[t5119]) ).
cnf(t5106,plain,
eq(v,w) = sF0,
inference(step,[status(thm)],[t103,t108]) ).
cnf(t115,plain,
eq(v,w) = sF0,
inference(orient,[status(thm)],[t5106]) ).
cnf(t4672,plain,
eq(w,w) = sF0,
inference(rw,[status(thm)],[t115]) ).
cnf(t0,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t99,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t5120,plain,
eq(X1,X1) = sF1,
inference(step,[status(thm)],[t99,t139]) ).
cnf(t140,plain,
eq(X1,X1) = sF1,
inference(orient,[status(thm)],[t5120]) ).
cnf(t5676,plain,
sF1 = sF0,
inference(step,[status(thm)],[t4672,t140]) ).
cnf(t4870,plain,
sF1 = sF0,
inference(orient,[status(thm)],[t5676]) ).
cnf(t5689,plain,
true = sF0,
inference(step,[status(thm)],[t139,t4870]) ).
cnf(t4883,plain,
true = sF0,
inference(orient,[status(thm)],[t5689]) ).
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(f58,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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(f61,axiom,
V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox/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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c9,c10,c11,c58,c59,c60,c61,c84]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t4883]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t108]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO053-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n001.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 10:41:49 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 14.90/2.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.90/2.33 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------