%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO011-1 : TPTP v9.2.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:18:58 PM UTC 2026
% Result : Unsatisfiable 1.26s 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of clauses : 36 ( 19 unt; 7 nHn; 30 RR)
% Number of literals : 64 ( 15 equ; 26 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 64 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(identity_for_betweeness,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',identity_for_betweeness) ).
cnf(outer_pasch1,axiom,
( between(X1,outer_pasch(X2,X1,X4,X5,X3),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X3,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',outer_pasch1) ).
cnf(colinearity1,axiom,
( between(X1,X2,X3)
| between(X2,X1,X3)
| between(X1,X3,X2)
| ~ colinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-1.ax',colinearity1) ).
cnf(prove_lower_dimension_points_not_colinear,negated_conjecture,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lower_dimension_points_not_colinear) ).
cnf(lower_dimension1,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',lower_dimension1) ).
cnf(identity_for_equidistance,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',identity_for_equidistance) ).
cnf(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',segment_construction2) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',segment_construction1) ).
cnf(outer_pasch2,axiom,
( between(X5,X2,outer_pasch(X2,X1,X4,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X3,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',outer_pasch2) ).
cnf(lower_dimension2,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',lower_dimension2) ).
cnf(lower_dimension3,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',lower_dimension3) ).
cnf(c_0_11,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
identity_for_betweeness ).
cnf(c_0_12,axiom,
( between(X1,outer_pasch(X2,X1,X4,X5,X3),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X3,X5) ),
outer_pasch1 ).
cnf(c_0_13,axiom,
( between(X1,X2,X3)
| between(X2,X1,X3)
| between(X1,X3,X2)
| ~ colinear(X1,X2,X3) ),
colinearity1 ).
cnf(c_0_14,negated_conjecture,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
prove_lower_dimension_points_not_colinear ).
cnf(c_0_15,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
lower_dimension1 ).
cnf(c_0_16,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
identity_for_equidistance ).
cnf(c_0_17,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_18,plain,
( outer_pasch(X1,X2,X2,X3,X4) = X2
| ~ between(X2,X4,X3)
| ~ between(X2,X1,X4) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_19,negated_conjecture,
( between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2)
| between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_20,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_21,plain,
extension(X1,X2,X3,X3) = X2,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( outer_pasch(X1,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) = lower_dimension_point_2
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2)
| ~ between(lower_dimension_point_2,X1,lower_dimension_point_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
between(X1,X2,X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
( outer_pasch(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) = lower_dimension_point_2
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,negated_conjecture,
( outer_pasch(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) = lower_dimension_point_2
| outer_pasch(X1,lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = lower_dimension_point_1
| ~ between(lower_dimension_point_1,X1,lower_dimension_point_3) ),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_26,axiom,
( between(X5,X2,outer_pasch(X2,X1,X4,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X3,X5) ),
outer_pasch2 ).
cnf(c_0_27,negated_conjecture,
( outer_pasch(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = lower_dimension_point_1
| outer_pasch(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) = lower_dimension_point_2 ),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_28,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
lower_dimension2 ).
cnf(c_0_29,negated_conjecture,
outer_pasch(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) = lower_dimension_point_2,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_23])]),c_0_28]),c_0_24]) ).
cnf(c_0_30,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
lower_dimension3 ).
cnf(c_0_31,negated_conjecture,
~ between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_3),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_29]),c_0_23])]),c_0_30]) ).
cnf(c_0_32,negated_conjecture,
between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2),
inference(sr,[status(thm)],[c_0_19,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
( outer_pasch(X1,lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = lower_dimension_point_1
| ~ between(lower_dimension_point_1,X1,lower_dimension_point_3) ),
inference(spm,[status(thm)],[c_0_18,c_0_32]) ).
cnf(c_0_34,negated_conjecture,
outer_pasch(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) = lower_dimension_point_1,
inference(spm,[status(thm)],[c_0_33,c_0_23]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_34]),c_0_32]),c_0_23])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO011-1 : TPTP v9.2.1. Bugfixed v2.5.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n019.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 17:36:59 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.26/1.71 % Version : CSE_E---1.7
% 1.26/1.71 % Problem : theBenchmark.p
% 1.26/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.71 % SZS output start CNFRefutation
% See solution above
% 1.26/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------