%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO062-3 : TPTP v9.2.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n014.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 04:19:11 PM UTC 2026
% Result : Unsatisfiable 1.82s 1.90s
% Output : CNFRefutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 26 ( 15 unt; 0 nHn; 19 RR)
% Number of literals : 44 ( 7 equ; 22 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 67 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i2_3,axiom,
( equidistant(X2,X3,insertion(X4,X5,X1,X2),X5)
| ~ between(X1,X2,X3)
| ~ equidistant(X1,X3,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i2_3) ).
cnf(insertion,axiom,
insertion(X1,X2,X3,X4) = extension(extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),X1,X3,X4),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-3.ax',insertion) ).
cnf(d1,axiom,
equidistant(X1,X2,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
cnf(d4_2,axiom,
( equidistant(X2,X1,X4,X3)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_2) ).
cnf(prove_v_equals_insertion,negated_conjecture,
v != insertion(u,w,u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_equals_insertion) ).
cnf(d15,axiom,
( X2 = X4
| ~ between(X1,X2,X3)
| ~ equidistant(X1,X2,X1,X4)
| ~ equidistant(X3,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15) ).
cnf(d2,axiom,
( equidistant(X3,X4,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
cnf(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
cnf(c_0_9,axiom,
( equidistant(X2,X3,insertion(X4,X5,X1,X2),X5)
| ~ between(X1,X2,X3)
| ~ equidistant(X1,X3,X4,X5) ),
i2_3 ).
cnf(c_0_10,axiom,
insertion(X1,X2,X3,X4) = extension(extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),X1,X3,X4),
insertion ).
cnf(c_0_11,plain,
( equidistant(X2,X3,extension(extension(X5,X4,lower_dimension_point_1,lower_dimension_point_2),X4,X1,X2),X5)
| ~ between(X1,X2,X3)
| ~ equidistant(X1,X3,X4,X5) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,axiom,
equidistant(X1,X2,X1,X2),
d1 ).
cnf(c_0_13,plain,
( equidistant(X1,X2,extension(extension(X2,X3,lower_dimension_point_1,lower_dimension_point_2),X3,X3,X1),X2)
| ~ between(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,hypothesis,
between(u,v,w),
v_between_u_and_w ).
cnf(c_0_15,axiom,
( equidistant(X2,X1,X4,X3)
| ~ equidistant(X1,X2,X3,X4) ),
d4_2 ).
cnf(c_0_16,hypothesis,
equidistant(v,w,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v),w),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
v != insertion(u,w,u,v),
prove_v_equals_insertion ).
cnf(c_0_18,axiom,
( X2 = X4
| ~ between(X1,X2,X3)
| ~ equidistant(X1,X2,X1,X4)
| ~ equidistant(X3,X2,X3,X4) ),
d15 ).
cnf(c_0_19,hypothesis,
equidistant(w,v,w,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
v != extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v),
inference(rw,[status(thm)],[c_0_17,c_0_10]) ).
cnf(c_0_21,axiom,
( equidistant(X3,X4,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
d2 ).
cnf(c_0_22,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_23,hypothesis,
( ~ between(X1,v,w)
| ~ equidistant(X1,v,X1,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_24,plain,
equidistant(X1,X2,X3,extension(X4,X3,X1,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_14]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO062-3 : TPTP v9.2.1. Bugfixed v1.2.1.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n014.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 17:38:21 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.82/1.90 % Version : CSE_E---1.7
% 1.82/1.90 % Problem : theBenchmark.p
% 1.82/1.90 % SZS status Unsatisfiable for theBenchmark.p
% 1.82/1.90 % SZS output start CNFRefutation
% See solution above
% 1.82/1.90 % Total time : 1.370s
%------------------------------------------------------------------------------