%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO029-3 : TPTP v9.2.1. Released v1.0.0.
% 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 : n006.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 04:19:04 PM UTC 2026
% Result : Unsatisfiable 7.07s 4.79s
% Output : CNFRefutation 7.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of clauses : 46 ( 19 unt; 8 nHn; 30 RR)
% Number of literals : 109 ( 20 equ; 59 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-5 aty)
% Number of variables : 188 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(inner_pasch2,axiom,
( between(X5,inner_pasch(X1,X2,X3,X5,X4),X1)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',inner_pasch2) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
cnf(e1,axiom,
X1 = extension(X2,X1,X3,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e1) ).
cnf(d8,axiom,
( equidistant(X1,X5,X3,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ between(X1,X2,X5)
| ~ between(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8) ).
cnf(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
cnf(inner_pasch1,axiom,
( between(X2,inner_pasch(X1,X2,X3,X5,X4),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',inner_pasch1) ).
cnf(d4_3,axiom,
( equidistant(X3,X4,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_3) ).
cnf(identity_for_betweeness,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).
cnf(outer_five_segment,axiom,
( X1 = X2
| equidistant(X5,X7,X6,X8)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X7,X3,X8)
| ~ equidistant(X2,X7,X4,X8)
| ~ between(X1,X2,X5)
| ~ between(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',outer_five_segment) ).
cnf(d4_1,axiom,
( equidistant(X1,X2,X4,X3)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_1) ).
cnf(identity_for_equidistance,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
cnf(prove_equal_extensions,negated_conjecture,
extension(u,v,u,v) != extension(u,v,v,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equal_extensions) ).
cnf(u_not_v,hypothesis,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_v) ).
cnf(c_0_13,axiom,
( between(X5,inner_pasch(X1,X2,X3,X5,X4),X1)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
inner_pasch2 ).
cnf(c_0_14,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_15,axiom,
X1 = extension(X2,X1,X3,X3),
e1 ).
cnf(c_0_16,axiom,
( equidistant(X1,X5,X3,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ between(X1,X2,X5)
| ~ between(X3,X4,X6) ),
d8 ).
cnf(c_0_17,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_18,axiom,
( between(X2,inner_pasch(X1,X2,X3,X5,X4),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
inner_pasch1 ).
cnf(c_0_19,plain,
( between(X1,inner_pasch(X2,X3,extension(X4,X1,X5,X6),X1,X4),X2)
| ~ between(X2,X3,extension(X4,X1,X5,X6)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
between(X1,X2,X2),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
( equidistant(X1,extension(X2,X3,X4,X5),X6,X5)
| ~ between(X1,X3,extension(X2,X3,X4,X5))
| ~ between(X6,X4,X5)
| ~ equidistant(X1,X3,X6,X4) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,axiom,
( equidistant(X3,X4,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
d4_3 ).
cnf(c_0_23,plain,
( between(X1,inner_pasch(X2,X1,extension(X3,X4,X5,X6),X4,X3),X3)
| ~ between(X2,X1,extension(X3,X4,X5,X6)) ),
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_24,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
identity_for_betweeness ).
cnf(c_0_25,plain,
between(X1,inner_pasch(X2,extension(X3,X1,X4,X5),extension(X3,X1,X4,X5),X1,X3),X2),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
( equidistant(X1,extension(X1,X2,X3,X4),X5,X4)
| ~ between(X5,X3,X4)
| ~ equidistant(X1,X2,X5,X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_14]) ).
cnf(c_0_27,plain,
equidistant(X1,X2,extension(X3,X4,X1,X2),X4),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_28,plain,
between(extension(X1,X2,X3,X4),inner_pasch(X5,extension(X1,X2,X3,X4),extension(X1,X2,X3,X4),X2,X1),X1),
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_29,plain,
inner_pasch(X1,extension(X2,X1,X3,X4),extension(X2,X1,X3,X4),X1,X2) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,axiom,
( X1 = X2
| equidistant(X5,X7,X6,X8)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X7,X3,X8)
| ~ equidistant(X2,X7,X4,X8)
| ~ between(X1,X2,X5)
| ~ between(X3,X4,X6) ),
outer_five_segment ).
cnf(c_0_31,plain,
( equidistant(X1,extension(X1,X2,X3,X4),extension(X5,X3,X1,X2),X4)
| ~ between(extension(X5,X3,X1,X2),X3,X4) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
between(extension(X1,X2,X3,X4),X2,X1),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
( X1 = X2
| equidistant(X3,extension(X4,X2,X5,X6),X7,X6)
| ~ between(X8,X5,X7)
| ~ between(X1,X2,X3)
| ~ equidistant(X1,extension(X4,X2,X5,X6),X8,X6)
| ~ equidistant(X2,X3,X5,X7)
| ~ equidistant(X1,X2,X8,X5) ),
inference(spm,[status(thm)],[c_0_30,c_0_17]) ).
cnf(c_0_34,plain,
equidistant(X1,extension(X1,X2,X3,X4),extension(X4,X3,X1,X2),X4),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
( X1 = X2
| equidistant(X3,extension(X1,X2,X4,X5),X6,X5)
| ~ between(extension(X5,X4,X1,X2),X4,X6)
| ~ between(X1,X2,X3)
| ~ equidistant(X2,X3,X4,X6) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_27])]) ).
cnf(c_0_36,axiom,
( equidistant(X1,X2,X4,X3)
| ~ equidistant(X1,X2,X3,X4) ),
d4_1 ).
cnf(c_0_37,plain,
( X1 = X2
| equidistant(X3,extension(X1,X2,X4,X5),X5,X5)
| ~ between(X1,X2,X3)
| ~ equidistant(X2,X3,X4,X5) ),
inference(spm,[status(thm)],[c_0_35,c_0_32]) ).
cnf(c_0_38,plain,
equidistant(X1,extension(X2,X1,X3,X4),X4,X3),
inference(spm,[status(thm)],[c_0_36,c_0_17]) ).
cnf(c_0_39,plain,
( X1 = X2
| equidistant(extension(X3,X2,X4,X5),extension(X1,X2,X5,X4),X4,X4)
| ~ between(X1,X2,extension(X3,X2,X4,X5)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
identity_for_equidistance ).
cnf(c_0_41,plain,
( X1 = X2
| equidistant(extension(X1,X2,X3,X4),extension(X1,X2,X4,X3),X3,X3) ),
inference(spm,[status(thm)],[c_0_39,c_0_14]) ).
cnf(c_0_42,negated_conjecture,
extension(u,v,u,v) != extension(u,v,v,u),
prove_equal_extensions ).
cnf(c_0_43,plain,
( extension(X1,X2,X3,X4) = extension(X1,X2,X4,X3)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,hypothesis,
u != v,
u_not_v ).
cnf(c_0_45,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO029-3 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.17/0.33 % Computer : n006.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Mon May 4 17:37:16 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 7.07/4.79 % Version : CSE_E---1.7
% 7.07/4.79 % Problem : theBenchmark.p
% 7.07/4.79 % SZS status Unsatisfiable for theBenchmark.p
% 7.07/4.79 % SZS output start CNFRefutation
% See solution above
% 7.17/4.81 % Total time : 3.368s
%------------------------------------------------------------------------------