%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO053-3 : 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 : n001.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 04:19:09 PM UTC 2026
% Result : Unsatisfiable 1.38s 1.75s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of clauses : 38 ( 23 unt; 7 nHn; 24 RR)
% Number of literals : 69 ( 23 equ; 29 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-4 aty)
% Number of variables : 77 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b7,axiom,
( between(X1,X2,X4)
| X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b7) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
cnf(t1,axiom,
( between(X3,X2,X1)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
cnf(d9,axiom,
( X1 = X2
| X3 = X4
| ~ between(X1,X2,X3)
| ~ between(X1,X2,X4)
| ~ equidistant(X2,X3,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9) ).
cnf(u_to_v_equals_u_to_w,hypothesis,
equidistant(u,v,u,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_v_equals_u_to_w) ).
cnf(prove_v_equals_w,negated_conjecture,
v != w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_equals_w) ).
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(r6,axiom,
X1 = reflection(reflection(X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r6) ).
cnf(reflection,axiom,
reflection(X1,X2) = extension(X1,X2,X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-2.ax',reflection) ).
cnf(t2,axiom,
between(X1,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).
cnf(e1,axiom,
X1 = extension(X2,X1,X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
cnf(d3,axiom,
( equidistant(X2,X1,X3,X4)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3) ).
cnf(c_0_13,axiom,
( between(X1,X2,X4)
| X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X2,X3,X4) ),
b7 ).
cnf(c_0_14,hypothesis,
between(u,v,w),
v_between_u_and_w ).
cnf(c_0_15,axiom,
( between(X3,X2,X1)
| ~ between(X1,X2,X3) ),
t1 ).
cnf(c_0_16,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_17,axiom,
( X1 = X2
| X3 = X4
| ~ between(X1,X2,X3)
| ~ between(X1,X2,X4)
| ~ equidistant(X2,X3,X2,X4) ),
d9 ).
cnf(c_0_18,hypothesis,
equidistant(u,v,u,w),
u_to_v_equals_u_to_w ).
cnf(c_0_19,negated_conjecture,
v != w,
prove_v_equals_w ).
cnf(c_0_20,hypothesis,
( v = u
| between(X1,u,w)
| ~ between(X1,u,v) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,plain,
between(extension(X1,X2,X3,X4),X2,X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,axiom,
( X2 = X4
| ~ between(X1,X2,X3)
| ~ equidistant(X1,X2,X1,X4)
| ~ equidistant(X3,X2,X3,X4) ),
d15 ).
cnf(c_0_23,axiom,
X1 = reflection(reflection(X1,X2),X2),
r6 ).
cnf(c_0_24,axiom,
reflection(X1,X2) = extension(X1,X2,X1,X2),
reflection ).
cnf(c_0_25,hypothesis,
( X1 = u
| ~ between(X1,u,w)
| ~ between(X1,u,v) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_26,hypothesis,
( v = u
| between(extension(v,u,X1,X2),u,w) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,hypothesis,
( ~ between(X1,v,u)
| ~ equidistant(X1,v,X1,w) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_18]),c_0_19]) ).
cnf(c_0_28,axiom,
between(X1,X1,X2),
t2 ).
cnf(c_0_29,plain,
X1 = extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_24]) ).
cnf(c_0_30,hypothesis,
( extension(v,u,X1,X2) = u
| v = u ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_21])]) ).
cnf(c_0_31,axiom,
X1 = extension(X2,X1,X3,X3),
e1 ).
cnf(c_0_32,axiom,
( equidistant(X2,X1,X3,X4)
| ~ equidistant(X1,X2,X3,X4) ),
d3 ).
cnf(c_0_33,hypothesis,
~ equidistant(v,v,v,w),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,hypothesis,
v = u,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_35,hypothesis,
equidistant(v,u,u,w),
inference(spm,[status(thm)],[c_0_32,c_0_18]) ).
cnf(c_0_36,hypothesis,
~ equidistant(u,u,u,w),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_34]),c_0_34]) ).
cnf(c_0_37,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_34]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO053-3 : 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
% 0.17/0.33 % Computer : n001.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 17:39:33 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 1.38/1.75 % Version : CSE_E---1.7
% 1.38/1.75 % Problem : theBenchmark.p
% 1.38/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 1.38/1.75 % SZS output start CNFRefutation
% See solution above
% 1.38/1.76 % Total time : 1.372s
%------------------------------------------------------------------------------