%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO030-2 : 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 : n023.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 1.38s 1.75s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 30 ( 19 unt; 4 nHn; 21 RR)
% Number of literals : 64 ( 11 equ; 34 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 70 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_for_equidistance,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
cnf(reflexivity_for_equidistance,axiom,
equidistant(X1,X2,X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).
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(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
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(v_to_w_equals_v_to_w1,hypothesis,
equidistant(v,w,v,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_to_w_equals_v_to_w1) ).
cnf(u_to_w_equals_u_to_w1,hypothesis,
equidistant(u,w,u,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_w_equals_u_to_w1) ).
cnf(u_not_v,hypothesis,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_v) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
cnf(prove_w_is_w1,negated_conjecture,
w != w1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_w_is_w1) ).
cnf(c_0_10,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
transitivity_for_equidistance ).
cnf(c_0_11,axiom,
equidistant(X1,X2,X2,X1),
reflexivity_for_equidistance ).
cnf(c_0_12,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
identity_for_equidistance ).
cnf(c_0_13,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_14,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_15,hypothesis,
equidistant(v,w,v,w1),
v_to_w_equals_v_to_w1 ).
cnf(c_0_16,plain,
( equidistant(X1,X2,X3,X4)
| ~ equidistant(X4,X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,plain,
extension(X1,X2,X3,X3) = X2,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,hypothesis,
( X1 = v
| equidistant(X2,w,X3,w1)
| ~ between(X4,v,X3)
| ~ between(X1,v,X2)
| ~ equidistant(v,X2,v,X3)
| ~ equidistant(X1,w,X4,w1)
| ~ equidistant(X1,v,X4,v) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
equidistant(X1,X2,X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_11]) ).
cnf(c_0_20,plain,
equidistant(X1,X1,X2,X2),
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_21,hypothesis,
( X1 = v
| equidistant(X2,w,X2,w1)
| ~ between(X3,v,X2)
| ~ between(X1,v,X2)
| ~ equidistant(X1,w,X3,w1)
| ~ equidistant(X1,v,X3,v) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,hypothesis,
equidistant(u,w,u,w1),
u_to_w_equals_u_to_w1 ).
cnf(c_0_23,hypothesis,
u != v,
u_not_v ).
cnf(c_0_24,plain,
( equidistant(X1,X2,X3,X3)
| ~ equidistant(X4,X4,X1,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_20]) ).
cnf(c_0_25,hypothesis,
( equidistant(X1,w,X1,w1)
| ~ between(u,v,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_19])]),c_0_23]) ).
cnf(c_0_26,hypothesis,
between(u,v,w),
v_between_u_and_w ).
cnf(c_0_27,hypothesis,
equidistant(w,w1,X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_28,negated_conjecture,
w != w1,
prove_w_is_w1 ).
cnf(c_0_29,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_27]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO030-2 : 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
% 0.14/0.32 % Computer : n023.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
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 17:38:08 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % 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
% 1.38/1.75 % Total time : 1.371s
%------------------------------------------------------------------------------