%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO068-3 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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 : 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 04:19:13 PM UTC 2026
% Result : Unsatisfiable 59.39s 34.52s
% Output : CNFRefutation 59.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of clauses : 46 ( 19 unt; 7 nHn; 46 RR)
% Number of literals : 93 ( 0 equ; 36 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 64 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d4_5,axiom,
( equidistant(X4,X3,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_5) ).
cnf(u_to_v_equals_u1_to_v1,hypothesis,
equidistant(u,v,u1,v1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_u1_to_v1) ).
cnf(d2,axiom,
( equidistant(X3,X4,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
cnf(v_to_w_equals_v1_to_w1,hypothesis,
equidistant(v,w,v1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_to_w_equals_v1_to_w1) ).
cnf(u_to_w_equals_u1_to_w1,hypothesis,
equidistant(u,w,u1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_w_equals_u1_to_w1) ).
cnf(b11,axiom,
( between(X3,X4,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X5,X3,X6)
| ~ between(X1,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b11) ).
cnf(t10_1,axiom,
( colinear(X3,X2,X1)
| ~ colinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_1) ).
cnf(uvw_colinear,hypothesis,
colinear(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uvw_colinear) ).
cnf(colinearity4,axiom,
( between(X1,X2,X3)
| between(X2,X3,X1)
| between(X3,X1,X2)
| ~ colinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity4) ).
cnf(c2_1,axiom,
( colinear(X3,X2,X1)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c2_1) ).
cnf(prove_u1v1w1_colinear,negated_conjecture,
~ colinear(u1,v1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_u1v1w1_colinear) ).
cnf(c2_3,axiom,
( colinear(X2,X1,X3)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c2_3) ).
cnf(c2_2,axiom,
( colinear(X1,X3,X2)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c2_2) ).
cnf(c_0_13,axiom,
( equidistant(X4,X3,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
d4_5 ).
cnf(c_0_14,hypothesis,
equidistant(u,v,u1,v1),
u_to_v_equals_u1_to_v1 ).
cnf(c_0_15,axiom,
( equidistant(X3,X4,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
d2 ).
cnf(c_0_16,hypothesis,
equidistant(v1,u1,v,u),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,hypothesis,
equidistant(v,w,v1,w1),
v_to_w_equals_v1_to_w1 ).
cnf(c_0_18,hypothesis,
equidistant(u,w,u1,w1),
u_to_w_equals_u1_to_w1 ).
cnf(c_0_19,axiom,
( between(X3,X4,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X5,X3,X6)
| ~ between(X1,X2,X5) ),
b11 ).
cnf(c_0_20,hypothesis,
equidistant(v,u,v1,u1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,hypothesis,
equidistant(w1,v1,w,v),
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_22,hypothesis,
equidistant(w1,u1,w,u),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_23,axiom,
( colinear(X3,X2,X1)
| ~ colinear(X1,X2,X3) ),
t10_1 ).
cnf(c_0_24,hypothesis,
colinear(u,v,w),
uvw_colinear ).
cnf(c_0_25,hypothesis,
( between(X1,v1,u1)
| ~ between(X2,v,u)
| ~ equidistant(X2,u,X1,u1)
| ~ equidistant(X2,v,X1,v1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,hypothesis,
equidistant(w,v,w1,v1),
inference(spm,[status(thm)],[c_0_15,c_0_21]) ).
cnf(c_0_27,hypothesis,
equidistant(w,u,w1,u1),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_28,axiom,
( between(X1,X2,X3)
| between(X2,X3,X1)
| between(X3,X1,X2)
| ~ colinear(X1,X2,X3) ),
colinearity4 ).
cnf(c_0_29,hypothesis,
colinear(w,v,u),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,hypothesis,
( between(X1,u1,w1)
| ~ between(X2,u,w)
| ~ equidistant(X2,w,X1,w1)
| ~ equidistant(X2,u,X1,u1) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_31,hypothesis,
( between(w1,v1,u1)
| ~ between(w,v,u) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_32,hypothesis,
( between(w,v,u)
| between(v,u,w)
| between(u,w,v) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,hypothesis,
( between(X1,w1,v1)
| ~ between(X2,w,v)
| ~ equidistant(X2,v,X1,v1)
| ~ equidistant(X2,w,X1,w1) ),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
cnf(c_0_34,hypothesis,
( between(v1,u1,w1)
| ~ between(v,u,w) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_17]),c_0_20])]) ).
cnf(c_0_35,hypothesis,
( between(u,w,v)
| between(v,u,w)
| between(w1,v1,u1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,hypothesis,
( between(u1,w1,v1)
| ~ between(u,w,v) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_18]),c_0_14])]) ).
cnf(c_0_37,hypothesis,
( between(w1,v1,u1)
| between(u,w,v)
| between(v1,u1,w1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,axiom,
( colinear(X3,X2,X1)
| ~ between(X1,X2,X3) ),
c2_1 ).
cnf(c_0_39,hypothesis,
( between(v1,u1,w1)
| between(w1,v1,u1)
| between(u1,w1,v1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
~ colinear(u1,v1,w1),
prove_u1v1w1_colinear ).
cnf(c_0_41,axiom,
( colinear(X2,X1,X3)
| ~ between(X1,X2,X3) ),
c2_3 ).
cnf(c_0_42,hypothesis,
( between(u1,w1,v1)
| between(v1,u1,w1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_43,axiom,
( colinear(X1,X3,X2)
| ~ between(X1,X2,X3) ),
c2_2 ).
cnf(c_0_44,hypothesis,
between(u1,w1,v1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_40]) ).
cnf(c_0_45,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO068-3 : TPTP v9.2.1. Bugfixed v1.2.1.
% 0.11/0.12 % 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
% 0.15/0.33 % Computer : n014.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 17:39:21 EDT 2026
% 0.18/0.33 % CPUTime :
% 0.18/0.34 % start to proof: theBenchmark
% 59.39/34.52 % Version : CSE_E---1.7
% 59.39/34.52 % Problem : theBenchmark.p
% 59.39/34.52 % SZS status Unsatisfiable for theBenchmark.p
% 59.39/34.52 % SZS output start CNFRefutation
% See solution above
% 59.59/34.73 % Total time : 26.450s
%------------------------------------------------------------------------------