%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO028-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:26:56 PM UTC 2026
% Result : Unsatisfiable 3.52s 1.00s
% Output : CNFRefutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 38 ( 18 unt; 6 nHn; 28 RR)
% Number of literals : 73 ( 18 equ; 35 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 115 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d4_5,axiom,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X4,X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_5) ).
cnf(transitivity_for_equidistance,axiom,
( ~ equidistant(X1,X2,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
cnf(w_to_x_equals_y_to_z,hypothesis,
equidistant(w,x,y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_to_x_equals_y_to_z) ).
cnf(d4_4,axiom,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X4,X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_4) ).
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(d9,axiom,
( ~ equidistant(X2,X3,X2,X4)
| ~ between(X1,X2,X4)
| ~ between(X1,X2,X3)
| X3 = X4
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9) ).
cnf(d2,axiom,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
cnf(prove_equal_extensions,negated_conjecture,
extension(u,v,w,x) != extension(u,v,y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equal_extensions) ).
cnf(u_not_v,hypothesis,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_not_v) ).
cnf(c_0_10,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X4,X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[d4_5]) ).
cnf(c_0_11,plain,
( ~ equidistant(X1,X2,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X5,X6) ),
inference(fof_simplification,[status(thm)],[transitivity_for_equidistance]) ).
cnf(c_0_12,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X4,X3,X2,X1) ),
c_0_10 ).
cnf(c_0_13,hypothesis,
equidistant(w,x,y,z),
w_to_x_equals_y_to_z ).
cnf(c_0_14,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X4,X3,X1,X2) ),
inference(fof_simplification,[status(thm)],[d4_4]) ).
cnf(c_0_15,plain,
( ~ equidistant(X1,X2,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X5,X6) ),
c_0_11 ).
cnf(c_0_16,hypothesis,
equidistant(z,y,x,w),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X4,X3,X1,X2) ),
c_0_14 ).
cnf(c_0_18,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_19,plain,
( ~ equidistant(X2,X3,X2,X4)
| ~ between(X1,X2,X4)
| ~ between(X1,X2,X3)
| X3 = X4
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[d9]) ).
cnf(c_0_20,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X1,X2) ),
inference(fof_simplification,[status(thm)],[d2]) ).
cnf(c_0_21,hypothesis,
( ~ equidistant(z,y,X1,X2)
| equidistant(X1,X2,x,w) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
equidistant(X1,X2,X3,extension(X4,X3,X2,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( ~ equidistant(X2,X3,X2,X4)
| ~ between(X1,X2,X4)
| ~ between(X1,X2,X3)
| X3 = X4
| X1 = X2 ),
c_0_19 ).
cnf(c_0_24,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_25,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X1,X2) ),
c_0_20 ).
cnf(c_0_26,hypothesis,
equidistant(X1,extension(X2,X1,y,z),x,w),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( ~ equidistant(X3,X1,X3,extension(X2,X3,X4,X5))
| ~ between(X2,X3,X1)
| X2 = X3
| X1 = extension(X2,X3,X4,X5) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
( ~ equidistant(X6,X5,X1,X2)
| equidistant(X1,X2,X3,extension(X4,X3,X5,X6)) ),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_29,hypothesis,
equidistant(x,w,X1,extension(X2,X1,y,z)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
extension(u,v,w,x) != extension(u,v,y,z),
inference(fof_simplification,[status(thm)],[prove_equal_extensions]) ).
cnf(c_0_31,plain,
( ~ equidistant(X2,extension(X1,X2,X3,X4),X2,extension(X1,X2,X5,X6))
| X1 = X2
| extension(X1,X2,X3,X4) = extension(X1,X2,X5,X6) ),
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_32,hypothesis,
equidistant(X1,extension(X2,X1,y,z),X3,extension(X4,X3,w,x)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,hypothesis,
u != v,
inference(fof_simplification,[status(thm)],[u_not_v]) ).
cnf(c_0_34,negated_conjecture,
extension(u,v,w,x) != extension(u,v,y,z),
c_0_30 ).
cnf(c_0_35,hypothesis,
( X1 = X2
| extension(X1,X2,y,z) = extension(X1,X2,w,x) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,hypothesis,
u != v,
c_0_33 ).
cnf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO028-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 % Computer : n014.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 20 08:28:04 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.49 Running first-order theorem proving
% 0.19/0.49 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.52/1.00 % Version: 3.5.1
% 3.52/1.00 % Preprocessing class: FSMSSMSMSSSNFFN.
% 3.52/1.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.52/1.00 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 3.52/1.00 % Starting new_bool_3 with 300s (1) cores
% 3.52/1.00 % Starting new_bool_1 with 300s (1) cores
% 3.52/1.00 % Starting sh5l with 300s (1) cores
% 3.52/1.00 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1391682 completed with status 0
% 3.52/1.00 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 3.52/1.00 % Preprocessing class: FSMSSMSMSSSNFFN.
% 3.52/1.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.52/1.00 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 3.52/1.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.52/1.00 % No SInE strategy applied
% 3.52/1.00 % Search class: FGUSM-FFMF33-SFFFFFNN
% 3.52/1.00 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.52/1.00 % Starting SubtermCWHack with 136s (1) cores
% 3.52/1.00 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 3.52/1.00 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 3.52/1.00 % Starting new_bool_3 with 136s (1) cores
% 3.52/1.00 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S070I with 136s (1) cores
% 3.52/1.00 % new_bool_3 with pid 1391690 completed with status 0
% 3.52/1.00 % Result found by new_bool_3
% 3.52/1.00 % Preprocessing class: FSMSSMSMSSSNFFN.
% 3.52/1.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.52/1.00 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 3.52/1.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.52/1.00 % No SInE strategy applied
% 3.52/1.00 % Search class: FGUSM-FFMF33-SFFFFFNN
% 3.52/1.00 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.52/1.00 % Starting SubtermCWHack with 136s (1) cores
% 3.52/1.00 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 3.52/1.00 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 3.52/1.00 % Starting new_bool_3 with 136s (1) cores
% 3.52/1.00 % Preprocessing time : 0.002 s
% 3.52/1.00 % Presaturation interreduction done
% 3.52/1.00
% 3.52/1.00 % Proof found!
% 3.52/1.00 % SZS status Unsatisfiable
% 3.52/1.00 % SZS output start CNFRefutation
% See solution above
% 3.52/1.00 % Parsed axioms : 41
% 3.52/1.00 % Removed by relevancy pruning/SinE : 0
% 3.52/1.00 % Initial clauses : 41
% 3.52/1.00 % Removed in clause preprocessing : 1
% 3.52/1.00 % Initial clauses in saturation : 40
% 3.52/1.00 % Processed clauses : 1078
% 3.52/1.00 % ...of these trivial : 481
% 3.52/1.00 % ...subsumed : 61
% 3.52/1.00 % ...remaining for further processing : 536
% 3.52/1.00 % Other redundant clauses eliminated : 2
% 3.52/1.00 % Clauses deleted for lack of memory : 0
% 3.52/1.00 % Backward-subsumed : 0
% 3.52/1.00 % Backward-rewritten : 8
% 3.52/1.00 % Generated clauses : 12802
% 3.52/1.00 % ...of the previous two non-redundant : 10063
% 3.52/1.00 % ...aggressively subsumed : 0
% 3.52/1.00 % Contextual simplify-reflections : 0
% 3.52/1.00 % Paramodulations : 12800
% 3.52/1.00 % Factorizations : 0
% 3.52/1.00 % NegExts : 0
% 3.52/1.00 % Equation resolutions : 2
% 3.52/1.00 % Disequality decompositions : 0
% 3.52/1.00 % Total rewrite steps : 3586
% 3.52/1.00 % ...of those cached : 3246
% 3.52/1.00 % Propositional unsat checks : 0
% 3.52/1.00 % Propositional check models : 0
% 3.52/1.00 % Propositional check unsatisfiable : 0
% 3.52/1.00 % Propositional clauses : 0
% 3.52/1.00 % Propositional clauses after purity: 0
% 3.52/1.00 % Propositional unsat core size : 0
% 3.52/1.00 % Propositional preprocessing time : 0.000
% 3.52/1.00 % Propositional encoding time : 0.000
% 3.52/1.00 % Propositional solver time : 0.000
% 3.52/1.00 % Success case prop preproc time : 0.000
% 3.52/1.00 % Success case prop encoding time : 0.000
% 3.52/1.00 % Success case prop solver time : 0.000
% 3.52/1.00 % Current number of processed clauses : 491
% 3.52/1.00 % Positive orientable unit clauses : 201
% 3.52/1.00 % Positive unorientable unit clauses: 0
% 3.52/1.00 % Negative unit clauses : 5
% 3.52/1.00 % Non-unit-clauses : 285
% 3.52/1.00 % Current number of unprocessed clauses: 9024
% 3.52/1.00 % ...number of literals in the above : 12237
% 3.52/1.00 % Current number of archived formulas : 0
% 3.52/1.00 % Current number of archived clauses : 44
% 3.52/1.00 % Clause-clause subsumption calls (NU) : 18530
% 3.52/1.00 % Rec. Clause-clause subsumption calls : 12554
% 3.52/1.00 % Non-unit clause-clause subsumptions : 61
% 3.52/1.00 % Unit Clause-clause subsumption calls : 3228
% 3.52/1.00 % Rewrite failures with RHS unbound : 0
% 3.52/1.00 % BW rewrite match attempts : 4689
% 3.52/1.00 % BW rewrite match successes : 8
% 3.52/1.00 % Condensation attempts : 0
% 3.52/1.00 % Condensation successes : 0
% 3.52/1.00 % Termbank termtop insertions : 197980
% 3.52/1.00 % Search garbage collected termcells : 103
% 3.52/1.01
% 3.52/1.01 % -------------------------------------------------
% 3.52/1.01 % User time : 0.272 s
% 3.52/1.01 % System time : 0.017 s
% 3.52/1.01 % Total time : 0.289 s
% 3.52/1.01 % Maximum resident set size: 3664 pages
% 3.52/1.01
% 3.52/1.01 % -------------------------------------------------
% 3.52/1.01 % User time : 1.771 s
% 3.52/1.01 % System time : 0.073 s
% 3.52/1.01 % Total time : 1.845 s
% 3.52/1.01 % Maximum resident set size: 4608 pages
% 3.52/1.01 % E exiting
%------------------------------------------------------------------------------