%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : HAL006+1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:45:14 PM UTC 2026
% Result : Theorem 26.21s 4.40s
% Output : CNFRefutation 26.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 14 unt; 0 def)
% Number of atoms : 100 ( 27 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 100 ( 38 ~; 35 |; 19 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 61 ( 0 sgn 30 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(lemma12,conjecture,
! [X19] :
( element(X19,e)
=> ? [X21,X24] :
( apply(g,subtract(b,X21,X24)) = X19
& element(X24,b)
& element(X21,b) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma12) ).
fof(morphism,axiom,
! [X1,X2,X3] :
( morphism(X1,X2,X3)
=> ( apply(X1,zero(X2)) = zero(X3)
& ! [X4] :
( element(X4,X2)
=> element(apply(X1,X4),X3) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',morphism) ).
fof(lemma8,axiom,
! [X19] :
( element(X19,e)
=> ? [X21,X22,X23] :
( apply(g,apply(alpha,X23)) = X22
& apply(gamma,apply(f,X23)) = X22
& element(X23,a)
& subtract(e,apply(g,X21),X19) = X22
& element(X22,e)
& element(X21,b) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma8) ).
fof(subtract_distribution,axiom,
! [X1,X2,X3] :
( morphism(X1,X2,X3)
=> ! [X5,X6] :
( ( element(X6,X2)
& element(X5,X2) )
=> apply(X1,subtract(X2,X5,X6)) = subtract(X3,apply(X1,X5),apply(X1,X6)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',subtract_distribution) ).
fof(alpha_morphism,axiom,
morphism(alpha,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_morphism) ).
fof(subtract_cancellation,axiom,
! [X2,X5,X6] :
( ( element(X6,X2)
& element(X5,X2) )
=> subtract(X2,X5,subtract(X2,X5,X6)) = X6 ),
file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',subtract_cancellation) ).
fof(g_morphism,axiom,
morphism(g,b,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_morphism) ).
fof(c_0_7,negated_conjecture,
~ ! [X19] :
( element(X19,e)
=> ? [X21,X24] :
( apply(g,subtract(b,X21,X24)) = X19
& element(X24,b)
& element(X21,b) ) ),
inference(assume_negation,[status(cth)],[lemma12]) ).
fof(c_0_8,plain,
! [X25,X26,X27,X28] :
( ( ~ morphism(X25,X26,X27)
| apply(X25,zero(X26)) = zero(X27) )
& ( ~ morphism(X25,X26,X27)
| element(apply(X25,X28),X27)
| ~ element(X28,X26) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[morphism])])])])]) ).
fof(c_0_9,plain,
! [X100] :
( ( ~ element(X100,e)
| apply(g,apply(alpha,esk13_1(X100))) = esk12_1(X100) )
& ( ~ element(X100,e)
| apply(gamma,apply(f,esk13_1(X100))) = esk12_1(X100) )
& ( ~ element(X100,e)
| element(esk13_1(X100),a) )
& ( ~ element(X100,e)
| subtract(e,apply(g,esk11_1(X100)),X100) = esk12_1(X100) )
& ( ~ element(X100,e)
| element(esk12_1(X100),e) )
& ( ~ element(X100,e)
| element(esk11_1(X100),b) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lemma8])])])])]) ).
fof(c_0_10,negated_conjecture,
! [X105,X106] :
( ( apply(g,subtract(b,X105,X106)) != esk14_0
| ~ element(X106,b)
| ~ element(X105,b) )
& element(esk14_0,e) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
fof(c_0_11,plain,
! [X92,X93,X94,X95,X96] :
( apply(X92,subtract(X93,X95,X96)) = subtract(X94,apply(X92,X95),apply(X92,X96))
| ~ element(X96,X93)
| ~ element(X95,X93)
| ~ morphism(X92,X93,X94) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_distribution])])])]) ).
cnf(c_0_12,plain,
( ~ morphism(X3,X2,X4)
| ~ element(X1,X2)
| element(apply(X3,X1),X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
morphism(alpha,a,b),
inference(split_conjunct,[status(thm)],[alpha_morphism]) ).
cnf(c_0_14,plain,
( ~ element(X1,e)
| element(esk13_1(X1),a) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
element(esk14_0,e),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X89,X90,X91] :
( subtract(X89,X90,subtract(X89,X90,X91)) = X91
| ~ element(X91,X89)
| ~ element(X90,X89) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_cancellation])])]) ).
cnf(c_0_17,plain,
morphism(g,b,e),
inference(split_conjunct,[status(thm)],[g_morphism]) ).
cnf(c_0_18,plain,
( ~ element(X1,e)
| element(esk11_1(X1),b) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,plain,
( ~ element(X5,X2)
| ~ element(X4,X2)
| ~ morphism(X1,X2,X3)
| apply(X1,subtract(X2,X4,X5)) = subtract(X3,apply(X1,X4),apply(X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
( ~ element(X1,a)
| element(apply(alpha,X1),b) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_21,negated_conjecture,
element(esk13_1(esk14_0),a),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
( ~ element(X1,e)
| apply(g,apply(alpha,esk13_1(X1))) = esk12_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_23,plain,
( ~ element(X3,X2)
| ~ element(X1,X2)
| subtract(X2,X1,subtract(X2,X1,X3)) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( ~ element(X1,b)
| element(apply(g,X1),e) ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_25,negated_conjecture,
element(esk11_1(esk14_0),b),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_26,plain,
( ~ element(X1,e)
| subtract(e,apply(g,esk11_1(X1)),X1) = esk12_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,plain,
( ~ element(X1,b)
| ~ element(X2,b)
| subtract(e,apply(g,X1),apply(g,X2)) = apply(g,subtract(b,X1,X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_28,negated_conjecture,
element(apply(alpha,esk13_1(esk14_0)),b),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,negated_conjecture,
apply(g,apply(alpha,esk13_1(esk14_0))) = esk12_1(esk14_0),
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_30,negated_conjecture,
( ~ element(X1,e)
| subtract(e,X1,subtract(e,X1,esk14_0)) = esk14_0 ),
inference(spm,[status(thm)],[c_0_23,c_0_15]) ).
cnf(c_0_31,negated_conjecture,
element(apply(g,esk11_1(esk14_0)),e),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,negated_conjecture,
subtract(e,apply(g,esk11_1(esk14_0)),esk14_0) = esk12_1(esk14_0),
inference(spm,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_33,negated_conjecture,
( ~ element(X1,b)
| apply(g,subtract(b,X1,apply(alpha,esk13_1(esk14_0)))) = subtract(e,apply(g,X1),esk12_1(esk14_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_34,negated_conjecture,
subtract(e,apply(g,esk11_1(esk14_0)),esk12_1(esk14_0)) = esk14_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_35,negated_conjecture,
( apply(g,subtract(b,X1,X2)) != esk14_0
| ~ element(X2,b)
| ~ element(X1,b) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_36,negated_conjecture,
apply(g,subtract(b,esk11_1(esk14_0),apply(alpha,esk13_1(esk14_0)))) = esk14_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_25]),c_0_34]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_28]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HAL006+1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n007.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sun Sep 20 20:42:35 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.51 Running first-order theorem proving
% 0.23/0.52 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 26.21/4.40 % Version: 3.5.1
% 26.21/4.40 % Preprocessing class: FSMSSMSMSSSNFFN.
% 26.21/4.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 26.21/4.40 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 26.21/4.40 % Starting new_bool_3 with 300s (1) cores
% 26.21/4.40 % Starting new_bool_1 with 300s (1) cores
% 26.21/4.40 % Starting sh5l with 300s (1) cores
% 26.21/4.40 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 3555051 completed with status 0
% 26.21/4.40 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 26.21/4.40 % Preprocessing class: FSMSSMSMSSSNFFN.
% 26.21/4.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 26.21/4.40 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 26.21/4.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 26.21/4.40 % No SInE strategy applied
% 26.21/4.40 % Search class: FGHSF-FFMM32-MFFFFFNN
% 26.21/4.40 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 26.21/4.40 % Starting SubtermCWHack with 136s (1) cores
% 26.21/4.40 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 26.21/4.40 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S2q with 136s (1) cores
% 26.21/4.40 % Starting new_bool_3 with 136s (1) cores
% 26.21/4.40 % Starting new_bool_1 with 136s (1) cores
% 26.21/4.40 % new_bool_1 with pid 3555059 completed with status 0
% 26.21/4.40 % Result found by new_bool_1
% 26.21/4.40 % Preprocessing class: FSMSSMSMSSSNFFN.
% 26.21/4.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 26.21/4.40 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 26.21/4.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 26.21/4.40 % No SInE strategy applied
% 26.21/4.40 % Search class: FGHSF-FFMM32-MFFFFFNN
% 26.21/4.40 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 26.21/4.40 % Starting SubtermCWHack with 136s (1) cores
% 26.21/4.40 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 26.21/4.40 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S2q with 136s (1) cores
% 26.21/4.40 % Starting new_bool_3 with 136s (1) cores
% 26.21/4.40 % Starting new_bool_1 with 136s (1) cores
% 26.21/4.40 % Preprocessing time : 0.003 s
% 26.21/4.40 % Presaturation interreduction done
% 26.21/4.40
% 26.21/4.40 % Proof found!
% 26.21/4.40 % SZS status Theorem
% 26.21/4.40 % SZS output start CNFRefutation
% See solution above
% 26.21/4.40 % Parsed axioms : 33
% 26.21/4.40 % Removed by relevancy pruning/SinE : 0
% 26.21/4.40 % Initial clauses : 57
% 26.21/4.40 % Removed in clause preprocessing : 0
% 26.21/4.40 % Initial clauses in saturation : 57
% 26.21/4.40 % Processed clauses : 2377
% 26.21/4.40 % ...of these trivial : 150
% 26.21/4.40 % ...subsumed : 47
% 26.21/4.40 % ...remaining for further processing : 2180
% 26.21/4.40 % Other redundant clauses eliminated : 2
% 26.21/4.40 % Clauses deleted for lack of memory : 0
% 26.21/4.40 % Backward-subsumed : 0
% 26.21/4.40 % Backward-rewritten : 43
% 26.21/4.40 % Generated clauses : 182528
% 26.21/4.40 % ...of the previous two non-redundant : 182369
% 26.21/4.40 % ...aggressively subsumed : 0
% 26.21/4.40 % Contextual simplify-reflections : 0
% 26.21/4.40 % Paramodulations : 182524
% 26.21/4.40 % Factorizations : 0
% 26.21/4.40 % NegExts : 0
% 26.21/4.40 % Equation resolutions : 4
% 26.21/4.40 % Disequality decompositions : 0
% 26.21/4.40 % Total rewrite steps : 7553
% 26.21/4.40 % ...of those cached : 7280
% 26.21/4.40 % Propositional unsat checks : 0
% 26.21/4.40 % Propositional check models : 0
% 26.21/4.40 % Propositional check unsatisfiable : 0
% 26.21/4.40 % Propositional clauses : 0
% 26.21/4.40 % Propositional clauses after purity: 0
% 26.21/4.40 % Propositional unsat core size : 0
% 26.21/4.40 % Propositional preprocessing time : 0.000
% 26.21/4.40 % Propositional encoding time : 0.000
% 26.21/4.40 % Propositional solver time : 0.000
% 26.21/4.40 % Success case prop preproc time : 0.000
% 26.21/4.40 % Success case prop encoding time : 0.000
% 26.21/4.40 % Success case prop solver time : 0.000
% 26.21/4.40 % Current number of processed clauses : 2079
% 26.21/4.40 % Positive orientable unit clauses : 1236
% 26.21/4.40 % Positive unorientable unit clauses: 0
% 26.21/4.40 % Negative unit clauses : 7
% 26.21/4.40 % Non-unit-clauses : 836
% 26.21/4.40 % Current number of unprocessed clauses: 180001
% 26.21/4.40 % ...number of literals in the above : 224882
% 26.21/4.40 % Current number of archived formulas : 0
% 26.21/4.40 % Current number of archived clauses : 99
% 26.21/4.40 % Clause-clause subsumption calls (NU) : 17447
% 26.21/4.40 % Rec. Clause-clause subsumption calls : 15058
% 26.21/4.40 % Non-unit clause-clause subsumptions : 39
% 26.21/4.40 % Unit Clause-clause subsumption calls : 791
% 26.21/4.40 % Rewrite failures with RHS unbound : 0
% 26.21/4.40 % BW rewrite match attempts : 59092
% 26.21/4.40 % BW rewrite match successes : 38
% 26.21/4.40 % Condensation attempts : 0
% 26.21/4.40 % Condensation successes : 0
% 26.21/4.40 % Termbank termtop insertions : 4799568
% 26.21/4.40 % Search garbage collected termcells : 990
% 26.21/4.40
% 26.21/4.40 % -------------------------------------------------
% 26.21/4.40 % User time : 3.503 s
% 26.21/4.40 % System time : 0.229 s
% 26.21/4.40 % Total time : 3.731 s
% 26.21/4.40 % Maximum resident set size: 3680 pages
% 26.21/4.40
% 26.21/4.40 % -------------------------------------------------
% 26.21/4.40 % User time : 17.635 s
% 26.21/4.40 % System time : 0.951 s
% 26.21/4.40 % Total time : 18.586 s
% 26.21/4.40 % Maximum resident set size: 4608 pages
% 26.21/4.40 % E exiting
%------------------------------------------------------------------------------