%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : HAL004+1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 184.61s 32.74s
% Output : CNFRefutation 184.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 16 unt; 0 def)
% Number of atoms : 144 ( 33 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 183 ( 84 ~; 73 |; 18 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-4 aty)
% Number of variables : 97 ( 0 sgn 38 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commute_properties,axiom,
! [X13,X14,X15,X16,X2,X17,X18,X3] :
( ( morphism(X16,X18,X3)
& morphism(X15,X2,X18)
& morphism(X14,X17,X3)
& morphism(X13,X2,X17)
& commute(X13,X14,X15,X16) )
=> ! [X8] :
( element(X8,X2)
=> apply(X14,apply(X13,X8)) = apply(X16,apply(X15,X8)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',commute_properties) ).
fof(lemma3,conjecture,
! [X19] :
( element(X19,e)
=> ? [X20,X21] :
( apply(delta,apply(g,X21)) = X20
& apply(h,apply(beta,X21)) = X20
& element(X21,b)
& apply(delta,X19) = X20
& element(X20,r) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma3) ).
fof(beta_h_g_delta_commute,axiom,
commute(beta,h,g,delta),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta_h_g_delta_commute) ).
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/sandbox2/benchmark/Axioms/HAL001+0.ax',morphism) ).
fof(delta_morphism,axiom,
morphism(delta,e,r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',delta_morphism) ).
fof(g_morphism,axiom,
morphism(g,b,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_morphism) ).
fof(h_morphism,axiom,
morphism(h,c,r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_morphism) ).
fof(beta_morphism,axiom,
morphism(beta,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta_morphism) ).
fof(surjection_properties,axiom,
! [X1,X2,X3] :
( ( morphism(X1,X2,X3)
& surjection(X1) )
=> ! [X7] :
( element(X7,X3)
=> ? [X8] :
( apply(X1,X8) = X7
& element(X8,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',surjection_properties) ).
fof(beta_surjection,axiom,
surjection(beta),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta_surjection) ).
fof(h_surjection,hypothesis,
surjection(h),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_surjection) ).
fof(c_0_11,plain,
! [X35,X36,X37,X38,X39,X40,X41,X42,X43] :
( apply(X36,apply(X35,X43)) = apply(X38,apply(X37,X43))
| ~ element(X43,X39)
| ~ morphism(X38,X41,X42)
| ~ morphism(X37,X39,X41)
| ~ morphism(X36,X40,X42)
| ~ morphism(X35,X39,X40)
| ~ commute(X35,X36,X37,X38) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[commute_properties])])])]) ).
fof(c_0_12,negated_conjecture,
~ ! [X19] :
( element(X19,e)
=> ? [X20,X21] :
( apply(delta,apply(g,X21)) = X20
& apply(h,apply(beta,X21)) = X20
& element(X21,b)
& apply(delta,X19) = X20
& element(X20,r) ) ),
inference(assume_negation,[status(cth)],[lemma3]) ).
cnf(c_0_13,plain,
( ~ element(X9,X5)
| ~ morphism(X4,X8,X7)
| ~ morphism(X3,X5,X8)
| ~ morphism(X2,X6,X7)
| ~ morphism(X1,X5,X6)
| ~ commute(X1,X2,X3,X4)
| apply(X2,apply(X1,X9)) = apply(X4,apply(X3,X9)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,plain,
commute(beta,h,g,delta),
inference(split_conjunct,[status(thm)],[beta_h_g_delta_commute]) ).
fof(c_0_15,negated_conjecture,
! [X23,X24] :
( ( apply(delta,apply(g,X24)) != X23
| apply(h,apply(beta,X24)) != X23
| ~ element(X24,b)
| apply(delta,esk1_0) != X23
| ~ element(X23,r) )
& element(esk1_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_12])])])])]) ).
fof(c_0_16,plain,
! [X80,X81,X82,X83] :
( ( ~ morphism(X80,X81,X82)
| apply(X80,zero(X81)) = zero(X82) )
& ( ~ morphism(X80,X81,X82)
| element(apply(X80,X83),X82)
| ~ element(X83,X81) ) ),
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])])])])]) ).
cnf(c_0_17,plain,
( ~ morphism(beta,X2,X5)
| ~ morphism(h,X5,X4)
| ~ morphism(g,X2,X3)
| ~ morphism(delta,X3,X4)
| ~ element(X1,X2)
| apply(h,apply(beta,X1)) = apply(delta,apply(g,X1)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
morphism(delta,e,r),
inference(split_conjunct,[status(thm)],[delta_morphism]) ).
cnf(c_0_19,negated_conjecture,
( apply(delta,apply(g,X2)) != X1
| apply(h,apply(beta,X2)) != X1
| ~ element(X2,b)
| apply(delta,esk1_0) != X1
| ~ element(X1,r) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( ~ morphism(X3,X2,X4)
| ~ element(X1,X2)
| element(apply(X3,X1),X4) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
morphism(g,b,e),
inference(split_conjunct,[status(thm)],[g_morphism]) ).
cnf(c_0_22,plain,
( ~ morphism(beta,X2,X3)
| ~ morphism(h,X3,r)
| ~ morphism(g,X2,e)
| ~ element(X1,X2)
| apply(h,apply(beta,X1)) = apply(delta,apply(g,X1)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( ~ element(X1,b)
| ~ element(apply(delta,apply(g,X1)),r)
| apply(delta,apply(g,X1)) != apply(delta,esk1_0)
| apply(h,apply(beta,X1)) != apply(delta,apply(g,X1)) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
( ~ element(X1,e)
| element(apply(delta,X1),r) ),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_25,plain,
( ~ element(X1,b)
| element(apply(g,X1),e) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( ~ morphism(beta,b,X2)
| ~ morphism(h,X2,r)
| ~ element(X1,b)
| apply(h,apply(beta,X1)) = apply(delta,apply(g,X1)) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_27,plain,
morphism(h,c,r),
inference(split_conjunct,[status(thm)],[h_morphism]) ).
cnf(c_0_28,plain,
morphism(beta,b,c),
inference(split_conjunct,[status(thm)],[beta_morphism]) ).
fof(c_0_29,plain,
! [X25,X26,X27,X28] :
( ( ~ morphism(X25,X26,X27)
| ~ surjection(X25)
| ~ element(X28,X27)
| apply(X25,esk2_4(X25,X26,X27,X28)) = X28 )
& ( ~ morphism(X25,X26,X27)
| ~ surjection(X25)
| ~ element(X28,X27)
| element(esk2_4(X25,X26,X27,X28),X26) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[surjection_properties])])])])])]) ).
cnf(c_0_30,negated_conjecture,
( ~ element(X1,b)
| apply(delta,apply(g,X1)) != apply(delta,esk1_0)
| apply(h,apply(beta,X1)) != apply(delta,apply(g,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_31,plain,
( ~ element(X1,b)
| apply(h,apply(beta,X1)) = apply(delta,apply(g,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_32,plain,
( ~ morphism(X1,X2,X3)
| ~ surjection(X1)
| ~ element(X4,X3)
| apply(X1,esk2_4(X1,X2,X3,X4)) = X4 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,plain,
surjection(beta),
inference(split_conjunct,[status(thm)],[beta_surjection]) ).
cnf(c_0_34,negated_conjecture,
( ~ element(X1,b)
| apply(delta,apply(g,X1)) != apply(delta,esk1_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
( ~ morphism(beta,X1,X2)
| ~ element(X3,X2)
| ~ element(esk2_4(beta,X1,X2,X3),b)
| apply(delta,apply(g,esk2_4(beta,X1,X2,X3))) = apply(h,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_36,negated_conjecture,
( ~ morphism(beta,X2,X3)
| ~ element(X1,X3)
| ~ element(esk2_4(beta,X2,X3,X1),b)
| apply(h,X1) != apply(delta,esk1_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_37,plain,
( ~ morphism(X1,X2,X3)
| ~ surjection(X1)
| ~ element(X4,X3)
| element(esk2_4(X1,X2,X3,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,negated_conjecture,
( ~ morphism(beta,b,X2)
| ~ element(X1,X2)
| apply(h,X1) != apply(delta,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_33])]) ).
cnf(c_0_39,negated_conjecture,
( ~ morphism(X1,X2,X3)
| ~ morphism(beta,b,X2)
| ~ element(X4,X3)
| ~ surjection(X1)
| apply(h,esk2_4(X1,X2,X3,X4)) != apply(delta,esk1_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_37]) ).
cnf(c_0_40,hypothesis,
surjection(h),
inference(split_conjunct,[status(thm)],[h_surjection]) ).
cnf(c_0_41,negated_conjecture,
( ~ morphism(h,X2,X1)
| ~ morphism(beta,b,X2)
| ~ element(apply(delta,esk1_0),X1) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_32]),c_0_40])])]) ).
cnf(c_0_42,negated_conjecture,
element(esk1_0,e),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_43,negated_conjecture,
( ~ morphism(h,X1,r)
| ~ morphism(beta,b,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_24]),c_0_42])]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_27]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HAL004+1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.09 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.55 % Computer : n001.cluster.edu
% 0.22/0.55 % Model : x86_64 x86_64
% 0.22/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.55 % Memory : 8046.5625MB
% 0.22/0.55 % OS : Linux 6.8.0-71-generic
% 0.22/0.55 % CPULimit : 300
% 0.22/0.55 % WCLimit : 300
% 0.22/0.55 % DateTime : Sun Sep 20 20:49:58 UTC 2026
% 0.22/0.56 % CPUTime :
% 0.22/0.56 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.65 Running first-order theorem proving
% 0.27/0.65 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
% 184.61/32.74 % Version: 3.5.1
% 184.61/32.74 % Preprocessing class: FSMSSMSMSSSNFFN.
% 184.61/32.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 184.61/32.74 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 184.61/32.74 % Starting new_bool_3 with 300s (1) cores
% 184.61/32.74 % Starting new_bool_1 with 300s (1) cores
% 184.61/32.74 % Starting sh5l with 300s (1) cores
% 184.61/32.74 % new_bool_3 with pid 1384246 completed with status 0
% 184.61/32.74 % Result found by new_bool_3
% 184.61/32.74 % Preprocessing class: FSMSSMSMSSSNFFN.
% 184.61/32.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 184.61/32.74 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 184.61/32.74 % Starting new_bool_3 with 300s (1) cores
% 184.61/32.74 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 184.61/32.74 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 184.61/32.74 % Search class: FGHSF-FFMM33-MFFFFFNN
% 184.61/32.74 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 184.61/32.74 % Starting SubtermCWHack with 31s (1) cores
% 184.61/32.74 % SubtermCWHack with pid 1384252 completed with status 8
% 184.61/32.74 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 184.61/32.74 % G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 1384658 completed with status 0
% 184.61/32.74 % Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 184.61/32.74 % Preprocessing class: FSMSSMSMSSSNFFN.
% 184.61/32.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 184.61/32.74 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 184.61/32.74 % Starting new_bool_3 with 300s (1) cores
% 184.61/32.74 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 184.61/32.74 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 184.61/32.74 % Search class: FGHSF-FFMM33-MFFFFFNN
% 184.61/32.74 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 184.61/32.74 % Starting SubtermCWHack with 31s (1) cores
% 184.61/32.74 % SubtermCWHack with pid 1384252 completed with status 8
% 184.61/32.74 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 184.61/32.74 % Preprocessing time : 0.003 s
% 184.61/32.74 % Presaturation interreduction done
% 184.61/32.74
% 184.61/32.74 % Proof found!
% 184.61/32.74 % SZS status Theorem
% 184.61/32.74 % SZS output start CNFRefutation
% See solution above
% 184.61/32.74 % Parsed axioms : 31
% 184.61/32.74 % Removed by relevancy pruning/SinE : 4
% 184.61/32.74 % Initial clauses : 42
% 184.61/32.74 % Removed in clause preprocessing : 0
% 184.61/32.74 % Initial clauses in saturation : 42
% 184.61/32.74 % Processed clauses : 739
% 184.61/32.74 % ...of these trivial : 0
% 184.61/32.74 % ...subsumed : 178
% 184.61/32.74 % ...remaining for further processing : 561
% 184.61/32.74 % Other redundant clauses eliminated : 24
% 184.61/32.74 % Clauses deleted for lack of memory : 0
% 184.61/32.74 % Backward-subsumed : 45
% 184.61/32.74 % Backward-rewritten : 0
% 184.61/32.74 % Generated clauses : 908
% 184.61/32.74 % ...of the previous two non-redundant : 821
% 184.61/32.74 % ...aggressively subsumed : 0
% 184.61/32.74 % Contextual simplify-reflections : 71
% 184.61/32.74 % Paramodulations : 878
% 184.61/32.74 % Factorizations : 0
% 184.61/32.74 % NegExts : 0
% 184.61/32.74 % Equation resolutions : 30
% 184.61/32.74 % Disequality decompositions : 0
% 184.61/32.74 % Total rewrite steps : 189
% 184.61/32.74 % ...of those cached : 166
% 184.61/32.74 % Propositional unsat checks : 0
% 184.61/32.74 % Propositional check models : 0
% 184.61/32.74 % Propositional check unsatisfiable : 0
% 184.61/32.74 % Propositional clauses : 0
% 184.61/32.74 % Propositional clauses after purity: 0
% 184.61/32.74 % Propositional unsat core size : 0
% 184.61/32.74 % Propositional preprocessing time : 0.000
% 184.61/32.74 % Propositional encoding time : 0.000
% 184.61/32.74 % Propositional solver time : 0.000
% 184.61/32.74 % Success case prop preproc time : 0.000
% 184.61/32.74 % Success case prop encoding time : 0.000
% 184.61/32.74 % Success case prop solver time : 0.000
% 184.61/32.74 % Current number of processed clauses : 472
% 184.61/32.74 % Positive orientable unit clauses : 24
% 184.61/32.74 % Positive unorientable unit clauses: 0
% 184.61/32.74 % Negative unit clauses : 0
% 184.61/32.74 % Non-unit-clauses : 448
% 184.61/32.74 % Current number of unprocessed clauses: 149
% 184.61/32.74 % ...number of literals in the above : 857
% 184.61/32.74 % Current number of archived formulas : 0
% 184.61/32.74 % Current number of archived clauses : 86
% 184.61/32.74 % Clause-clause subsumption calls (NU) : 12860
% 184.61/32.74 % Rec. Clause-clause subsumption calls : 4392
% 184.61/32.74 % Non-unit clause-clause subsumptions : 294
% 184.61/32.74 % Unit Clause-clause subsumption calls : 1
% 184.61/32.74 % Rewrite failures with RHS unbound : 0
% 184.61/32.74 % BW rewrite match attempts : 0
% 184.61/32.74 % BW rewrite match successes : 0
% 184.61/32.74 % Condensation attempts : 0
% 184.61/32.74 % Condensation successes : 0
% 184.61/32.74 % Termbank termtop insertions : 26152
% 184.61/32.74 % Search garbage collected termcells : 920
% 184.61/32.74
% 184.61/32.74 % -------------------------------------------------
% 184.61/32.74 % User time : 30.727 s
% 184.61/32.74 % System time : 0.475 s
% 184.61/32.74 % Total time : 31.202 s
% 184.61/32.74 % Maximum resident set size: 3676 pages
% 184.61/32.74
% 184.61/32.74 % -------------------------------------------------
% 184.61/32.74 % User time : 30.732 s
% 184.61/32.74 % System time : 0.484 s
% 184.61/32.74 % Total time : 31.216 s
% 184.61/32.74 % Maximum resident set size: 4608 pages
% 184.61/32.74 % E exiting
%------------------------------------------------------------------------------