%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU309+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 02:24:39 PM UTC 2026
% Result : Theorem 0.08s 0.36s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 17 unt; 0 def)
% Number of atoms : 90 ( 30 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 83 ( 36 ~; 30 |; 6 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 72 ( 1 sgn 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t22_pre_topc,conjecture,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_pre_topc) ).
fof(redefinition_k6_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X3,powerset(X1))
& element(X2,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(redefinition_k5_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X3,powerset(X1))
& element(X2,powerset(X1)) )
=> subset_intersection2(X1,X2,X3) = set_intersection2(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
fof(t48_xboole_1,axiom,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(t15_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_intersection2(the_carrier(X1),X2,cast_as_carrier_subset(X1)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_pre_topc) ).
fof(d3_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(dt_k6_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X3,powerset(X1))
& element(X2,powerset(X1)) )
=> element(subset_difference(X1,X2,X3),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2)) = X2 ) ),
inference(assume_negation,[status(cth)],[t22_pre_topc]) ).
fof(c_0_11,negated_conjecture,
( subset_difference(the_carrier(esk6_0),cast_as_carrier_subset(esk6_0),subset_difference(the_carrier(esk6_0),cast_as_carrier_subset(esk6_0),esk7_0)) != esk7_0
& element(esk7_0,powerset(the_carrier(esk6_0)))
& one_sorted_str(esk6_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_12,plain,
! [X90,X91,X92] :
( subset_difference(X90,X91,X92) = set_difference(X91,X92)
| ~ element(X92,powerset(X90))
| ~ element(X91,powerset(X90)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1])])]) ).
fof(c_0_13,plain,
! [X87,X88,X89] :
( subset_intersection2(X87,X88,X89) = set_intersection2(X88,X89)
| ~ element(X89,powerset(X87))
| ~ element(X88,powerset(X87)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_subset_1])])]) ).
fof(c_0_14,plain,
! [X106,X107] : set_difference(X106,set_difference(X106,X107)) = set_intersection2(X106,X107),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_15,plain,
! [X94,X95] :
( subset_intersection2(the_carrier(X94),X95,cast_as_carrier_subset(X94)) = X95
| ~ element(X95,powerset(the_carrier(X94)))
| ~ one_sorted_str(X94) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t15_pre_topc])])])]) ).
fof(c_0_16,plain,
! [X36] :
( cast_as_carrier_subset(X36) = the_carrier(X36)
| ~ one_sorted_str(X36) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_pre_topc])])]) ).
fof(c_0_17,plain,
! [X104,X105] :
( ( element(X104,powerset(X105))
| ~ subset(X104,X105) )
& ( subset(X104,X105)
| ~ element(X104,powerset(X105)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
fof(c_0_18,plain,
! [X93] : subset(X93,X93),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_19,negated_conjecture,
subset_difference(the_carrier(esk6_0),cast_as_carrier_subset(esk6_0),subset_difference(the_carrier(esk6_0),cast_as_carrier_subset(esk6_0),esk7_0)) != esk7_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
( ~ element(X3,powerset(X2))
| ~ element(X1,powerset(X2))
| subset_difference(X2,X1,X3) = set_difference(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_21,plain,
! [X41,X42,X43] :
( element(subset_difference(X41,X42,X43),powerset(X41))
| ~ element(X43,powerset(X41))
| ~ element(X42,powerset(X41)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_subset_1])])]) ).
cnf(c_0_22,plain,
( ~ element(X3,powerset(X2))
| ~ element(X1,powerset(X2))
| subset_intersection2(X2,X1,X3) = set_intersection2(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,plain,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,plain,
( ~ element(X2,powerset(the_carrier(X1)))
| ~ one_sorted_str(X1)
| subset_intersection2(the_carrier(X1),X2,cast_as_carrier_subset(X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,plain,
( ~ one_sorted_str(X1)
| cast_as_carrier_subset(X1) = the_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,plain,
( ~ subset(X1,X2)
| element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,negated_conjecture,
( ~ element(cast_as_carrier_subset(esk6_0),powerset(the_carrier(esk6_0)))
| ~ element(subset_difference(the_carrier(esk6_0),cast_as_carrier_subset(esk6_0),esk7_0),powerset(the_carrier(esk6_0)))
| set_difference(cast_as_carrier_subset(esk6_0),subset_difference(the_carrier(esk6_0),cast_as_carrier_subset(esk6_0),esk7_0)) != esk7_0 ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_29,plain,
( ~ element(X3,powerset(X2))
| ~ element(X1,powerset(X2))
| element(subset_difference(X2,X1,X3),powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,negated_conjecture,
element(esk7_0,powerset(the_carrier(esk6_0))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_31,plain,
! [X31,X32] : set_intersection2(X31,X32) = set_intersection2(X32,X31),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_32,plain,
( ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| subset_intersection2(X2,X1,X3) = set_difference(X1,set_difference(X1,X3)) ),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_33,plain,
( ~ element(X2,powerset(the_carrier(X1)))
| ~ one_sorted_str(X1)
| subset_intersection2(the_carrier(X1),X2,the_carrier(X1)) = X2 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_34,plain,
element(X1,powerset(X1)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( ~ element(cast_as_carrier_subset(esk6_0),powerset(the_carrier(esk6_0)))
| set_difference(cast_as_carrier_subset(esk6_0),subset_difference(the_carrier(esk6_0),cast_as_carrier_subset(esk6_0),esk7_0)) != esk7_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_36,negated_conjecture,
one_sorted_str(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_37,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,plain,
( ~ element(X1,powerset(the_carrier(X2)))
| ~ one_sorted_str(X2)
| set_difference(X1,set_difference(X1,the_carrier(X2))) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_39,negated_conjecture,
set_difference(the_carrier(esk6_0),subset_difference(the_carrier(esk6_0),the_carrier(esk6_0),esk7_0)) != esk7_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_25]),c_0_34]),c_0_36])]) ).
cnf(c_0_40,plain,
set_difference(X1,set_difference(X1,X2)) = set_difference(X2,set_difference(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_23]),c_0_23]) ).
cnf(c_0_41,negated_conjecture,
set_difference(esk7_0,set_difference(esk7_0,the_carrier(esk6_0))) = esk7_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_30]),c_0_36])]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_20]),c_0_30]),c_0_34])]),c_0_40]),c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU309+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Mon Sep 21 06:10:08 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 Running first-order theorem proving
% 0.08/0.33 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
% 0.08/0.36 % Version: 3.5.1
% 0.08/0.36 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.08/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.36 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.08/0.36 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.36 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.36 % Starting sh5l with 300s (1) cores
% 0.08/0.36 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1715648 completed with status 0
% 0.08/0.36 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.08/0.36 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.08/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.36 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.08/0.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.36 % No SInE strategy applied
% 0.08/0.36 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.08/0.36 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.36 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.36 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.08/0.36 % Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I with 113s (1) cores
% 0.08/0.36 % Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SE_S0Y with 113s (1) cores
% 0.08/0.36 % Starting G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with 113s (1) cores
% 0.08/0.36 % G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with pid 1715659 completed with status 0
% 0.08/0.36 % Result found by G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y
% 0.08/0.36 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.08/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.36 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.08/0.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.36 % No SInE strategy applied
% 0.08/0.36 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.08/0.36 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.36 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.36 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.08/0.36 % Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I with 113s (1) cores
% 0.08/0.36 % Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SE_S0Y with 113s (1) cores
% 0.08/0.36 % Starting G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with 113s (1) cores
% 0.08/0.36 % Preprocessing time : 0.001 s
% 0.08/0.36
% 0.08/0.36 % Proof found!
% 0.08/0.36 % SZS status Theorem
% 0.08/0.36 % SZS output start CNFRefutation
% See solution above
% 0.08/0.36 % Parsed axioms : 70
% 0.08/0.36 % Removed by relevancy pruning/SinE : 0
% 0.08/0.36 % Initial clauses : 139
% 0.08/0.36 % Removed in clause preprocessing : 8
% 0.08/0.36 % Initial clauses in saturation : 131
% 0.08/0.36 % Processed clauses : 544
% 0.08/0.36 % ...of these trivial : 1
% 0.08/0.36 % ...subsumed : 196
% 0.08/0.36 % ...remaining for further processing : 346
% 0.08/0.36 % Other redundant clauses eliminated : 0
% 0.08/0.36 % Clauses deleted for lack of memory : 0
% 0.08/0.36 % Backward-subsumed : 3
% 0.08/0.36 % Backward-rewritten : 6
% 0.08/0.36 % Generated clauses : 963
% 0.08/0.36 % ...of the previous two non-redundant : 790
% 0.08/0.36 % ...aggressively subsumed : 0
% 0.08/0.36 % Contextual simplify-reflections : 1
% 0.08/0.36 % Paramodulations : 960
% 0.08/0.36 % Factorizations : 0
% 0.08/0.36 % NegExts : 0
% 0.08/0.36 % Equation resolutions : 0
% 0.08/0.36 % Disequality decompositions : 0
% 0.08/0.36 % Total rewrite steps : 314
% 0.08/0.36 % ...of those cached : 285
% 0.08/0.36 % Propositional unsat checks : 0
% 0.08/0.36 % Propositional check models : 0
% 0.08/0.36 % Propositional check unsatisfiable : 0
% 0.08/0.36 % Propositional clauses : 0
% 0.08/0.36 % Propositional clauses after purity: 0
% 0.08/0.36 % Propositional unsat core size : 0
% 0.08/0.36 % Propositional preprocessing time : 0.000
% 0.08/0.36 % Propositional encoding time : 0.000
% 0.08/0.36 % Propositional solver time : 0.000
% 0.08/0.36 % Success case prop preproc time : 0.000
% 0.08/0.36 % Success case prop encoding time : 0.000
% 0.08/0.36 % Success case prop solver time : 0.000
% 0.08/0.36 % Current number of processed clauses : 336
% 0.08/0.36 % Positive orientable unit clauses : 24
% 0.08/0.36 % Positive unorientable unit clauses: 1
% 0.08/0.36 % Negative unit clauses : 9
% 0.08/0.36 % Non-unit-clauses : 302
% 0.08/0.36 % Current number of unprocessed clauses: 329
% 0.08/0.36 % ...number of literals in the above : 1101
% 0.08/0.36 % Current number of archived formulas : 0
% 0.08/0.36 % Current number of archived clauses : 10
% 0.08/0.36 % Clause-clause subsumption calls (NU) : 11821
% 0.08/0.36 % Rec. Clause-clause subsumption calls : 10656
% 0.08/0.36 % Non-unit clause-clause subsumptions : 192
% 0.08/0.36 % Unit Clause-clause subsumption calls : 371
% 0.08/0.36 % Rewrite failures with RHS unbound : 0
% 0.08/0.36 % BW rewrite match attempts : 20
% 0.08/0.36 % BW rewrite match successes : 4
% 0.08/0.36 % Condensation attempts : 0
% 0.08/0.36 % Condensation successes : 0
% 0.08/0.36 % Termbank termtop insertions : 17981
% 0.08/0.36 % Search garbage collected termcells : 1014
% 0.08/0.36
% 0.08/0.36 % -------------------------------------------------
% 0.08/0.36 % User time : 0.019 s
% 0.08/0.36 % System time : 0.003 s
% 0.08/0.36 % Total time : 0.022 s
% 0.08/0.36 % Maximum resident set size: 3952 pages
% 0.08/0.36
% 0.08/0.36 % -------------------------------------------------
% 0.08/0.36 % User time : 0.088 s
% 0.08/0.36 % System time : 0.010 s
% 0.08/0.36 % Total time : 0.098 s
% 0.08/0.36 % Maximum resident set size: 4608 pages
% 0.08/0.36 % E exiting
%------------------------------------------------------------------------------