%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG090+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 02:05:48 PM UTC 2026
% Result : Theorem 0.14s 0.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 24 unt; 0 def)
% Number of atoms : 107 ( 21 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 99 ( 36 ~; 29 |; 23 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__870,hypothesis,
( aIdeal0(xJ)
& ! [X1] :
( aElementOf0(X1,xJ)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),xJ) )
& ! [X2] :
( aElementOf0(X2,xJ)
=> aElementOf0(sdtpldt0(X1,X2),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [X1] :
( aElementOf0(X1,xI)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),xI) )
& ! [X2] :
( aElementOf0(X2,xI)
=> aElementOf0(sdtpldt0(X1,X2),xI) ) ) )
& aSet0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__870) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aElement0(X3)
& aElement0(X2)
& aElement0(X1) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(m__967,hypothesis,
( xy = sdtpldt0(xm,xn)
& aElementOf0(xn,xJ)
& aElementOf0(xm,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__967) ).
fof(m__994,hypothesis,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__994) ).
fof(m__934,hypothesis,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__934) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(c_0_9,negated_conjecture,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_10,plain,
! [X34,X35] :
( aElement0(X35)
| ~ aElementOf0(X35,X34)
| ~ aSet0(X34) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
fof(c_0_11,hypothesis,
! [X70,X71,X72,X73,X74,X75] :
( aIdeal0(xJ)
& ( ~ aElementOf0(X73,xJ)
| aElementOf0(sdtasdt0(X75,X73),xJ)
| ~ aElement0(X75) )
& ( ~ aElementOf0(X73,xJ)
| aElementOf0(sdtpldt0(X73,X74),xJ)
| ~ aElementOf0(X74,xJ) )
& aSet0(xJ)
& aIdeal0(xI)
& ( ~ aElementOf0(X70,xI)
| aElementOf0(sdtasdt0(X72,X70),xI)
| ~ aElement0(X72) )
& ( ~ aElementOf0(X70,xI)
| aElementOf0(sdtpldt0(X70,X71),xI)
| ~ aElementOf0(X71,xI) )
& aSet0(xI) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__870])])])])]) ).
fof(c_0_12,negated_conjecture,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X15,X16,X17] :
( sdtpldt0(sdtpldt0(X15,X16),X17) = sdtpldt0(X15,sdtpldt0(X16,X17))
| ~ aElement0(X17)
| ~ aElement0(X16)
| ~ aElement0(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).
cnf(c_0_14,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,hypothesis,
aElementOf0(xn,xJ),
inference(split_conjunct,[status(thm)],[m__967]) ).
cnf(c_0_16,hypothesis,
aSet0(xJ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,hypothesis,
aElementOf0(xm,xI),
inference(split_conjunct,[status(thm)],[m__967]) ).
cnf(c_0_18,hypothesis,
aSet0(xI),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_19,negated_conjecture,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(fof_nnf,[status(thm)],[c_0_12]) ).
cnf(c_0_20,hypothesis,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(split_conjunct,[status(thm)],[m__994]) ).
cnf(c_0_21,hypothesis,
aElementOf0(xk,xI),
inference(split_conjunct,[status(thm)],[m__934]) ).
cnf(c_0_22,plain,
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,hypothesis,
xy = sdtpldt0(xm,xn),
inference(split_conjunct,[status(thm)],[m__967]) ).
cnf(c_0_24,hypothesis,
aElement0(xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_25,hypothesis,
aElement0(xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_17]),c_0_18])]) ).
fof(c_0_26,plain,
! [X13,X14] :
( sdtpldt0(X13,X14) = sdtpldt0(X14,X13)
| ~ aElement0(X14)
| ~ aElement0(X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
cnf(c_0_27,negated_conjecture,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,hypothesis,
aElement0(sdtpldt0(xl,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_20]),c_0_16])]) ).
cnf(c_0_29,hypothesis,
aElement0(xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_21]),c_0_18])]) ).
cnf(c_0_30,hypothesis,
( ~ aElement0(X1)
| sdtpldt0(xm,sdtpldt0(xn,X1)) = sdtpldt0(xy,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_31,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,hypothesis,
aElementOf0(xl,xJ),
inference(split_conjunct,[status(thm)],[m__934]) ).
fof(c_0_33,plain,
! [X9,X10] :
( aElement0(sdtpldt0(X9,X10))
| ~ aElement0(X10)
| ~ aElement0(X9) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
cnf(c_0_34,negated_conjecture,
sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) != sdtpldt0(xx,xy),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_22]),c_0_28]),c_0_25]),c_0_29])]) ).
cnf(c_0_35,hypothesis,
( ~ aElement0(X1)
| sdtpldt0(xm,sdtpldt0(X1,xn)) = sdtpldt0(xy,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_24])]) ).
cnf(c_0_36,hypothesis,
aElement0(xl),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_32]),c_0_16])]) ).
cnf(c_0_37,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElement0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
sdtpldt0(xk,sdtpldt0(xy,xl)) != sdtpldt0(xx,xy),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_39,hypothesis,
aElement0(xy),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_40,hypothesis,
xx = sdtpldt0(xk,xl),
inference(split_conjunct,[status(thm)],[m__934]) ).
cnf(c_0_41,negated_conjecture,
sdtpldt0(xk,sdtpldt0(xl,xy)) != sdtpldt0(xx,xy),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_31]),c_0_36]),c_0_39])]) ).
cnf(c_0_42,hypothesis,
( ~ aElement0(X1)
| sdtpldt0(xk,sdtpldt0(xl,X1)) = sdtpldt0(xx,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_40]),c_0_36]),c_0_29])]) ).
cnf(c_0_43,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG090+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 04:20:46 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 0.14/0.45 % Version: 3.5.1
% 0.14/0.45 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.14/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.45 % Starting sh5l with 300s (1) cores
% 0.14/0.45 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 3390247 completed with status 0
% 0.14/0.45 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.14/0.45 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.14/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.45 % No SInE strategy applied
% 0.14/0.45 % Search class: FGUSF-FFMM32-SFFFFFNN
% 0.14/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.14/0.45 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.45 % new_bool_3 with pid 3390257 completed with status 0
% 0.14/0.45 % Result found by new_bool_3
% 0.14/0.45 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.14/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.45 % No SInE strategy applied
% 0.14/0.45 % Search class: FGUSF-FFMM32-SFFFFFNN
% 0.14/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.14/0.45 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.45 % Preprocessing time : 0.002 s
% 0.14/0.45 % Presaturation interreduction done
% 0.14/0.45
% 0.14/0.45 % Proof found!
% 0.14/0.45 % SZS status Theorem
% 0.14/0.45 % SZS output start CNFRefutation
% See solution above
% 0.14/0.46 % Parsed axioms : 31
% 0.14/0.46 % Removed by relevancy pruning/SinE : 0
% 0.14/0.46 % Initial clauses : 82
% 0.14/0.46 % Removed in clause preprocessing : 2
% 0.14/0.46 % Initial clauses in saturation : 80
% 0.14/0.46 % Processed clauses : 207
% 0.14/0.46 % ...of these trivial : 6
% 0.14/0.46 % ...subsumed : 4
% 0.14/0.46 % ...remaining for further processing : 197
% 0.14/0.46 % Other redundant clauses eliminated : 10
% 0.14/0.46 % Clauses deleted for lack of memory : 0
% 0.14/0.46 % Backward-subsumed : 0
% 0.14/0.46 % Backward-rewritten : 2
% 0.14/0.46 % Generated clauses : 375
% 0.14/0.46 % ...of the previous two non-redundant : 346
% 0.14/0.46 % ...aggressively subsumed : 0
% 0.14/0.46 % Contextual simplify-reflections : 0
% 0.14/0.46 % Paramodulations : 366
% 0.14/0.46 % Factorizations : 0
% 0.14/0.46 % NegExts : 0
% 0.14/0.46 % Equation resolutions : 10
% 0.14/0.46 % Disequality decompositions : 0
% 0.14/0.46 % Total rewrite steps : 270
% 0.14/0.46 % ...of those cached : 243
% 0.14/0.46 % Propositional unsat checks : 0
% 0.14/0.46 % Propositional check models : 0
% 0.14/0.46 % Propositional check unsatisfiable : 0
% 0.14/0.46 % Propositional clauses : 0
% 0.14/0.46 % Propositional clauses after purity: 0
% 0.14/0.46 % Propositional unsat core size : 0
% 0.14/0.46 % Propositional preprocessing time : 0.000
% 0.14/0.46 % Propositional encoding time : 0.000
% 0.14/0.46 % Propositional solver time : 0.000
% 0.14/0.46 % Success case prop preproc time : 0.000
% 0.14/0.46 % Success case prop encoding time : 0.000
% 0.14/0.46 % Success case prop solver time : 0.000
% 0.14/0.46 % Current number of processed clauses : 106
% 0.14/0.46 % Positive orientable unit clauses : 50
% 0.14/0.46 % Positive unorientable unit clauses: 0
% 0.14/0.46 % Negative unit clauses : 5
% 0.14/0.46 % Non-unit-clauses : 51
% 0.14/0.46 % Current number of unprocessed clauses: 299
% 0.14/0.46 % ...number of literals in the above : 1151
% 0.14/0.46 % Current number of archived formulas : 0
% 0.14/0.46 % Current number of archived clauses : 82
% 0.14/0.46 % Clause-clause subsumption calls (NU) : 865
% 0.14/0.46 % Rec. Clause-clause subsumption calls : 300
% 0.14/0.46 % Non-unit clause-clause subsumptions : 4
% 0.14/0.46 % Unit Clause-clause subsumption calls : 91
% 0.14/0.46 % Rewrite failures with RHS unbound : 0
% 0.14/0.46 % BW rewrite match attempts : 2
% 0.14/0.46 % BW rewrite match successes : 2
% 0.14/0.46 % Condensation attempts : 0
% 0.14/0.46 % Condensation successes : 0
% 0.14/0.46 % Termbank termtop insertions : 11521
% 0.14/0.46 % Search garbage collected termcells : 1124
% 0.14/0.46
% 0.14/0.46 % -------------------------------------------------
% 0.14/0.46 % User time : 0.014 s
% 0.14/0.46 % System time : 0.005 s
% 0.14/0.46 % Total time : 0.019 s
% 0.14/0.46 % Maximum resident set size: 3676 pages
% 0.14/0.46
% 0.14/0.46 % -------------------------------------------------
% 0.14/0.46 % User time : 0.057 s
% 0.14/0.46 % System time : 0.017 s
% 0.14/0.46 % Total time : 0.074 s
% 0.14/0.46 % Maximum resident set size: 4608 pages
% 0.14/0.46 % E exiting
%------------------------------------------------------------------------------