%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG090+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 0.17s 0.51s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 26 unt; 0 def)
% Number of atoms : 119 ( 21 equ)
% Maximal formula atoms : 29 ( 2 avg)
% Number of connectives : 116 ( 45 ~; 43 |; 19 &)
% ( 1 <=>; 8 =>; 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 : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefIdeal,axiom,
! [X1] :
( aIdeal0(X1)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> ( ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X2),X1) )
& ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(sdtpldt0(X2,X3),X1) ) ) )
& aSet0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
fof(m__,conjecture,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__870,hypothesis,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(m__967,hypothesis,
( xy = sdtpldt0(xm,xn)
& aElementOf0(xn,xJ)
& aElementOf0(xm,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__967) ).
fof(m__994,hypothesis,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__994) ).
fof(m__934,hypothesis,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__934) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(c_0_10,plain,
! [X7,X8,X9,X10,X11] :
( ( aIdeal0(X11)
| ~ aSet0(X11)
| ~ aElementOf0(sdtpldt0(esk1_1(X11),esk2_1(X11)),X11)
| ~ aElementOf0(sdtasdt0(esk3_1(X11),esk1_1(X11)),X11) )
& ( aIdeal0(X11)
| ~ aSet0(X11)
| ~ aElementOf0(sdtpldt0(esk1_1(X11),esk2_1(X11)),X11)
| aElement0(esk3_1(X11)) )
& ( aIdeal0(X11)
| ~ aSet0(X11)
| aElementOf0(esk2_1(X11),X11)
| ~ aElementOf0(sdtasdt0(esk3_1(X11),esk1_1(X11)),X11) )
& ( aIdeal0(X11)
| ~ aSet0(X11)
| aElementOf0(esk2_1(X11),X11)
| aElement0(esk3_1(X11)) )
& ( aIdeal0(X11)
| ~ aSet0(X11)
| aElementOf0(esk1_1(X11),X11) )
& ( ~ aIdeal0(X7)
| ~ aElementOf0(X8,X7)
| aElementOf0(sdtasdt0(X10,X8),X7)
| ~ aElement0(X10) )
& ( ~ aIdeal0(X7)
| ~ aElementOf0(X8,X7)
| aElementOf0(sdtpldt0(X8,X9),X7)
| ~ aElementOf0(X9,X7) )
& ( ~ aIdeal0(X7)
| aSet0(X7) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefIdeal])])])])])])]) ).
fof(c_0_11,negated_conjecture,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_12,plain,
! [X49,X50] :
( aElement0(X50)
| ~ aElementOf0(X50,X49)
| ~ aSet0(X49) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
cnf(c_0_13,plain,
( ~ aIdeal0(X1)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[m__870]) ).
cnf(c_0_15,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__870]) ).
fof(c_0_16,negated_conjecture,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X35,X36,X37] :
( sdtpldt0(sdtpldt0(X35,X36),X37) = sdtpldt0(X35,sdtpldt0(X36,X37))
| ~ aElement0(X37)
| ~ aElement0(X36)
| ~ aElement0(X35) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).
cnf(c_0_18,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,hypothesis,
aElementOf0(xn,xJ),
inference(split_conjunct,[status(thm)],[m__967]) ).
cnf(c_0_20,hypothesis,
aSet0(xJ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,hypothesis,
aElementOf0(xm,xI),
inference(split_conjunct,[status(thm)],[m__967]) ).
cnf(c_0_22,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
fof(c_0_23,negated_conjecture,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(fof_nnf,[status(thm)],[c_0_16]) ).
cnf(c_0_24,hypothesis,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(split_conjunct,[status(thm)],[m__994]) ).
cnf(c_0_25,hypothesis,
aElementOf0(xk,xI),
inference(split_conjunct,[status(thm)],[m__934]) ).
cnf(c_0_26,plain,
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,hypothesis,
xy = sdtpldt0(xm,xn),
inference(split_conjunct,[status(thm)],[m__967]) ).
cnf(c_0_28,hypothesis,
aElement0(xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_29,hypothesis,
aElement0(xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_21]),c_0_22])]) ).
fof(c_0_30,plain,
! [X33,X34] :
( sdtpldt0(X33,X34) = sdtpldt0(X34,X33)
| ~ aElement0(X34)
| ~ aElement0(X33) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
cnf(c_0_31,negated_conjecture,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,hypothesis,
aElement0(sdtpldt0(xl,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_24]),c_0_20])]) ).
cnf(c_0_33,hypothesis,
aElement0(xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_25]),c_0_22])]) ).
cnf(c_0_34,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_26,c_0_27]),c_0_28]),c_0_29])]) ).
cnf(c_0_35,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,hypothesis,
aElementOf0(xl,xJ),
inference(split_conjunct,[status(thm)],[m__934]) ).
fof(c_0_37,plain,
! [X31,X32] :
( aElement0(sdtpldt0(X31,X32))
| ~ aElement0(X32)
| ~ aElement0(X31) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
cnf(c_0_38,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_31,c_0_26]),c_0_32]),c_0_29]),c_0_33])]) ).
cnf(c_0_39,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_34,c_0_35]),c_0_28])]) ).
cnf(c_0_40,hypothesis,
aElement0(xl),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_36]),c_0_20])]) ).
cnf(c_0_41,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElement0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,negated_conjecture,
sdtpldt0(xk,sdtpldt0(xy,xl)) != sdtpldt0(xx,xy),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_43,hypothesis,
aElement0(xy),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_27]),c_0_28]),c_0_29])]) ).
cnf(c_0_44,hypothesis,
xx = sdtpldt0(xk,xl),
inference(split_conjunct,[status(thm)],[m__934]) ).
cnf(c_0_45,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_42,c_0_35]),c_0_40]),c_0_43])]) ).
cnf(c_0_46,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_26,c_0_44]),c_0_40]),c_0_33])]) ).
cnf(c_0_47,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG090+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 04:14:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 Running first-order theorem proving
% 0.17/0.43 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
% 0.17/0.51 % Version: 3.5.1
% 0.17/0.51 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.17/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.17/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.51 % Starting sh5l with 300s (1) cores
% 0.17/0.51 % new_bool_3 with pid 1404713 completed with status 0
% 0.17/0.51 % Result found by new_bool_3
% 0.17/0.51 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.17/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.17/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.51 % Search class: FGUSF-FFMM32-SFFFFFNN
% 0.17/0.51 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.51 % Starting SubtermCWHack with 31s (1) cores
% 0.17/0.51 % SubtermCWHack with pid 1404717 completed with status 0
% 0.17/0.51 % Result found by SubtermCWHack
% 0.17/0.51 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.17/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.17/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.51 % Search class: FGUSF-FFMM32-SFFFFFNN
% 0.17/0.51 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.51 % Starting SubtermCWHack with 31s (1) cores
% 0.17/0.51 % Preprocessing time : 0.003 s
% 0.17/0.51
% 0.17/0.51 % Proof found!
% 0.17/0.51 % SZS status Theorem
% 0.17/0.51 % SZS output start CNFRefutation
% See solution above
% 0.17/0.51 % Parsed axioms : 31
% 0.17/0.51 % Removed by relevancy pruning/SinE : 11
% 0.17/0.51 % Initial clauses : 48
% 0.17/0.51 % Removed in clause preprocessing : 2
% 0.17/0.51 % Initial clauses in saturation : 46
% 0.17/0.51 % Processed clauses : 207
% 0.17/0.51 % ...of these trivial : 7
% 0.17/0.51 % ...subsumed : 73
% 0.17/0.51 % ...remaining for further processing : 127
% 0.17/0.51 % Other redundant clauses eliminated : 3
% 0.17/0.51 % Clauses deleted for lack of memory : 0
% 0.17/0.51 % Backward-subsumed : 4
% 0.17/0.51 % Backward-rewritten : 2
% 0.17/0.51 % Generated clauses : 315
% 0.17/0.51 % ...of the previous two non-redundant : 296
% 0.17/0.51 % ...aggressively subsumed : 0
% 0.17/0.51 % Contextual simplify-reflections : 1
% 0.17/0.51 % Paramodulations : 313
% 0.17/0.51 % Factorizations : 0
% 0.17/0.51 % NegExts : 0
% 0.17/0.51 % Equation resolutions : 3
% 0.17/0.51 % Disequality decompositions : 0
% 0.17/0.51 % Total rewrite steps : 271
% 0.17/0.51 % ...of those cached : 246
% 0.17/0.51 % Propositional unsat checks : 0
% 0.17/0.51 % Propositional check models : 0
% 0.17/0.51 % Propositional check unsatisfiable : 0
% 0.17/0.51 % Propositional clauses : 0
% 0.17/0.51 % Propositional clauses after purity: 0
% 0.17/0.51 % Propositional unsat core size : 0
% 0.17/0.51 % Propositional preprocessing time : 0.000
% 0.17/0.51 % Propositional encoding time : 0.000
% 0.17/0.51 % Propositional solver time : 0.000
% 0.17/0.51 % Success case prop preproc time : 0.000
% 0.17/0.51 % Success case prop encoding time : 0.000
% 0.17/0.51 % Success case prop solver time : 0.000
% 0.17/0.51 % Current number of processed clauses : 119
% 0.17/0.51 % Positive orientable unit clauses : 36
% 0.17/0.51 % Positive unorientable unit clauses: 0
% 0.17/0.51 % Negative unit clauses : 4
% 0.17/0.51 % Non-unit-clauses : 79
% 0.17/0.51 % Current number of unprocessed clauses: 127
% 0.17/0.51 % ...number of literals in the above : 593
% 0.17/0.51 % Current number of archived formulas : 0
% 0.17/0.51 % Current number of archived clauses : 6
% 0.17/0.51 % Clause-clause subsumption calls (NU) : 1807
% 0.17/0.51 % Rec. Clause-clause subsumption calls : 1662
% 0.17/0.51 % Non-unit clause-clause subsumptions : 78
% 0.17/0.51 % Unit Clause-clause subsumption calls : 72
% 0.17/0.51 % Rewrite failures with RHS unbound : 0
% 0.17/0.51 % BW rewrite match attempts : 2
% 0.17/0.51 % BW rewrite match successes : 2
% 0.17/0.51 % Condensation attempts : 0
% 0.17/0.51 % Condensation successes : 0
% 0.17/0.51 % Termbank termtop insertions : 7948
% 0.17/0.51 % Search garbage collected termcells : 783
% 0.17/0.51
% 0.17/0.51 % -------------------------------------------------
% 0.17/0.51 % User time : 0.025 s
% 0.17/0.51 % System time : 0.006 s
% 0.17/0.51 % Total time : 0.031 s
% 0.17/0.51 % Maximum resident set size: 3668 pages
% 0.17/0.51
% 0.17/0.51 % -------------------------------------------------
% 0.17/0.51 % User time : 0.029 s
% 0.17/0.51 % System time : 0.011 s
% 0.17/0.51 % Total time : 0.041 s
% 0.17/0.51 % Maximum resident set size: 4608 pages
% 0.17/0.51 % E exiting
%------------------------------------------------------------------------------