%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWX187+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 03:14:12 PM UTC 2026
% Result : Theorem 1.18s 0.90s
% Output : CNFRefutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 40 unt; 0 def)
% Number of atoms : 92 ( 64 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 71 ( 31 ~; 23 |; 1 &)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 119 ( 8 sgn 37 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_016,axiom,
! [X3] : rotate(z,X3) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
fof(axiom_015,axiom,
! [X5,X2,X7] : rotate(s(X5),cons(X2,X7)) = rotate(X5,x(X7,cons(X2,nil))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
fof(goal_017,conjecture,
? [X8,X9,X10,X4] :
~ ( x2(X8,length(X4))
=> ( x2(X9,length(X10))
=> ( X4 = X10
=> ( rotate(s(z),X4) != X4
=> ( rotate(X8,X4) = rotate(X9,X10)
=> X8 = X9 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_017) ).
fof(axiom_013,axiom,
! [X3,X5,X4] : x(cons(X5,X4),X3) = cons(X5,x(X4,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
fof(axiom_012,axiom,
! [X3] : x(nil,X3) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
fof(axiom_008,axiom,
! [X5,X6] :
( x2(s(X5),s(X6))
<=> x2(X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
fof(axiom_010,axiom,
! [X2] : x2(z,s(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
fof(axiom_005,axiom,
! [X1] : s(X1) != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
fof(axiom_007,axiom,
! [X3,X4] : length(cons(X3,X4)) = s(length(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
fof(axiom_001,axiom,
! [X1,X2] : head(cons(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
fof(c_0_10,plain,
! [X33] : rotate(z,X33) = X33,
inference(variable_rename,[status(thm)],[axiom_016]) ).
fof(c_0_11,plain,
! [X30,X31,X32] : rotate(s(X30),cons(X31,X32)) = rotate(X30,x(X32,cons(X31,nil))),
inference(variable_rename,[status(thm)],[axiom_015]) ).
fof(c_0_12,negated_conjecture,
~ ? [X8,X9,X10,X4] :
~ ( x2(X8,length(X4))
=> ( x2(X9,length(X10))
=> ( X4 = X10
=> ( rotate(s(z),X4) != X4
=> ( rotate(X8,X4) = rotate(X9,X10)
=> X8 = X9 ) ) ) ) ),
inference(assume_negation,[status(cth)],[goal_017]) ).
cnf(c_0_13,plain,
rotate(z,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
rotate(s(X1),cons(X2,X3)) = rotate(X1,x(X3,cons(X2,nil))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X26,X27,X28] : x(cons(X27,X28),X26) = cons(X27,x(X28,X26)),
inference(variable_rename,[status(thm)],[axiom_013]) ).
fof(c_0_16,negated_conjecture,
~ ? [X8,X9,X10,X4] :
~ ( x2(X8,length(X4))
=> ( x2(X9,length(X10))
=> ( X4 = X10
=> ( rotate(s(z),X4) != X4
=> ( rotate(X8,X4) = rotate(X9,X10)
=> X8 = X9 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
x(X1,cons(X2,nil)) = rotate(s(z),cons(X2,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
x(cons(X1,X2),X3) = cons(X1,x(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X25] : x(nil,X25) = X25,
inference(variable_rename,[status(thm)],[axiom_012]) ).
fof(c_0_20,negated_conjecture,
! [X34,X35,X36,X37] :
( X34 = X35
| rotate(X34,X37) != rotate(X35,X36)
| rotate(s(z),X37) = X37
| X37 != X36
| ~ x2(X35,length(X36))
| ~ x2(X34,length(X37)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
cnf(c_0_21,plain,
rotate(X1,rotate(s(z),cons(X2,X3))) = rotate(s(X1),cons(X2,X3)),
inference(rw,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_22,plain,
rotate(s(z),cons(X1,cons(X2,X3))) = cons(X2,rotate(s(z),cons(X1,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_17]) ).
fof(c_0_23,plain,
! [X21,X22] :
( ( x2(s(X21),s(X22))
| ~ x2(X21,X22) )
& ( x2(X21,X22)
| ~ x2(s(X21),s(X22)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_008])])]) ).
fof(c_0_24,plain,
! [X24] : x2(z,s(X24)),
inference(variable_rename,[status(thm)],[axiom_010]) ).
cnf(c_0_25,plain,
x(nil,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
( rotate(X1,X2) != rotate(X3,X4)
| X2 != X4
| ~ x2(X3,length(X4))
| ~ x2(X1,length(X2))
| X1 = X3
| rotate(s(z),X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
rotate(X1,cons(X2,rotate(s(z),cons(X3,X4)))) = rotate(s(X1),cons(X3,cons(X2,X4))),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
( ~ x2(X1,X2)
| x2(s(X1),s(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
x2(z,s(X1)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_30,plain,
! [X1] : s(X1) != z,
inference(fof_simplification,[status(thm)],[axiom_005]) ).
cnf(c_0_31,plain,
rotate(s(z),cons(X1,nil)) = cons(X1,nil),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_32,negated_conjecture,
( ~ x2(X2,length(X1))
| ~ x2(X3,length(X1))
| rotate(X2,X1) != rotate(X3,X1)
| X2 = X3
| rotate(s(z),X1) = X1 ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
rotate(X1,cons(X2,cons(X3,rotate(s(z),cons(X4,X5))))) = rotate(s(X1),cons(X4,cons(X2,cons(X3,X5)))),
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
fof(c_0_34,plain,
! [X19,X20] : length(cons(X19,X20)) = s(length(X20)),
inference(variable_rename,[status(thm)],[axiom_007]) ).
cnf(c_0_35,plain,
x2(s(z),s(s(X1))),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_36,plain,
! [X18] : s(X18) != z,
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_30])]) ).
cnf(c_0_37,plain,
rotate(s(X1),cons(X2,nil)) = rotate(X1,cons(X2,nil)),
inference(spm,[status(thm)],[c_0_21,c_0_31]) ).
cnf(c_0_38,negated_conjecture,
( ~ x2(X2,length(X1))
| ~ x2(z,length(X1))
| rotate(X2,X1) != X1
| X2 = z
| rotate(s(z),X1) = X1 ),
inference(spm,[status(thm)],[c_0_32,c_0_13]) ).
cnf(c_0_39,plain,
rotate(s(s(z)),cons(X1,cons(X2,cons(X3,X4)))) = cons(X3,rotate(s(s(z)),cons(X1,cons(X2,X4)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_33]),c_0_27]) ).
cnf(c_0_40,plain,
length(cons(X1,X2)) = s(length(X2)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
x2(s(s(z)),s(s(s(X1)))),
inference(spm,[status(thm)],[c_0_28,c_0_35]) ).
cnf(c_0_42,plain,
s(X1) != z,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,plain,
rotate(s(X1),cons(X2,cons(X3,nil))) = rotate(X1,cons(X3,cons(X2,nil))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_37]),c_0_13]) ).
cnf(c_0_44,negated_conjecture,
( cons(X2,rotate(s(s(z)),cons(X3,cons(X1,X4)))) != cons(X3,cons(X1,cons(X2,X4)))
| cons(X1,cons(X2,rotate(s(z),cons(X3,X4)))) = cons(X3,cons(X1,cons(X2,X4))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_22]),c_0_22]),c_0_40]),c_0_40]),c_0_40]),c_0_29]),c_0_40]),c_0_40]),c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_45,plain,
rotate(s(X1),cons(X2,cons(X3,cons(X4,nil)))) = rotate(X1,cons(X3,cons(X4,cons(X2,nil)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_43]),c_0_13]) ).
fof(c_0_46,plain,
! [X11,X12] : head(cons(X11,X12)) = X11,
inference(variable_rename,[status(thm)],[axiom_001]) ).
cnf(c_0_47,negated_conjecture,
( cons(X2,cons(X3,cons(X4,cons(X1,nil)))) != cons(X4,cons(X1,cons(X2,cons(X3,nil))))
| cons(X1,cons(X2,cons(X3,cons(X4,nil)))) = cons(X4,cons(X1,cons(X2,cons(X3,nil)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_43]),c_0_13]),c_0_45]),c_0_13]) ).
cnf(c_0_48,plain,
head(cons(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_49,negated_conjecture,
cons(X1,cons(X2,cons(X1,cons(X2,nil)))) = cons(X2,cons(X1,cons(X2,cons(X1,nil)))),
inference(er,[status(thm)],[c_0_47]) ).
cnf(c_0_50,negated_conjecture,
X1 = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_48]) ).
cnf(c_0_51,plain,
$false,
inference(sr,[status(thm)],[c_0_42,c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX187+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.64 % Computer : n005.cluster.edu
% 0.19/0.64 % Model : x86_64 x86_64
% 0.19/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.64 % Memory : 8046.5625MB
% 0.19/0.64 % OS : Linux 6.8.0-71-generic
% 0.19/0.64 % CPULimit : 300
% 0.19/0.64 % WCLimit : 300
% 0.19/0.64 % DateTime : Mon Sep 21 10:31:33 UTC 2026
% 0.19/0.65 % CPUTime :
% 0.19/0.65 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.70 Running first-order theorem proving
% 0.19/0.70 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
% 1.18/0.90 % Version: 3.5.1
% 1.18/0.90 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.18/0.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.18/0.90 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.18/0.90 % Starting new_bool_3 with 300s (1) cores
% 1.18/0.90 % Starting new_bool_1 with 300s (1) cores
% 1.18/0.90 % Starting sh5l with 300s (1) cores
% 1.18/0.90 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3235405 completed with status 0
% 1.18/0.90 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.18/0.90 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.18/0.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.18/0.90 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.18/0.90 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.18/0.90 % No SInE strategy applied
% 1.18/0.90 % Search class: FGUSM-FFSF21-MFFFFFNN
% 1.18/0.90 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.18/0.90 % Starting SubtermCWHack with 136s (1) cores
% 1.18/0.90 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.18/0.90 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 1.18/0.90 % Starting new_bool_3 with 136s (1) cores
% 1.18/0.90 % Starting new_bool_1 with 136s (1) cores
% 1.18/0.90 % new_bool_1 with pid 3235414 completed with status 0
% 1.18/0.90 % Result found by new_bool_1
% 1.18/0.90 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.18/0.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.18/0.90 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.18/0.90 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.18/0.90 % No SInE strategy applied
% 1.18/0.90 % Search class: FGUSM-FFSF21-MFFFFFNN
% 1.18/0.90 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.18/0.90 % Starting SubtermCWHack with 136s (1) cores
% 1.18/0.90 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.18/0.90 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 1.18/0.90 % Starting new_bool_3 with 136s (1) cores
% 1.18/0.90 % Starting new_bool_1 with 136s (1) cores
% 1.18/0.90 % Preprocessing time : 0.002 s
% 1.18/0.90 % Presaturation interreduction done
% 1.18/0.90
% 1.18/0.90 % Proof found!
% 1.18/0.90 % SZS status Theorem
% 1.18/0.90 % SZS output start CNFRefutation
% See solution above
% 1.18/0.90 % Parsed axioms : 17
% 1.18/0.90 % Removed by relevancy pruning/SinE : 0
% 1.18/0.90 % Initial clauses : 18
% 1.18/0.90 % Removed in clause preprocessing : 0
% 1.18/0.90 % Initial clauses in saturation : 18
% 1.18/0.90 % Processed clauses : 188
% 1.18/0.90 % ...of these trivial : 3
% 1.18/0.90 % ...subsumed : 26
% 1.18/0.90 % ...remaining for further processing : 159
% 1.18/0.90 % Other redundant clauses eliminated : 1
% 1.18/0.90 % Clauses deleted for lack of memory : 0
% 1.18/0.90 % Backward-subsumed : 74
% 1.18/0.90 % Backward-rewritten : 3
% 1.18/0.90 % Generated clauses : 6847
% 1.18/0.90 % ...of the previous two non-redundant : 309
% 1.18/0.90 % ...aggressively subsumed : 0
% 1.18/0.90 % Contextual simplify-reflections : 0
% 1.18/0.90 % Paramodulations : 6838
% 1.18/0.90 % Factorizations : 0
% 1.18/0.90 % NegExts : 0
% 1.18/0.90 % Equation resolutions : 7
% 1.18/0.90 % Disequality decompositions : 0
% 1.18/0.90 % Total rewrite steps : 1427
% 1.18/0.90 % ...of those cached : 1047
% 1.18/0.90 % Propositional unsat checks : 0
% 1.18/0.90 % Propositional check models : 0
% 1.18/0.90 % Propositional check unsatisfiable : 0
% 1.18/0.90 % Propositional clauses : 0
% 1.18/0.90 % Propositional clauses after purity: 0
% 1.18/0.90 % Propositional unsat core size : 0
% 1.18/0.90 % Propositional preprocessing time : 0.000
% 1.18/0.90 % Propositional encoding time : 0.000
% 1.18/0.90 % Propositional solver time : 0.000
% 1.18/0.90 % Success case prop preproc time : 0.000
% 1.18/0.90 % Success case prop encoding time : 0.000
% 1.18/0.90 % Success case prop solver time : 0.000
% 1.18/0.90 % Current number of processed clauses : 61
% 1.18/0.90 % Positive orientable unit clauses : 56
% 1.18/0.90 % Positive unorientable unit clauses: 1
% 1.18/0.90 % Negative unit clauses : 2
% 1.18/0.90 % Non-unit-clauses : 2
% 1.18/0.90 % Current number of unprocessed clauses: 152
% 1.18/0.90 % ...number of literals in the above : 475
% 1.18/0.90 % Current number of archived formulas : 0
% 1.18/0.90 % Current number of archived clauses : 97
% 1.18/0.90 % Clause-clause subsumption calls (NU) : 472
% 1.18/0.90 % Rec. Clause-clause subsumption calls : 423
% 1.18/0.90 % Non-unit clause-clause subsumptions : 26
% 1.18/0.90 % Unit Clause-clause subsumption calls : 139
% 1.18/0.90 % Rewrite failures with RHS unbound : 518
% 1.18/0.90 % BW rewrite match attempts : 3093
% 1.18/0.90 % BW rewrite match successes : 513
% 1.18/0.90 % Condensation attempts : 0
% 1.18/0.90 % Condensation successes : 0
% 1.18/0.90 % Termbank termtop insertions : 397271
% 1.18/0.90 % Search garbage collected termcells : 99
% 1.18/0.90
% 1.18/0.90 % -------------------------------------------------
% 1.18/0.90 % User time : 0.149 s
% 1.18/0.90 % System time : 0.014 s
% 1.18/0.90 % Total time : 0.163 s
% 1.18/0.90 % Maximum resident set size: 3644 pages
% 1.18/0.90
% 1.18/0.90 % -------------------------------------------------
% 1.18/0.90 % User time : 0.558 s
% 1.18/0.90 % System time : 0.044 s
% 1.18/0.90 % Total time : 0.602 s
% 1.18/0.90 % Maximum resident set size: 4864 pages
% 1.18/0.90 % E exiting
%------------------------------------------------------------------------------