%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COM008+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:13:06 PM UTC 2026
% Result : Theorem 1.32s 1.72s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 15 unt; 0 def)
% Number of atoms : 170 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 198 ( 88 ~; 91 |; 12 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 94 ( 0 sgn 34 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(found,axiom,
! [X1] :
( ( transitive_reflexive_rewrite(b,X1)
& transitive_reflexive_rewrite(c,X1) )
=> goal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',found) ).
fof(goal_to_be_proved,conjecture,
goal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_to_be_proved) ).
fof(ih_cfl,axiom,
! [X1,X2,X3] :
( ( rewrite(a,X1)
& transitive_reflexive_rewrite(X1,X2)
& transitive_reflexive_rewrite(X1,X3) )
=> ? [X4] :
( transitive_reflexive_rewrite(X2,X4)
& transitive_reflexive_rewrite(X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ih_cfl) ).
fof(transitivity_of_transitive_reflexive_rewrite,axiom,
! [X1,X2,X3] :
( ( transitive_reflexive_rewrite(X1,X2)
& transitive_reflexive_rewrite(X2,X3) )
=> transitive_reflexive_rewrite(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_transitive_reflexive_rewrite) ).
fof(equalish_or_rewrite,axiom,
! [X1,X2] :
( transitive_reflexive_rewrite(X1,X2)
=> ( equalish(X1,X2)
| ? [X3] :
( rewrite(X1,X3)
& transitive_reflexive_rewrite(X3,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equalish_or_rewrite) ).
fof(assumption,axiom,
( transitive_reflexive_rewrite(a,b)
& transitive_reflexive_rewrite(a,c) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption) ).
fof(lo_cfl,axiom,
! [X1,X2,X3] :
( ( rewrite(X1,X2)
& rewrite(X1,X3) )
=> ? [X4] :
( transitive_reflexive_rewrite(X2,X4)
& transitive_reflexive_rewrite(X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lo_cfl) ).
fof(equality_in_transitive_reflexive_rewrite,axiom,
! [X1,X2] :
( equalish(X1,X2)
=> transitive_reflexive_rewrite(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality_in_transitive_reflexive_rewrite) ).
fof(reflexivity,axiom,
! [X1] : equalish(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(symmetry,axiom,
! [X1,X2] :
( equalish(X1,X2)
=> equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
fof(c_0_10,plain,
! [X27] :
( ~ transitive_reflexive_rewrite(b,X27)
| ~ transitive_reflexive_rewrite(c,X27)
| goal ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[found])]) ).
fof(c_0_11,negated_conjecture,
~ goal,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goal_to_be_proved])]) ).
cnf(c_0_12,plain,
( goal
| ~ transitive_reflexive_rewrite(b,X1)
| ~ transitive_reflexive_rewrite(c,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
~ goal,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X42,X43,X44] :
( ( transitive_reflexive_rewrite(X43,esk2_3(X42,X43,X44))
| ~ rewrite(a,X42)
| ~ transitive_reflexive_rewrite(X42,X43)
| ~ transitive_reflexive_rewrite(X42,X44) )
& ( transitive_reflexive_rewrite(X44,esk2_3(X42,X43,X44))
| ~ rewrite(a,X42)
| ~ transitive_reflexive_rewrite(X42,X43)
| ~ transitive_reflexive_rewrite(X42,X44) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ih_cfl])])])]) ).
fof(c_0_15,plain,
! [X35,X36,X37] :
( ~ transitive_reflexive_rewrite(X35,X36)
| ~ transitive_reflexive_rewrite(X36,X37)
| transitive_reflexive_rewrite(X35,X37) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitivity_of_transitive_reflexive_rewrite])]) ).
cnf(c_0_16,plain,
( ~ transitive_reflexive_rewrite(b,X1)
| ~ transitive_reflexive_rewrite(c,X1) ),
inference(sr,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( transitive_reflexive_rewrite(X1,esk2_3(X2,X1,X3))
| ~ rewrite(a,X2)
| ~ transitive_reflexive_rewrite(X2,X1)
| ~ transitive_reflexive_rewrite(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( transitive_reflexive_rewrite(X1,X3)
| ~ transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( transitive_reflexive_rewrite(X1,esk2_3(X2,X3,X1))
| ~ rewrite(a,X2)
| ~ transitive_reflexive_rewrite(X2,X3)
| ~ transitive_reflexive_rewrite(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_20,plain,
! [X46,X47] :
( ( rewrite(X46,esk3_2(X46,X47))
| equalish(X46,X47)
| ~ transitive_reflexive_rewrite(X46,X47) )
& ( transitive_reflexive_rewrite(esk3_2(X46,X47),X47)
| equalish(X46,X47)
| ~ transitive_reflexive_rewrite(X46,X47) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equalish_or_rewrite])])])]) ).
cnf(c_0_21,plain,
( ~ rewrite(a,X1)
| ~ transitive_reflexive_rewrite(b,esk2_3(X1,c,X2))
| ~ transitive_reflexive_rewrite(X1,c)
| ~ transitive_reflexive_rewrite(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( transitive_reflexive_rewrite(X1,esk2_3(X2,X3,X4))
| ~ rewrite(a,X2)
| ~ transitive_reflexive_rewrite(X1,X4)
| ~ transitive_reflexive_rewrite(X2,X3)
| ~ transitive_reflexive_rewrite(X2,X4) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( rewrite(X1,esk3_2(X1,X2))
| equalish(X1,X2)
| ~ transitive_reflexive_rewrite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
transitive_reflexive_rewrite(a,c),
inference(split_conjunct,[status(thm)],[assumption]) ).
cnf(c_0_25,plain,
( transitive_reflexive_rewrite(esk3_2(X1,X2),X2)
| equalish(X1,X2)
| ~ transitive_reflexive_rewrite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
( ~ rewrite(a,X1)
| ~ transitive_reflexive_rewrite(X1,c)
| ~ transitive_reflexive_rewrite(b,X2)
| ~ transitive_reflexive_rewrite(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( rewrite(a,esk3_2(a,c))
| equalish(a,c) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
( equalish(a,c)
| transitive_reflexive_rewrite(esk3_2(a,c),c) ),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_29,plain,
( equalish(a,c)
| ~ transitive_reflexive_rewrite(esk3_2(a,c),X1)
| ~ transitive_reflexive_rewrite(b,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
fof(c_0_30,plain,
! [X38,X39,X40] :
( ( transitive_reflexive_rewrite(X39,esk1_3(X38,X39,X40))
| ~ rewrite(X38,X39)
| ~ rewrite(X38,X40) )
& ( transitive_reflexive_rewrite(X40,esk1_3(X38,X39,X40))
| ~ rewrite(X38,X39)
| ~ rewrite(X38,X40) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lo_cfl])])])]) ).
cnf(c_0_31,plain,
( equalish(a,c)
| ~ rewrite(a,X1)
| ~ transitive_reflexive_rewrite(b,esk2_3(X1,X2,X3))
| ~ transitive_reflexive_rewrite(esk3_2(a,c),X3)
| ~ transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X1,X3) ),
inference(spm,[status(thm)],[c_0_29,c_0_22]) ).
cnf(c_0_32,plain,
( transitive_reflexive_rewrite(X1,esk1_3(X2,X3,X1))
| ~ rewrite(X2,X3)
| ~ rewrite(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_33,plain,
( equalish(a,c)
| ~ rewrite(a,X1)
| ~ transitive_reflexive_rewrite(esk3_2(a,c),X2)
| ~ transitive_reflexive_rewrite(X1,b)
| ~ transitive_reflexive_rewrite(X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_17]) ).
cnf(c_0_34,plain,
( transitive_reflexive_rewrite(X1,esk1_3(X2,X3,X4))
| ~ rewrite(X2,X3)
| ~ rewrite(X2,X4)
| ~ transitive_reflexive_rewrite(X1,X4) ),
inference(spm,[status(thm)],[c_0_18,c_0_32]) ).
fof(c_0_35,plain,
! [X31,X32] :
( ~ equalish(X31,X32)
| transitive_reflexive_rewrite(X31,X32) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equality_in_transitive_reflexive_rewrite])]) ).
fof(c_0_36,plain,
! [X28] : equalish(X28,X28),
inference(variable_rename,[status(thm)],[reflexivity]) ).
cnf(c_0_37,plain,
( equalish(a,c)
| ~ rewrite(a,X1)
| ~ rewrite(X2,X3)
| ~ rewrite(X2,X4)
| ~ transitive_reflexive_rewrite(esk3_2(a,c),X4)
| ~ transitive_reflexive_rewrite(X1,esk1_3(X2,X3,X4))
| ~ transitive_reflexive_rewrite(X1,b) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
( transitive_reflexive_rewrite(X1,esk1_3(X2,X1,X3))
| ~ rewrite(X2,X1)
| ~ rewrite(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,plain,
( transitive_reflexive_rewrite(X1,X2)
| ~ equalish(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,plain,
equalish(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,plain,
( equalish(a,c)
| ~ rewrite(a,X1)
| ~ rewrite(X2,X1)
| ~ rewrite(X2,X3)
| ~ transitive_reflexive_rewrite(esk3_2(a,c),X3)
| ~ transitive_reflexive_rewrite(X1,b) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
transitive_reflexive_rewrite(X1,X1),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,plain,
( equalish(a,c)
| ~ rewrite(X1,esk3_2(a,c))
| ~ rewrite(a,X2)
| ~ rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X2,b) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_44,plain,
transitive_reflexive_rewrite(a,b),
inference(split_conjunct,[status(thm)],[assumption]) ).
fof(c_0_45,plain,
! [X29,X30] :
( ~ equalish(X29,X30)
| equalish(X30,X29) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry])]) ).
cnf(c_0_46,plain,
( equalish(a,c)
| ~ rewrite(a,X1)
| ~ transitive_reflexive_rewrite(X1,b) ),
inference(spm,[status(thm)],[c_0_43,c_0_27]) ).
cnf(c_0_47,plain,
( rewrite(a,esk3_2(a,b))
| equalish(a,b) ),
inference(spm,[status(thm)],[c_0_23,c_0_44]) ).
cnf(c_0_48,plain,
( equalish(a,b)
| transitive_reflexive_rewrite(esk3_2(a,b),b) ),
inference(spm,[status(thm)],[c_0_25,c_0_44]) ).
cnf(c_0_49,plain,
( equalish(X2,X1)
| ~ equalish(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_50,plain,
( equalish(a,b)
| equalish(a,c) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_51,plain,
( transitive_reflexive_rewrite(X1,b)
| ~ transitive_reflexive_rewrite(X1,a) ),
inference(spm,[status(thm)],[c_0_18,c_0_44]) ).
cnf(c_0_52,plain,
( equalish(a,b)
| equalish(c,a) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_53,plain,
~ transitive_reflexive_rewrite(c,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_51]),c_0_42])]) ).
cnf(c_0_54,plain,
equalish(a,b),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_52]),c_0_53]) ).
cnf(c_0_55,plain,
~ transitive_reflexive_rewrite(b,c),
inference(spm,[status(thm)],[c_0_16,c_0_42]) ).
cnf(c_0_56,plain,
( transitive_reflexive_rewrite(X1,c)
| ~ transitive_reflexive_rewrite(X1,a) ),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_57,plain,
equalish(b,a),
inference(spm,[status(thm)],[c_0_49,c_0_54]) ).
cnf(c_0_58,plain,
~ transitive_reflexive_rewrite(b,a),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_59,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_57]),c_0_58]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM008+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n031.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 16:21:23 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.32/1.72 % Version : CSE_E---1.7
% 1.32/1.72 % Problem : theBenchmark.p
% 1.32/1.72 % SZS status Theorem for theBenchmark.p
% 1.32/1.72 % SZS output start CNFRefutation
% See solution above
% 1.32/1.73 % Total time : 1.366s
%------------------------------------------------------------------------------