%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COM008+2 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.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 1.34s 1.74s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 11 unt; 0 def)
% Number of atoms : 158 ( 22 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 192 ( 86 ~; 88 |; 12 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 85 ( 0 sgn 28 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(found,axiom,
! [X1] :
( ( transitive_reflexive_rewrite(b,X1)
& transitive_reflexive_rewrite(c,X1) )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',found) ).
fof(goal_to_be_proved,conjecture,
goal,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',transitivity_of_transitive_reflexive_rewrite) ).
fof(equal_or_rewrite,axiom,
! [X1,X2] :
( transitive_reflexive_rewrite(X1,X2)
=> ( X1 = X2
| ? [X3] :
( rewrite(X1,X3)
& transitive_reflexive_rewrite(X3,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_or_rewrite) ).
fof(assumption,axiom,
( transitive_reflexive_rewrite(a,b)
& transitive_reflexive_rewrite(a,c) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',lo_cfl) ).
fof(equality_in_transitive_reflexive_rewrite,axiom,
! [X1,X2] :
( X1 = X2
=> transitive_reflexive_rewrite(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality_in_transitive_reflexive_rewrite) ).
fof(c_0_8,plain,
! [X24] :
( ~ transitive_reflexive_rewrite(b,X24)
| ~ transitive_reflexive_rewrite(c,X24)
| goal ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[found])]) ).
fof(c_0_9,negated_conjecture,
~ goal,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goal_to_be_proved])]) ).
cnf(c_0_10,plain,
( goal
| ~ transitive_reflexive_rewrite(b,X1)
| ~ transitive_reflexive_rewrite(c,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
~ goal,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X36,X37,X38] :
( ( transitive_reflexive_rewrite(X37,esk2_3(X36,X37,X38))
| ~ rewrite(a,X36)
| ~ transitive_reflexive_rewrite(X36,X37)
| ~ transitive_reflexive_rewrite(X36,X38) )
& ( transitive_reflexive_rewrite(X38,esk2_3(X36,X37,X38))
| ~ rewrite(a,X36)
| ~ transitive_reflexive_rewrite(X36,X37)
| ~ transitive_reflexive_rewrite(X36,X38) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ih_cfl])])])]) ).
fof(c_0_13,plain,
! [X29,X30,X31] :
( ~ transitive_reflexive_rewrite(X29,X30)
| ~ transitive_reflexive_rewrite(X30,X31)
| transitive_reflexive_rewrite(X29,X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitivity_of_transitive_reflexive_rewrite])]) ).
cnf(c_0_14,plain,
( ~ transitive_reflexive_rewrite(b,X1)
| ~ transitive_reflexive_rewrite(c,X1) ),
inference(sr,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,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_12]) ).
cnf(c_0_16,plain,
( transitive_reflexive_rewrite(X1,X3)
| ~ transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,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_12]) ).
fof(c_0_18,plain,
! [X40,X41] :
( ( rewrite(X40,esk3_2(X40,X41))
| X40 = X41
| ~ transitive_reflexive_rewrite(X40,X41) )
& ( transitive_reflexive_rewrite(esk3_2(X40,X41),X41)
| X40 = X41
| ~ transitive_reflexive_rewrite(X40,X41) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_or_rewrite])])])]) ).
cnf(c_0_19,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_14,c_0_15]) ).
cnf(c_0_20,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_16,c_0_17]) ).
cnf(c_0_21,plain,
( rewrite(X1,esk3_2(X1,X2))
| X1 = X2
| ~ transitive_reflexive_rewrite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
transitive_reflexive_rewrite(a,c),
inference(split_conjunct,[status(thm)],[assumption]) ).
cnf(c_0_23,plain,
( transitive_reflexive_rewrite(esk3_2(X1,X2),X2)
| X1 = X2
| ~ transitive_reflexive_rewrite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,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_19,c_0_20]) ).
cnf(c_0_25,plain,
( c = a
| rewrite(a,esk3_2(a,c)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( c = a
| transitive_reflexive_rewrite(esk3_2(a,c),c) ),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_27,plain,
( c = a
| ~ transitive_reflexive_rewrite(esk3_2(a,c),X1)
| ~ transitive_reflexive_rewrite(b,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
fof(c_0_28,plain,
! [X32,X33,X34] :
( ( transitive_reflexive_rewrite(X33,esk1_3(X32,X33,X34))
| ~ rewrite(X32,X33)
| ~ rewrite(X32,X34) )
& ( transitive_reflexive_rewrite(X34,esk1_3(X32,X33,X34))
| ~ rewrite(X32,X33)
| ~ rewrite(X32,X34) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lo_cfl])])])]) ).
cnf(c_0_29,plain,
( c = a
| ~ 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_27,c_0_20]) ).
cnf(c_0_30,plain,
( transitive_reflexive_rewrite(X1,esk1_3(X2,X3,X1))
| ~ rewrite(X2,X3)
| ~ rewrite(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_31,plain,
( c = a
| ~ 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_29,c_0_15]) ).
cnf(c_0_32,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_16,c_0_30]) ).
fof(c_0_33,plain,
! [X25,X26] :
( X25 != X26
| transitive_reflexive_rewrite(X25,X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equality_in_transitive_reflexive_rewrite])]) ).
cnf(c_0_34,plain,
( c = a
| ~ 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_31,c_0_32]) ).
cnf(c_0_35,plain,
( transitive_reflexive_rewrite(X1,esk1_3(X2,X1,X3))
| ~ rewrite(X2,X1)
| ~ rewrite(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
( transitive_reflexive_rewrite(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
( c = a
| ~ 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_34,c_0_35]) ).
cnf(c_0_38,plain,
transitive_reflexive_rewrite(X1,X1),
inference(er,[status(thm)],[c_0_36]) ).
cnf(c_0_39,plain,
transitive_reflexive_rewrite(a,b),
inference(split_conjunct,[status(thm)],[assumption]) ).
cnf(c_0_40,plain,
( c = a
| ~ rewrite(X1,esk3_2(a,c))
| ~ rewrite(a,X2)
| ~ rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X2,b) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,plain,
( transitive_reflexive_rewrite(X1,b)
| ~ transitive_reflexive_rewrite(X1,a) ),
inference(spm,[status(thm)],[c_0_16,c_0_39]) ).
cnf(c_0_42,plain,
( c = a
| ~ rewrite(a,X1)
| ~ transitive_reflexive_rewrite(X1,b) ),
inference(spm,[status(thm)],[c_0_40,c_0_25]) ).
cnf(c_0_43,plain,
( b = a
| rewrite(a,esk3_2(a,b)) ),
inference(spm,[status(thm)],[c_0_21,c_0_39]) ).
cnf(c_0_44,plain,
( b = a
| transitive_reflexive_rewrite(esk3_2(a,b),b) ),
inference(spm,[status(thm)],[c_0_23,c_0_39]) ).
cnf(c_0_45,plain,
~ transitive_reflexive_rewrite(b,c),
inference(spm,[status(thm)],[c_0_14,c_0_38]) ).
cnf(c_0_46,plain,
( transitive_reflexive_rewrite(X1,c)
| ~ transitive_reflexive_rewrite(X1,a) ),
inference(spm,[status(thm)],[c_0_16,c_0_22]) ).
cnf(c_0_47,plain,
~ transitive_reflexive_rewrite(c,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_41]),c_0_38])]) ).
cnf(c_0_48,plain,
( b = a
| c = a ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_49,plain,
~ transitive_reflexive_rewrite(b,a),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,plain,
b = a,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_38])]) ).
cnf(c_0_51,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : COM008+2 : TPTP v9.2.1. Released v3.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.34 % Computer : n022.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon May 4 16:19:21 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 1.34/1.74 % Version : CSE_E---1.7
% 1.34/1.74 % Problem : theBenchmark.p
% 1.34/1.74 % SZS status Theorem for theBenchmark.p
% 1.34/1.74 % SZS output start CNFRefutation
% See solution above
% 1.34/1.74 % Total time : 1.371s
%------------------------------------------------------------------------------