%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COM007+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 : n005.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 1.22s 1.72s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 10 unt; 0 def)
% Number of atoms : 77 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 75 ( 34 ~; 31 |; 5 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 41 ( 0 sgn 20 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goal_ax,axiom,
! [X1] :
( ( reflexive_rewrite(b,X1)
& reflexive_rewrite(c,X1) )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_ax) ).
fof(goal_to_be_proved,conjecture,
goal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_to_be_proved) ).
fof(rewrite_in_reflexive_rewrite,axiom,
! [X1,X2] :
( rewrite(X1,X2)
=> reflexive_rewrite(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_in_reflexive_rewrite) ).
fof(rewrite_diamond,axiom,
! [X1,X2,X3] :
( ( rewrite(X1,X2)
& rewrite(X1,X3) )
=> ? [X4] :
( rewrite(X2,X4)
& rewrite(X3,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_diamond) ).
fof(equal_or_rewrite,axiom,
! [X1,X2] :
( reflexive_rewrite(X1,X2)
=> ( X1 = X2
| rewrite(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_or_rewrite) ).
fof(equal_in_reflexive_rewrite,axiom,
! [X1,X2] :
( X1 = X2
=> reflexive_rewrite(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_in_reflexive_rewrite) ).
fof(assumption,axiom,
( reflexive_rewrite(a,b)
& reflexive_rewrite(a,c) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption) ).
fof(c_0_7,plain,
! [X16] :
( ~ reflexive_rewrite(b,X16)
| ~ reflexive_rewrite(c,X16)
| goal ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[goal_ax])]) ).
fof(c_0_8,negated_conjecture,
~ goal,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goal_to_be_proved])]) ).
cnf(c_0_9,plain,
( goal
| ~ reflexive_rewrite(b,X1)
| ~ reflexive_rewrite(c,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
~ goal,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X19,X20] :
( ~ rewrite(X19,X20)
| reflexive_rewrite(X19,X20) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rewrite_in_reflexive_rewrite])]) ).
cnf(c_0_12,plain,
( ~ reflexive_rewrite(b,X1)
| ~ reflexive_rewrite(c,X1) ),
inference(sr,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( reflexive_rewrite(X1,X2)
| ~ rewrite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,plain,
( ~ rewrite(c,X1)
| ~ reflexive_rewrite(b,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_15,plain,
! [X23,X24,X25] :
( ( rewrite(X24,esk1_3(X23,X24,X25))
| ~ rewrite(X23,X24)
| ~ rewrite(X23,X25) )
& ( rewrite(X25,esk1_3(X23,X24,X25))
| ~ rewrite(X23,X24)
| ~ rewrite(X23,X25) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rewrite_diamond])])])]) ).
cnf(c_0_16,plain,
( ~ rewrite(c,X1)
| ~ rewrite(b,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_17,plain,
( rewrite(X1,esk1_3(X2,X3,X1))
| ~ rewrite(X2,X3)
| ~ rewrite(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X21,X22] :
( ~ reflexive_rewrite(X21,X22)
| X21 = X22
| rewrite(X21,X22) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_or_rewrite])]) ).
fof(c_0_19,plain,
! [X17,X18] :
( X17 != X18
| reflexive_rewrite(X17,X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_in_reflexive_rewrite])]) ).
cnf(c_0_20,plain,
( ~ rewrite(b,esk1_3(X1,X2,c))
| ~ rewrite(X1,c)
| ~ rewrite(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( rewrite(X1,esk1_3(X2,X1,X3))
| ~ rewrite(X2,X1)
| ~ rewrite(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( X1 = X2
| rewrite(X1,X2)
| ~ reflexive_rewrite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
reflexive_rewrite(a,c),
inference(split_conjunct,[status(thm)],[assumption]) ).
cnf(c_0_24,plain,
( reflexive_rewrite(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( ~ rewrite(X1,c)
| ~ rewrite(X1,b) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( c = a
| rewrite(a,c) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
reflexive_rewrite(a,b),
inference(split_conjunct,[status(thm)],[assumption]) ).
cnf(c_0_28,plain,
reflexive_rewrite(X1,X1),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
( c = a
| ~ rewrite(a,b) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
( a = b
| rewrite(a,b) ),
inference(spm,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_31,plain,
~ rewrite(c,b),
inference(spm,[status(thm)],[c_0_14,c_0_28]) ).
cnf(c_0_32,plain,
( a = b
| c = a ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,plain,
a = b,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_30]) ).
cnf(c_0_34,plain,
~ reflexive_rewrite(b,c),
inference(spm,[status(thm)],[c_0_12,c_0_28]) ).
cnf(c_0_35,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_33]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : COM007+2 : TPTP v9.2.1. Released v3.2.0.
% 0.11/0.13 % 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
% 0.15/0.34 % Computer : n005.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon May 4 16:19:15 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.18/0.35 % start to proof: theBenchmark
% 1.22/1.72 % Version : CSE_E---1.7
% 1.22/1.72 % Problem : theBenchmark.p
% 1.22/1.72 % SZS status Theorem for theBenchmark.p
% 1.22/1.72 % SZS output start CNFRefutation
% See solution above
% 1.22/1.72 % Total time : 1.370s
%------------------------------------------------------------------------------