%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COM007+1 : 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 : n009.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 1.26s 1.70s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 13 unt; 0 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 97 ( 40 ~; 44 |; 6 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 65 ( 0 sgn 32 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(equalish_or_rewrite,axiom,
! [X1,X2] :
( reflexive_rewrite(X1,X2)
=> ( equalish(X1,X2)
| rewrite(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equalish_or_rewrite) ).
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(symmtery,axiom,
! [X1,X2] :
( equalish(X1,X2)
=> equalish(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmtery) ).
fof(assumption,axiom,
( reflexive_rewrite(a,b)
& reflexive_rewrite(a,c) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption) ).
fof(equalish_in_reflexive_rewrite,axiom,
! [X1,X2] :
( equalish(X1,X2)
=> reflexive_rewrite(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equalish_in_reflexive_rewrite) ).
fof(reflexivity,axiom,
! [X1] : equalish(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
fof(substitution,axiom,
! [X1,X2,X3] :
( ( equalish(X1,X2)
& reflexive_rewrite(X2,X3) )
=> reflexive_rewrite(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution) ).
fof(c_0_10,plain,
! [X33,X34] :
( ~ reflexive_rewrite(X33,X34)
| equalish(X33,X34)
| rewrite(X33,X34) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equalish_or_rewrite])]) ).
fof(c_0_11,plain,
! [X22] :
( ~ reflexive_rewrite(b,X22)
| ~ reflexive_rewrite(c,X22)
| goal ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[goal_ax])]) ).
fof(c_0_12,negated_conjecture,
~ goal,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goal_to_be_proved])]) ).
fof(c_0_13,plain,
! [X31,X32] :
( ~ rewrite(X31,X32)
| reflexive_rewrite(X31,X32) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rewrite_in_reflexive_rewrite])]) ).
fof(c_0_14,plain,
! [X35,X36,X37] :
( ( rewrite(X36,esk1_3(X35,X36,X37))
| ~ rewrite(X35,X36)
| ~ rewrite(X35,X37) )
& ( rewrite(X37,esk1_3(X35,X36,X37))
| ~ rewrite(X35,X36)
| ~ rewrite(X35,X37) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rewrite_diamond])])])]) ).
fof(c_0_15,plain,
! [X24,X25] :
( ~ equalish(X24,X25)
| equalish(X25,X24) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmtery])]) ).
cnf(c_0_16,plain,
( equalish(X1,X2)
| rewrite(X1,X2)
| ~ reflexive_rewrite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
reflexive_rewrite(a,c),
inference(split_conjunct,[status(thm)],[assumption]) ).
cnf(c_0_18,plain,
reflexive_rewrite(a,b),
inference(split_conjunct,[status(thm)],[assumption]) ).
fof(c_0_19,plain,
! [X29,X30] :
( ~ equalish(X29,X30)
| reflexive_rewrite(X29,X30) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equalish_in_reflexive_rewrite])]) ).
fof(c_0_20,plain,
! [X23] : equalish(X23,X23),
inference(variable_rename,[status(thm)],[reflexivity]) ).
cnf(c_0_21,plain,
( goal
| ~ reflexive_rewrite(b,X1)
| ~ reflexive_rewrite(c,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,negated_conjecture,
~ goal,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,plain,
( reflexive_rewrite(X1,X2)
| ~ rewrite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,plain,
( rewrite(X1,esk1_3(X2,X3,X1))
| ~ rewrite(X2,X3)
| ~ rewrite(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_25,plain,
! [X26,X27,X28] :
( ~ equalish(X26,X27)
| ~ reflexive_rewrite(X27,X28)
| reflexive_rewrite(X26,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution])]) ).
cnf(c_0_26,plain,
( equalish(X2,X1)
| ~ equalish(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_27,plain,
( rewrite(a,c)
| equalish(a,c) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_28,plain,
( rewrite(a,b)
| equalish(a,b) ),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_29,plain,
( reflexive_rewrite(X1,X2)
| ~ equalish(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,plain,
equalish(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,plain,
( ~ reflexive_rewrite(b,X1)
| ~ reflexive_rewrite(c,X1) ),
inference(sr,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_32,plain,
( reflexive_rewrite(X1,esk1_3(X2,X3,X1))
| ~ rewrite(X2,X3)
| ~ rewrite(X2,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_33,plain,
( rewrite(X1,esk1_3(X2,X1,X3))
| ~ rewrite(X2,X1)
| ~ rewrite(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_34,plain,
( reflexive_rewrite(X1,X3)
| ~ equalish(X1,X2)
| ~ reflexive_rewrite(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,plain,
( rewrite(a,c)
| equalish(c,a) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_36,plain,
( rewrite(a,b)
| equalish(b,a) ),
inference(spm,[status(thm)],[c_0_26,c_0_28]) ).
cnf(c_0_37,plain,
reflexive_rewrite(X1,X1),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_38,plain,
( ~ rewrite(X1,c)
| ~ rewrite(X1,X2)
| ~ reflexive_rewrite(b,esk1_3(X1,X2,c)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,plain,
( reflexive_rewrite(X1,esk1_3(X2,X1,X3))
| ~ rewrite(X2,X3)
| ~ rewrite(X2,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_33]) ).
cnf(c_0_40,plain,
( rewrite(a,c)
| reflexive_rewrite(c,X1)
| ~ reflexive_rewrite(a,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
( rewrite(a,b)
| reflexive_rewrite(b,X1)
| ~ reflexive_rewrite(a,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_36]) ).
cnf(c_0_42,plain,
~ reflexive_rewrite(b,c),
inference(spm,[status(thm)],[c_0_31,c_0_37]) ).
cnf(c_0_43,plain,
( ~ rewrite(X1,c)
| ~ rewrite(X1,b) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
( rewrite(a,c)
| reflexive_rewrite(c,b) ),
inference(spm,[status(thm)],[c_0_40,c_0_18]) ).
cnf(c_0_45,plain,
rewrite(a,b),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_17]),c_0_42]) ).
cnf(c_0_46,plain,
reflexive_rewrite(c,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_47,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_46]),c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM007+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.14/0.31 % Computer : n009.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.31 % WCLimit : 300
% 0.14/0.31 % DateTime : Mon May 4 16:19:11 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.26/1.70 % Version : CSE_E---1.7
% 1.26/1.70 % Problem : theBenchmark.p
% 1.26/1.70 % SZS status Theorem for theBenchmark.p
% 1.26/1.70 % SZS output start CNFRefutation
% See solution above
% 1.26/1.70 % Total time : 1.368s
%------------------------------------------------------------------------------