%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COM129+1 : TPTP v9.2.1. Released v6.4.0.
% 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 : n021.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 04:13:17 PM UTC 2026
% Result : Theorem 1.86s 1.91s
% Output : CNFRefutation 1.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 3 unt; 0 def)
% Number of atoms : 62 ( 25 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 77 ( 36 ~; 29 |; 5 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 7 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(isFreeVar2,axiom,
! [X1,X4,X12,X14,X13] :
( ( X1 = X14
& X4 = vapp(X12,X13) )
=> ( ( ( visFreeVar(X14,X12)
| visFreeVar(X14,X13) )
=> visFreeVar(X1,X4) )
& ( visFreeVar(X1,X4)
=> ( visFreeVar(X14,X12)
| visFreeVar(X14,X13) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',isFreeVar2) ).
fof('gensym-is-fresh',axiom,
! [X14,X11] :
( vgensym(X11) = X14
=> ~ visFreeVar(X14,X11) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','gensym-is-fresh') ).
fof('fresh-free-2',conjecture,
! [X11,X9,X24,X12] :
( X24 = vgensym(vapp(vapp(X11,X12),vvar(X9)))
=> ~ visFreeVar(X24,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','fresh-free-2') ).
fof(c_0_3,plain,
! [X434,X435,X436,X437,X438] :
( ( ~ visFreeVar(X437,X436)
| visFreeVar(X434,X435)
| X434 != X437
| X435 != vapp(X436,X438) )
& ( ~ visFreeVar(X437,X438)
| visFreeVar(X434,X435)
| X434 != X437
| X435 != vapp(X436,X438) )
& ( ~ visFreeVar(X434,X435)
| visFreeVar(X437,X436)
| visFreeVar(X437,X438)
| X434 != X437
| X435 != vapp(X436,X438) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[isFreeVar2])])]) ).
fof(c_0_4,plain,
! [X14,X11] :
( vgensym(X11) = X14
=> ~ visFreeVar(X14,X11) ),
inference(fof_simplification,[status(thm)],['gensym-is-fresh']) ).
cnf(c_0_5,plain,
( visFreeVar(X3,X4)
| ~ visFreeVar(X1,X2)
| X3 != X1
| X4 != vapp(X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_6,plain,
! [X501,X502] :
( vgensym(X502) != X501
| ~ visFreeVar(X501,X502) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).
cnf(c_0_7,plain,
( visFreeVar(X1,X2)
| X2 != vapp(X3,X4)
| ~ visFreeVar(X1,X3) ),
inference(er,[status(thm)],[c_0_5]) ).
fof(c_0_8,negated_conjecture,
~ ! [X11,X9,X24,X12] :
( X24 = vgensym(vapp(vapp(X11,X12),vvar(X9)))
=> ~ visFreeVar(X24,X12) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['fresh-free-2'])]) ).
cnf(c_0_9,plain,
( vgensym(X1) != X2
| ~ visFreeVar(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( visFreeVar(X1,vapp(X2,X3))
| ~ visFreeVar(X1,X2) ),
inference(er,[status(thm)],[c_0_7]) ).
fof(c_0_11,negated_conjecture,
( esk34_0 = vgensym(vapp(vapp(esk32_0,esk35_0),vvar(esk33_0)))
& visFreeVar(esk34_0,esk35_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_12,plain,
( visFreeVar(X3,X4)
| ~ visFreeVar(X1,X2)
| X3 != X1
| X4 != vapp(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_13,plain,
( vgensym(vapp(X1,X2)) != X3
| ~ visFreeVar(X3,X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
esk34_0 = vgensym(vapp(vapp(esk32_0,esk35_0),vvar(esk33_0))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( visFreeVar(X1,X2)
| X2 != vapp(X3,X4)
| ~ visFreeVar(X1,X4) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( esk34_0 != X1
| ~ visFreeVar(X1,vapp(esk32_0,esk35_0)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( visFreeVar(X1,vapp(X2,X3))
| ~ visFreeVar(X1,X3) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( esk34_0 != X1
| ~ visFreeVar(X1,esk35_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,negated_conjecture,
visFreeVar(esk34_0,esk35_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_18,c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COM129+1 : TPTP v9.2.1. Released v6.4.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n021.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 16:23:10 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.86/1.91 % Version : CSE_E---1.7
% 1.86/1.91 % Problem : theBenchmark.p
% 1.86/1.91 % SZS status Theorem for theBenchmark.p
% 1.86/1.91 % SZS output start CNFRefutation
% See solution above
% 1.86/1.91 % Total time : 1.423s
%------------------------------------------------------------------------------