%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COM007+2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:03:28 PM UTC 2026
% Result : Theorem 9.74s 1.92s
% Output : Proof 9.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 10 unt; 0 def)
% Number of atoms : 132 ( 34 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 117 ( 38 ~; 66 |; 8 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 50 ( 0 sgn 30 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B] :
( reflexive_rewrite(A,B)
=> ( rewrite(A,B)
| A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_or_rewrite) ).
fof(f4_nnf,plain,
! [A,B] :
( rewrite(A,B)
| A = B
| ~ reflexive_rewrite(A,B) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( rewrite(A,B)
| A = B
| ~ reflexive_rewrite(A,B) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c5,plain,
( rewrite(X0,X1)
| X0 = X1
| ~ reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f0,axiom,
( reflexive_rewrite(a,c)
& reflexive_rewrite(a,b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption) ).
fof(f0_nnf,plain,
( reflexive_rewrite(a,c)
& reflexive_rewrite(a,b) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
( reflexive_rewrite(a,c)
& reflexive_rewrite(a,b) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
reflexive_rewrite(a,b),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p11,plain,
( rewrite(a,b)
| a = b ),
inference(resolution,[status(thm)],[c5,c0]) ).
fof(f5,axiom,
! [A,B,C] :
( ( rewrite(A,C)
& rewrite(A,B) )
=> ? [D] :
( rewrite(C,D)
& rewrite(B,D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_diamond) ).
fof(f5_nnf,plain,
! [A,B,C] :
( ? [D] :
( rewrite(C,D)
& rewrite(B,D) )
| ~ rewrite(A,C)
| ~ rewrite(A,B) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C] :
( ( rewrite(C,sk0(A,B,C))
& rewrite(B,sk0(A,B,C)) )
| ~ rewrite(A,C)
| ~ rewrite(A,B) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f5_nnf]) ).
cnf(c6,plain,
( rewrite(X1,sk0(X0,X1,X2))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p14,plain,
( rewrite(b,sk0(a,b,X0))
| ~ rewrite(a,X0)
| a = b ),
inference(resolution,[status(thm)],[p11,c6]) ).
cnf(c1,plain,
reflexive_rewrite(a,c),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p12,plain,
( rewrite(a,c)
| a = c ),
inference(resolution,[status(thm)],[c5,c1]) ).
cnf(p29,plain,
( a = c
| rewrite(b,sk0(a,b,c))
| a = b ),
inference(resolution,[status(thm)],[p14,p12]) ).
fof(f3,axiom,
! [A,B] :
( rewrite(A,B)
=> reflexive_rewrite(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_in_reflexive_rewrite) ).
fof(f3_nnf,plain,
! [A,B] :
( reflexive_rewrite(A,B)
| ~ rewrite(A,B) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( reflexive_rewrite(A,B)
| ~ rewrite(A,B) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c4,plain,
( reflexive_rewrite(X0,X1)
| ~ rewrite(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p35,plain,
( reflexive_rewrite(b,sk0(a,b,c))
| a = c
| a = b ),
inference(resolution,[status(thm)],[p29,c4]) ).
fof(f1,axiom,
! [A] :
( ( reflexive_rewrite(c,A)
& reflexive_rewrite(b,A) )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_ax) ).
fof(f1_nnf,plain,
! [A] :
( goal
| ~ reflexive_rewrite(c,A)
| ~ reflexive_rewrite(b,A) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A] :
( goal
| ~ reflexive_rewrite(c,A)
| ~ reflexive_rewrite(b,A) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c2,plain,
( goal
| ~ reflexive_rewrite(c,X0)
| ~ reflexive_rewrite(b,X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p65,plain,
( goal
| ~ reflexive_rewrite(c,sk0(a,b,c))
| a = c
| a = b ),
inference(resolution,[status(thm)],[p35,c2]) ).
cnf(c7,plain,
( rewrite(X2,sk0(X0,X1,X2))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p21,plain,
( a = b
| rewrite(X0,sk0(a,b,X0))
| ~ rewrite(a,X0) ),
inference(resolution,[status(thm)],[c7,p11]) ).
cnf(p31,plain,
( a = c
| a = b
| rewrite(c,sk0(a,b,c)) ),
inference(resolution,[status(thm)],[p21,p12]) ).
cnf(p48,plain,
( reflexive_rewrite(c,sk0(a,b,c))
| a = c
| a = b ),
inference(resolution,[status(thm)],[p31,c4]) ).
cnf(p85,plain,
( a = c
| a = b
| goal
| a = c
| a = b ),
inference(resolution,[status(thm)],[p65,p48]) ).
cnf(p100,plain,
( a = c
| goal
| a = c
| a = b ),
inference(factoring,[status(thm)],[p85]) ).
cnf(p102,plain,
( goal
| a = c
| a = b ),
inference(factoring,[status(thm)],[p100]) ).
fof(f2,axiom,
! [A,B] :
( A = B
=> reflexive_rewrite(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_in_reflexive_rewrite) ).
fof(f2_nnf,plain,
! [A,B] :
( reflexive_rewrite(A,B)
| A != B ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( reflexive_rewrite(A,B)
| A != B ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c3,plain,
( reflexive_rewrite(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p9,plain,
reflexive_rewrite(X0,X0),
inference(equality_resolution,[status(thm)],[c3]) ).
cnf(p10,plain,
( goal
| ~ reflexive_rewrite(c,b) ),
inference(resolution,[status(thm)],[p9,c2]) ).
cnf(p105,plain,
( goal
| ~ reflexive_rewrite(a,b)
| goal
| a = b ),
inference(superposition,[status(thm)],[p102,p10]) ).
cnf(p120,plain,
( ~ reflexive_rewrite(a,b)
| goal
| a = b ),
inference(factoring,[status(thm)],[p105]) ).
cnf(p121,plain,
( goal
| a = b ),
inference(resolution,[status(thm)],[p120,c0]) ).
cnf(p123,plain,
( goal
| ~ reflexive_rewrite(c,X0)
| ~ reflexive_rewrite(a,X0)
| goal ),
inference(superposition,[status(thm)],[p121,c2]) ).
cnf(p135,plain,
( ~ reflexive_rewrite(c,X0)
| ~ reflexive_rewrite(a,X0)
| goal ),
inference(factoring,[status(thm)],[p123]) ).
cnf(p140,plain,
( ~ reflexive_rewrite(c,c)
| goal ),
inference(resolution,[status(thm)],[p135,c1]) ).
cnf(p141,plain,
goal,
inference(resolution,[status(thm)],[p140,p9]) ).
fof(f6,conjecture,
goal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_to_be_proved) ).
fof(f6_neg,negated_conjecture,
~ goal,
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
~ goal,
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
~ goal,
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c8,plain,
~ goal,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p142,plain,
$false,
inference(resolution,[status(thm)],[p141,c8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM007+2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n013.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 07:44:23 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.74/1.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.74/1.92 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------