%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COM007+1 : 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 6.37s 1.38s
% Output : Proof 6.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 76 ( 14 unt; 0 def)
% Number of atoms : 187 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 157 ( 46 ~; 95 |; 9 &)
% ( 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 : 74 ( 0 sgn 48 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,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(f8_nnf,plain,
! [A,B,C] :
( ? [D] :
( rewrite(C,D)
& rewrite(B,D) )
| ~ rewrite(A,C)
| ~ rewrite(A,B) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_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])],[f8_nnf]) ).
cnf(c9,plain,
( rewrite(X1,sk0(X0,X1,X2))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f7,axiom,
! [A,B] :
( reflexive_rewrite(A,B)
=> ( rewrite(A,B)
| equalish(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equalish_or_rewrite) ).
fof(f7_nnf,plain,
! [A,B] :
( rewrite(A,B)
| equalish(A,B)
| ~ reflexive_rewrite(A,B) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B] :
( rewrite(A,B)
| equalish(A,B)
| ~ reflexive_rewrite(A,B) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c8,plain,
( rewrite(X0,X1)
| equalish(X0,X1)
| ~ reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_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(p14,plain,
( rewrite(a,b)
| equalish(a,b) ),
inference(resolution,[status(thm)],[c8,c0]) ).
cnf(p17,plain,
( equalish(a,b)
| rewrite(b,sk0(a,b,X0))
| ~ rewrite(a,X0) ),
inference(resolution,[status(thm)],[c9,p14]) ).
cnf(c1,plain,
reflexive_rewrite(a,c),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p15,plain,
( rewrite(a,c)
| equalish(a,c) ),
inference(resolution,[status(thm)],[c8,c1]) ).
cnf(p32,plain,
( equalish(a,c)
| equalish(a,b)
| rewrite(b,sk0(a,b,c)) ),
inference(resolution,[status(thm)],[p17,p15]) ).
fof(f6,axiom,
! [A,B] :
( rewrite(A,B)
=> reflexive_rewrite(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_in_reflexive_rewrite) ).
fof(f6_nnf,plain,
! [A,B] :
( reflexive_rewrite(A,B)
| ~ rewrite(A,B) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B] :
( reflexive_rewrite(A,B)
| ~ rewrite(A,B) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c7,plain,
( reflexive_rewrite(X0,X1)
| ~ rewrite(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p36,plain,
( reflexive_rewrite(b,sk0(a,b,c))
| equalish(a,c)
| equalish(a,b) ),
inference(resolution,[status(thm)],[p32,c7]) ).
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(p58,plain,
( goal
| ~ reflexive_rewrite(c,sk0(a,b,c))
| equalish(a,c)
| equalish(a,b) ),
inference(resolution,[status(thm)],[p36,c2]) ).
cnf(c10,plain,
( rewrite(X2,sk0(X0,X1,X2))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p28,plain,
( equalish(a,b)
| rewrite(X0,sk0(a,b,X0))
| ~ rewrite(a,X0) ),
inference(resolution,[status(thm)],[c10,p14]) ).
cnf(p34,plain,
( equalish(a,c)
| equalish(a,b)
| rewrite(c,sk0(a,b,c)) ),
inference(resolution,[status(thm)],[p28,p15]) ).
cnf(p49,plain,
( reflexive_rewrite(c,sk0(a,b,c))
| equalish(a,c)
| equalish(a,b) ),
inference(resolution,[status(thm)],[p34,c7]) ).
cnf(p62,plain,
( equalish(a,c)
| equalish(a,b)
| goal
| equalish(a,c)
| equalish(a,b) ),
inference(resolution,[status(thm)],[p58,p49]) ).
cnf(p71,plain,
( equalish(a,c)
| goal
| equalish(a,c)
| equalish(a,b) ),
inference(factoring,[status(thm)],[p62]) ).
cnf(p73,plain,
( goal
| equalish(a,c)
| equalish(a,b) ),
inference(factoring,[status(thm)],[p71]) ).
fof(f3,axiom,
! [A,B] :
( equalish(A,B)
=> equalish(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmtery) ).
fof(f3_nnf,plain,
! [A,B] :
( equalish(B,A)
| ~ equalish(A,B) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( equalish(B,A)
| ~ equalish(A,B) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c4,plain,
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p76,plain,
( equalish(c,a)
| goal
| equalish(a,b) ),
inference(resolution,[status(thm)],[p73,c4]) ).
fof(f5,axiom,
! [A,B] :
( equalish(A,B)
=> reflexive_rewrite(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equalish_in_reflexive_rewrite) ).
fof(f5_nnf,plain,
! [A,B] :
( reflexive_rewrite(A,B)
| ~ equalish(A,B) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B] :
( reflexive_rewrite(A,B)
| ~ equalish(A,B) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c6,plain,
( reflexive_rewrite(X0,X1)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p78,plain,
( reflexive_rewrite(c,a)
| goal
| equalish(a,b) ),
inference(resolution,[status(thm)],[p76,c6]) ).
cnf(p80,plain,
( equalish(b,a)
| reflexive_rewrite(c,a)
| goal ),
inference(resolution,[status(thm)],[p78,c4]) ).
fof(f4,axiom,
! [A,B,C] :
( ( reflexive_rewrite(B,C)
& equalish(A,B) )
=> reflexive_rewrite(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution) ).
fof(f4_nnf,plain,
! [A,B,C] :
( reflexive_rewrite(A,C)
| ~ reflexive_rewrite(B,C)
| ~ equalish(A,B) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] :
( reflexive_rewrite(A,C)
| ~ reflexive_rewrite(B,C)
| ~ equalish(A,B) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c5,plain,
( reflexive_rewrite(X0,X2)
| ~ reflexive_rewrite(X1,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p83,plain,
( reflexive_rewrite(b,X0)
| ~ reflexive_rewrite(a,X0)
| reflexive_rewrite(c,a)
| goal ),
inference(resolution,[status(thm)],[p80,c5]) ).
cnf(p119,plain,
( reflexive_rewrite(b,c)
| reflexive_rewrite(c,a)
| goal ),
inference(resolution,[status(thm)],[p83,c1]) ).
cnf(p79,plain,
( reflexive_rewrite(c,X0)
| ~ reflexive_rewrite(a,X0)
| goal
| equalish(a,b) ),
inference(resolution,[status(thm)],[p76,c5]) ).
cnf(p89,plain,
( reflexive_rewrite(c,b)
| goal
| equalish(a,b) ),
inference(resolution,[status(thm)],[p79,c0]) ).
cnf(p90,plain,
( equalish(b,a)
| reflexive_rewrite(c,b)
| goal ),
inference(resolution,[status(thm)],[p89,c4]) ).
cnf(p94,plain,
( reflexive_rewrite(b,a)
| reflexive_rewrite(c,b)
| goal ),
inference(resolution,[status(thm)],[p90,c6]) ).
fof(f2,axiom,
! [A] : equalish(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
fof(f2_nnf,plain,
! [A] : equalish(A,A),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A] : equalish(A,A),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c3,plain,
equalish(X0,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p12,plain,
reflexive_rewrite(X0,X0),
inference(resolution,[status(thm)],[c6,c3]) ).
cnf(p13,plain,
( goal
| ~ reflexive_rewrite(c,b) ),
inference(resolution,[status(thm)],[p12,c2]) ).
cnf(p96,plain,
( goal
| reflexive_rewrite(b,a)
| goal ),
inference(resolution,[status(thm)],[p94,p13]) ).
cnf(p98,plain,
( reflexive_rewrite(b,a)
| goal ),
inference(factoring,[status(thm)],[p96]) ).
cnf(p99,plain,
( goal
| ~ reflexive_rewrite(c,a)
| goal ),
inference(resolution,[status(thm)],[p98,c2]) ).
cnf(p102,plain,
( ~ reflexive_rewrite(c,a)
| goal ),
inference(factoring,[status(thm)],[p99]) ).
cnf(p121,plain,
( goal
| reflexive_rewrite(b,c)
| goal ),
inference(resolution,[status(thm)],[p119,p102]) ).
cnf(p126,plain,
( reflexive_rewrite(b,c)
| goal ),
inference(factoring,[status(thm)],[p121]) ).
cnf(p127,plain,
( goal
| ~ reflexive_rewrite(c,c)
| goal ),
inference(resolution,[status(thm)],[p126,c2]) ).
cnf(p129,plain,
( ~ reflexive_rewrite(c,c)
| goal ),
inference(factoring,[status(thm)],[p127]) ).
cnf(p130,plain,
goal,
inference(resolution,[status(thm)],[p129,p12]) ).
fof(f9,conjecture,
goal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_to_be_proved) ).
fof(f9_neg,negated_conjecture,
~ goal,
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f9_nnf,plain,
~ goal,
inference(nnf_transformation,[status(thm)],[f9_neg]) ).
fof(f9_sk,plain,
~ goal,
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c11,plain,
~ goal,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p133,plain,
$false,
inference(resolution,[status(thm)],[p130,c11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM007+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 07:44:06 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.37/1.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.37/1.38 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------