%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COM008+2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 : Sun Sep 27 06:59:37 AM UTC 2026
% Result : Theorem 175.04s 23.84s
% Output : CNFRefutation 175.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 72 ( 28 unt; 0 def)
% Number of atoms : 167 ( 17 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 168 ( 73 ~; 71 |; 18 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 94 ( 0 sgn 46 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(found,axiom,
! [A] :
( ( transitive_reflexive_rewrite(c,A)
& transitive_reflexive_rewrite(b,A) )
=> goal ),
file('theBenchmark.p',found) ).
fof(assumption,axiom,
( transitive_reflexive_rewrite(a,c)
& transitive_reflexive_rewrite(a,b) ),
file('theBenchmark.p',assumption) ).
fof(equality_in_transitive_reflexive_rewrite,axiom,
! [A,B] :
( A = B
=> transitive_reflexive_rewrite(A,B) ),
file('theBenchmark.p',equality_in_transitive_reflexive_rewrite) ).
fof(transitivity_of_transitive_reflexive_rewrite,axiom,
! [A,B,C] :
( ( transitive_reflexive_rewrite(B,C)
& transitive_reflexive_rewrite(A,B) )
=> transitive_reflexive_rewrite(A,C) ),
file('theBenchmark.p',transitivity_of_transitive_reflexive_rewrite) ).
fof(lo_cfl,axiom,
! [A,B,C] :
( ( rewrite(A,C)
& rewrite(A,B) )
=> ? [D] :
( transitive_reflexive_rewrite(C,D)
& transitive_reflexive_rewrite(B,D) ) ),
file('theBenchmark.p',lo_cfl) ).
fof(ih_cfl,axiom,
! [A,B,C] :
( ( transitive_reflexive_rewrite(A,C)
& transitive_reflexive_rewrite(A,B)
& rewrite(a,A) )
=> ? [D] :
( transitive_reflexive_rewrite(C,D)
& transitive_reflexive_rewrite(B,D) ) ),
file('theBenchmark.p',ih_cfl) ).
fof(equal_or_rewrite,axiom,
! [A,B] :
( transitive_reflexive_rewrite(A,B)
=> ( ? [C] :
( transitive_reflexive_rewrite(C,B)
& rewrite(A,C) )
| A = B ) ),
file('theBenchmark.p',equal_or_rewrite) ).
fof(goal_to_be_proved,conjecture,
goal,
file('theBenchmark.p',goal_to_be_proved) ).
fof(goal_to_be_proved_neg,negated_conjecture,
~ goal,
inference(assume_negation,[status(cth)],[goal_to_be_proved]) ).
cnf(c_10,plain,
( goal
| ~ transitive_reflexive_rewrite(c,A)
| ~ transitive_reflexive_rewrite(b,A) ),
inference(clausify,[status(thm)],[found]) ).
cnf(c_11,plain,
transitive_reflexive_rewrite(a,b),
inference(clausify,[status(thm)],[assumption]) ).
cnf(c_12,plain,
transitive_reflexive_rewrite(a,c),
inference(clausify,[status(thm)],[assumption]) ).
cnf(c_13,plain,
( transitive_reflexive_rewrite(B,A)
| A != B ),
inference(clausify,[status(thm)],[equality_in_transitive_reflexive_rewrite]) ).
cnf(c_15,plain,
( transitive_reflexive_rewrite(A,C)
| ~ transitive_reflexive_rewrite(B,C)
| ~ transitive_reflexive_rewrite(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_transitive_reflexive_rewrite]) ).
fof(nnf_6,plain,
! [A,B,C] :
( ? [D] :
( transitive_reflexive_rewrite(C,D)
& transitive_reflexive_rewrite(B,D) )
| ~ rewrite(A,C)
| ~ rewrite(A,B) ),
inference(fof_nnf,[status(thm)],[lo_cfl]) ).
fof(sk_lo_cfl_sk,plain,
! [A,B,C] :
( ( transitive_reflexive_rewrite(C,sK0(A,B,C))
& transitive_reflexive_rewrite(B,sK0(A,B,C)) )
| ~ rewrite(A,C)
| ~ rewrite(A,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(D,sK0(A,B,C))],[nnf_6]) ).
fof(sk_lo_cfl,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( transitive_reflexive_rewrite(VAR_2,sK0(VAR_0,VAR_1,VAR_2))
| ~ rewrite(VAR_0,VAR_2)
| ~ rewrite(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( transitive_reflexive_rewrite(VAR_1,sK0(VAR_0,VAR_1,VAR_2))
| ~ rewrite(VAR_0,VAR_2)
| ~ rewrite(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_lo_cfl_sk]) ).
cnf(c_16,plain,
( transitive_reflexive_rewrite(B,sK0(A,B,C))
| ~ rewrite(A,C)
| ~ rewrite(A,B) ),
inference(split_conjunct,[status(thm)],[sk_lo_cfl]) ).
cnf(c_17,plain,
( transitive_reflexive_rewrite(C,sK0(A,B,C))
| ~ rewrite(A,C)
| ~ rewrite(A,B) ),
inference(split_conjunct,[status(thm)],[sk_lo_cfl]) ).
fof(nnf_7,plain,
! [A,B,C] :
( ? [D] :
( transitive_reflexive_rewrite(C,D)
& transitive_reflexive_rewrite(B,D) )
| ~ transitive_reflexive_rewrite(A,C)
| ~ transitive_reflexive_rewrite(A,B)
| ~ rewrite(a,A) ),
inference(fof_nnf,[status(thm)],[ih_cfl]) ).
fof(sk_ih_cfl_sk,plain,
! [A,B,C] :
( ( transitive_reflexive_rewrite(C,sK1(A,B,C))
& transitive_reflexive_rewrite(B,sK1(A,B,C)) )
| ~ transitive_reflexive_rewrite(A,C)
| ~ transitive_reflexive_rewrite(A,B)
| ~ rewrite(a,A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(D,sK1(A,B,C))],[nnf_7]) ).
fof(sk_ih_cfl,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( transitive_reflexive_rewrite(VAR_2,sK1(VAR_0,VAR_1,VAR_2))
| ~ transitive_reflexive_rewrite(VAR_0,VAR_2)
| ~ transitive_reflexive_rewrite(VAR_0,VAR_1)
| ~ rewrite(a,VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( transitive_reflexive_rewrite(VAR_1,sK1(VAR_0,VAR_1,VAR_2))
| ~ transitive_reflexive_rewrite(VAR_0,VAR_2)
| ~ transitive_reflexive_rewrite(VAR_0,VAR_1)
| ~ rewrite(a,VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_ih_cfl_sk]) ).
cnf(c_18,plain,
( transitive_reflexive_rewrite(B,sK1(A,B,C))
| ~ transitive_reflexive_rewrite(A,C)
| ~ transitive_reflexive_rewrite(A,B)
| ~ rewrite(a,A) ),
inference(split_conjunct,[status(thm)],[sk_ih_cfl]) ).
cnf(c_19,plain,
( transitive_reflexive_rewrite(C,sK1(A,B,C))
| ~ transitive_reflexive_rewrite(A,C)
| ~ transitive_reflexive_rewrite(A,B)
| ~ rewrite(a,A) ),
inference(split_conjunct,[status(thm)],[sk_ih_cfl]) ).
fof(nnf_8,plain,
! [A,B] :
( ? [C] :
( transitive_reflexive_rewrite(C,B)
& rewrite(A,C) )
| B = A
| ~ transitive_reflexive_rewrite(A,B) ),
inference(fof_nnf,[status(thm)],[equal_or_rewrite]) ).
fof(sk_equal_or_rewrite_sk,plain,
! [A,B] :
( ( transitive_reflexive_rewrite(sK2(A,B),B)
& rewrite(A,sK2(A,B)) )
| B = A
| ~ transitive_reflexive_rewrite(A,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(C,sK2(A,B))],[nnf_8]) ).
fof(sk_equal_or_rewrite,plain,
( ! [VAR_0,VAR_1] :
( transitive_reflexive_rewrite(sK2(VAR_0,VAR_1),VAR_1)
| VAR_1 = VAR_0
| ~ transitive_reflexive_rewrite(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( rewrite(VAR_0,sK2(VAR_0,VAR_1))
| VAR_1 = VAR_0
| ~ transitive_reflexive_rewrite(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_equal_or_rewrite_sk]) ).
cnf(c_20,plain,
( rewrite(A,sK2(A,B))
| B = A
| ~ transitive_reflexive_rewrite(A,B) ),
inference(split_conjunct,[status(thm)],[sk_equal_or_rewrite]) ).
cnf(c_21,plain,
( transitive_reflexive_rewrite(sK2(A,B),B)
| B = A
| ~ transitive_reflexive_rewrite(A,B) ),
inference(split_conjunct,[status(thm)],[sk_equal_or_rewrite]) ).
cnf(c_22,negated_conjecture,
~ goal,
inference(clausify,[status(thm)],[goal_to_be_proved_neg]) ).
cnf(c_25,negated_conjecture,
( ~ transitive_reflexive_rewrite(c,A)
| ~ transitive_reflexive_rewrite(b,A) ),
inference(resolve,[status(thm)],[c_22,c_10]) ).
cnf(c_26,plain,
transitive_reflexive_rewrite(A,A),
inference(xxres,[status(thm)],[c_13]) ).
cnf(c_31,plain,
( rewrite(a,sK2(a,c))
| c = a ),
inference(resolve,[status(thm)],[c_20,c_12]) ).
cnf(c_32,plain,
( rewrite(a,sK2(a,b))
| b = a ),
inference(resolve,[status(thm)],[c_20,c_11]) ).
cnf(c_33,plain,
( transitive_reflexive_rewrite(sK2(a,c),c)
| c = a ),
inference(resolve,[status(thm)],[c_21,c_12]) ).
cnf(c_34,plain,
( transitive_reflexive_rewrite(sK2(a,b),b)
| b = a ),
inference(resolve,[status(thm)],[c_21,c_11]) ).
cnf(c_35,plain,
~ transitive_reflexive_rewrite(b,c),
inference(resolve,[status(thm)],[c_26,c_25]) ).
cnf(c_36,plain,
~ transitive_reflexive_rewrite(c,b),
inference(resolve,[status(thm)],[c_25,c_26]) ).
cnf(c_25503,plain,
( transitive_reflexive_rewrite(A,c)
| ~ transitive_reflexive_rewrite(A,a) ),
inference(resolve,[status(thm)],[c_15,c_12]) ).
cnf(c_37,plain,
~ transitive_reflexive_rewrite(b,a),
inference(resolve,[status(thm)],[c_25503,c_35]) ).
cnf(c_25504,plain,
( transitive_reflexive_rewrite(A,b)
| ~ transitive_reflexive_rewrite(A,a) ),
inference(resolve,[status(thm)],[c_15,c_11]) ).
cnf(c_40,plain,
~ transitive_reflexive_rewrite(c,a),
inference(resolve,[status(thm)],[c_25504,c_36]) ).
cnf(c_25505,plain,
a != b,
inference(resolve,[status(thm)],[c_13,c_37]) ).
cnf(c_43,plain,
b != a,
inference(copy,[status(thm)],[c_25505]) ).
cnf(c_44,plain,
transitive_reflexive_rewrite(sK2(a,b),b),
inference(resolve,[status(thm)],[c_43,c_34]) ).
cnf(c_45,plain,
rewrite(a,sK2(a,b)),
inference(resolve,[status(thm)],[c_43,c_32]) ).
cnf(c_53,plain,
( transitive_reflexive_rewrite(B,sK1(sK2(a,b),A,B))
| ~ transitive_reflexive_rewrite(sK2(a,b),B)
| ~ transitive_reflexive_rewrite(sK2(a,b),A) ),
inference(resolve,[status(thm)],[c_45,c_19]) ).
cnf(c_54,plain,
( transitive_reflexive_rewrite(A,sK1(sK2(a,b),A,B))
| ~ transitive_reflexive_rewrite(sK2(a,b),B)
| ~ transitive_reflexive_rewrite(sK2(a,b),A) ),
inference(resolve,[status(thm)],[c_45,c_18]) ).
cnf(c_56,plain,
( transitive_reflexive_rewrite(A,sK0(a,sK2(a,b),A))
| ~ rewrite(a,A) ),
inference(resolve,[status(thm)],[c_45,c_17]) ).
cnf(c_25506,plain,
a != c,
inference(resolve,[status(thm)],[c_13,c_40]) ).
cnf(c_65,plain,
c != a,
inference(copy,[status(thm)],[c_25506]) ).
cnf(c_66,plain,
transitive_reflexive_rewrite(sK2(a,c),c),
inference(resolve,[status(thm)],[c_65,c_33]) ).
cnf(c_67,plain,
rewrite(a,sK2(a,c)),
inference(resolve,[status(thm)],[c_65,c_31]) ).
cnf(c_75,plain,
( transitive_reflexive_rewrite(B,sK1(sK2(a,c),A,B))
| ~ transitive_reflexive_rewrite(sK2(a,c),B)
| ~ transitive_reflexive_rewrite(sK2(a,c),A) ),
inference(resolve,[status(thm)],[c_67,c_19]) ).
cnf(c_76,plain,
( transitive_reflexive_rewrite(A,sK1(sK2(a,c),A,B))
| ~ transitive_reflexive_rewrite(sK2(a,c),B)
| ~ transitive_reflexive_rewrite(sK2(a,c),A) ),
inference(resolve,[status(thm)],[c_67,c_18]) ).
cnf(c_79,plain,
( transitive_reflexive_rewrite(A,sK0(a,A,sK2(a,c)))
| ~ rewrite(a,A) ),
inference(resolve,[status(thm)],[c_67,c_16]) ).
cnf(c_100,plain,
transitive_reflexive_rewrite(sK2(a,c),sK0(a,sK2(a,b),sK2(a,c))),
inference(resolve,[status(thm)],[c_56,c_67]) ).
cnf(c_103,plain,
transitive_reflexive_rewrite(sK2(a,b),sK0(a,sK2(a,b),sK2(a,c))),
inference(resolve,[status(thm)],[c_79,c_45]) ).
cnf(c_162,plain,
( transitive_reflexive_rewrite(A,sK1(sK2(a,b),b,A))
| ~ transitive_reflexive_rewrite(sK2(a,b),A) ),
inference(resolve,[status(thm)],[c_53,c_44]) ).
cnf(c_187,plain,
( transitive_reflexive_rewrite(b,sK1(sK2(a,b),b,A))
| ~ transitive_reflexive_rewrite(sK2(a,b),A) ),
inference(resolve,[status(thm)],[c_54,c_44]) ).
cnf(c_221,plain,
( transitive_reflexive_rewrite(sK2(a,c),A)
| ~ transitive_reflexive_rewrite(sK0(a,sK2(a,b),sK2(a,c)),A) ),
inference(resolve,[status(thm)],[c_100,c_15]) ).
cnf(c_335,plain,
( transitive_reflexive_rewrite(A,sK1(sK2(a,c),c,A))
| ~ transitive_reflexive_rewrite(sK2(a,c),A) ),
inference(resolve,[status(thm)],[c_75,c_66]) ).
cnf(c_360,plain,
( transitive_reflexive_rewrite(c,sK1(sK2(a,c),c,A))
| ~ transitive_reflexive_rewrite(sK2(a,c),A) ),
inference(resolve,[status(thm)],[c_76,c_66]) ).
cnf(c_384,plain,
transitive_reflexive_rewrite(sK0(a,sK2(a,b),sK2(a,c)),sK1(sK2(a,b),b,sK0(a,sK2(a,b),sK2(a,c)))),
inference(resolve,[status(thm)],[c_162,c_103]) ).
cnf(c_476,plain,
transitive_reflexive_rewrite(b,sK1(sK2(a,b),b,sK0(a,sK2(a,b),sK2(a,c)))),
inference(resolve,[status(thm)],[c_187,c_103]) ).
cnf(c_1208,plain,
( transitive_reflexive_rewrite(b,A)
| ~ transitive_reflexive_rewrite(sK1(sK2(a,b),b,sK0(a,sK2(a,b),sK2(a,c))),A) ),
inference(resolve,[status(thm)],[c_476,c_15]) ).
cnf(c_8915,plain,
transitive_reflexive_rewrite(sK2(a,c),sK1(sK2(a,b),b,sK0(a,sK2(a,b),sK2(a,c)))),
inference(resolve,[status(thm)],[c_384,c_221]) ).
cnf(c_10029,plain,
transitive_reflexive_rewrite(c,sK1(sK2(a,c),c,sK1(sK2(a,b),b,sK0(a,sK2(a,b),sK2(a,c))))),
inference(resolve,[status(thm)],[c_8915,c_360]) ).
cnf(c_10041,plain,
transitive_reflexive_rewrite(sK1(sK2(a,b),b,sK0(a,sK2(a,b),sK2(a,c))),sK1(sK2(a,c),c,sK1(sK2(a,b),b,sK0(a,sK2(a,b),sK2(a,c))))),
inference(resolve,[status(thm)],[c_8915,c_335]) ).
cnf(c_20914,plain,
~ transitive_reflexive_rewrite(b,sK1(sK2(a,c),c,sK1(sK2(a,b),b,sK0(a,sK2(a,b),sK2(a,c))))),
inference(resolve,[status(thm)],[c_10029,c_25]) ).
cnf(c_25507,plain,
~ transitive_reflexive_rewrite(sK1(sK2(a,b),b,sK0(a,sK2(a,b),sK2(a,c))),sK1(sK2(a,c),c,sK1(sK2(a,b),b,sK0(a,sK2(a,b),sK2(a,c))))),
inference(resolve,[status(thm)],[c_1208,c_20914]) ).
cnf(c_25502,plain,
$false,
inference(resolve,[status(thm)],[c_10041,c_25507]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM008+2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 23:20:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2480654 was started by sandbox2 on n019,
% 0.09/0.36 % Sat Sep 26 23:20:18 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 175.04/23.84
% 175.04/23.84 % given #500 (F,wt=15): 1329 -transitive_reflexive_rewrite(f2(f3(a,c),f1(a,f3(a,c),f3(a,b)),c),b). [ur(15,a,559,a,c,36,a)].
% 175.04/23.84
% 175.04/23.84 % given #1000 (A,wt=27): 252 -transitive_reflexive_rewrite(f3(a,b),A) | transitive_reflexive_rewrite(f1(a,f3(a,b),f3(a,c)),f2(f3(a,b),A,f1(a,f3(a,b),f3(a,c)))). [resolve(103,a,53,b)].
% 175.04/23.84
% 175.04/23.84 % given #1500 (T,wt=7): 9173 transitive_reflexive_rewrite(a,f3(f3(a,c),c)). [back_unit_del(884),unit_del(a,8967)].
% 175.04/23.84
% 175.04/23.84 % given #2000 (F,wt=15): 12378 -transitive_reflexive_rewrite(f2(f3(a,c),f2(f3(a,c),c,c),f3(a,c)),a). [ur(15,a,1031,a,c,286,a)].
% 175.04/23.84
% 175.04/23.84 % given #2500 (T,wt=17): 16397 transitive_reflexive_rewrite(a,f3(f3(a,b),f2(f3(a,b),f2(f3(a,b),b,b),b))). [resolve(16241,a,63,a)].
% 175.04/23.84
% 175.04/23.84 % given #3000 (F,wt=19): 17484 -rewrite(f2(f3(a,c),f2(f3(a,c),f3(f3(a,c),c),c),c),f3(a,b)). [ur(14,b,10094,a)].
% 175.04/23.84
% 175.04/23.84 % given #3500 (T,wt=20): 16335 -transitive_reflexive_rewrite(A,a) | transitive_reflexive_rewrite(A,f3(f3(a,b),f2(f3(a,b),b,f2(f3(a,b),b,b)))). [resolve(16330,a,15,b)].
% 175.04/23.84
% 175.04/23.84 % given #4000 (F,wt=20): 12683 -transitive_reflexive_rewrite(f2(f3(a,b),f1(a,f3(a,b),f3(a,f2(f3(a,b),b,b))),b),a). [ur(15,a,2386,a,c,37,a)].
% 175.04/23.84
% 175.04/23.84 % SZS status Theorem for theBenchmark
% 175.04/23.84
% 175.04/23.84 % Proof 1 at 21.53 (+ 1.06) seconds.
% 175.04/23.84 % Length of proof is 57.
% 175.04/23.84 % Level of proof is 13.
% 175.04/23.84 % Maximum clause weight is 32.000.
% 175.04/23.84 % Given clauses 4496.
% 175.04/23.84
% 175.04/23.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------