%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET791+4 : 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 : n003.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 08:36:58 AM UTC 2026
% Result : Theorem 6.61s 1.37s
% Output : CNFRefutation 6.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 9 unt; 0 def)
% Number of atoms : 134 ( 19 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 152 ( 54 ~; 58 |; 28 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 79 ( 1 sgn 46 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(order,axiom,
! [R,E] :
( order(R,E)
<=> ( ! [X,Y,Z] :
( ( member(Z,E)
& member(Y,E)
& member(X,E) )
=> ( ( apply(R,Y,Z)
& apply(R,X,Y) )
=> apply(R,X,Z) ) )
& ! [X,Y] :
( ( member(Y,E)
& member(X,E) )
=> ( ( apply(R,Y,X)
& apply(R,X,Y) )
=> X = Y ) )
& ! [X] :
( member(X,E)
=> apply(R,X,X) ) ) ),
file('theBenchmark.p',order) ).
fof(greatest,axiom,
! [R,E,M] :
( greatest(M,R,E)
<=> ( ! [X] :
( member(X,E)
=> apply(R,X,M) )
& member(M,E) ) ),
file('theBenchmark.p',greatest) ).
fof(max,axiom,
! [R,E,M] :
( max(M,R,E)
<=> ( ! [X] :
( ( apply(R,M,X)
& member(X,E) )
=> M = X )
& member(M,E) ) ),
file('theBenchmark.p',max) ).
fof(thIV3,conjecture,
! [R,E,M] :
( ( greatest(M,R,E)
& order(R,E) )
=> max(M,R,E) ),
file('theBenchmark.p',thIV3) ).
fof(thIV3_neg,negated_conjecture,
~ ! [R,E,M] :
( ( greatest(M,R,E)
& order(R,E) )
=> max(M,R,E) ),
inference(assume_negation,[status(cth)],[thIV3]) ).
cnf(c_14,plain,
( D = C
| ~ apply(A,D,C)
| ~ apply(A,C,D)
| ~ member(D,B)
| ~ member(C,B)
| ~ order(A,B) ),
inference(clausify,[status(thm)],[order]) ).
fof(nnf_11,plain,
? [R,E,M] :
( ~ max(M,R,E)
& greatest(M,R,E)
& order(R,E) ),
inference(fof_nnf,[status(thm)],[thIV3_neg]) ).
fof(sk_thIV3_neg,plain,
( ~ max(sK2,sK0,sK1)
& greatest(sK2,sK0,sK1)
& order(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(R,sK0),skolemize(E,sK1),skolemize(M,sK2)],[nnf_11]) ).
cnf(c_80,negated_conjecture,
order(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thIV3_neg]) ).
cnf(c_329,plain,
( apply(B,D,A)
| ~ member(D,C)
| ~ greatest(A,B,C) ),
inference(clausify,[status(thm)],[greatest]) ).
cnf(c_330,plain,
( member(A,C)
| ~ greatest(A,B,C) ),
inference(clausify,[status(thm)],[greatest]) ).
cnf(c_332,negated_conjecture,
greatest(sK2,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thIV3_neg]) ).
cnf(c_368,negated_conjecture,
member(sK2,sK1),
inference(resolve,[status(thm)],[c_332,c_330]) ).
cnf(c_369,negated_conjecture,
( apply(sK0,A,sK2)
| ~ member(A,sK1) ),
inference(resolve,[status(thm)],[c_332,c_329]) ).
cnf(c_373,negated_conjecture,
( B = A
| ~ apply(sK0,B,A)
| ~ apply(sK0,A,B)
| ~ member(B,sK1)
| ~ member(A,sK1) ),
inference(resolve,[status(thm)],[c_80,c_14]) ).
cnf(c_555,negated_conjecture,
~ max(sK2,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thIV3_neg]) ).
fof(nnf_7,plain,
! [R,E,M] :
( ( ? [X] :
( M != X
& apply(R,M,X)
& member(X,E) )
| ~ member(M,E)
| max(M,R,E) )
& ( ( ! [X7] :
( M = X7
| ~ apply(R,M,X7)
| ~ member(X7,E) )
& member(M,E) )
| ~ max(M,R,E) ) ),
inference(fof_nnf,[status(thm)],[max]) ).
fof(sk_max_sk,plain,
! [R,E,M] :
( ( ( M != sK3(R,E,M)
& apply(R,M,sK3(R,E,M))
& member(sK3(R,E,M),E) )
| ~ member(M,E)
| max(M,R,E) )
& ( ( ! [X7] :
( M = X7
| ~ apply(R,M,X7)
| ~ member(X7,E) )
& member(M,E) )
| ~ max(M,R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X,sK3(R,E,M))],[nnf_7]) ).
fof(sk_max,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( VAR_0 != sK3(VAR_1,VAR_2,VAR_0)
| ~ member(VAR_0,VAR_2)
| max(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( apply(VAR_1,VAR_0,sK3(VAR_1,VAR_2,VAR_0))
| ~ member(VAR_0,VAR_2)
| max(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(sK3(VAR_1,VAR_2,VAR_0),VAR_2)
| ~ member(VAR_0,VAR_2)
| max(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_0 = VAR_3
| ~ apply(VAR_1,VAR_0,VAR_3)
| ~ member(VAR_3,VAR_2)
| ~ max(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_2)
| ~ max(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_max_sk]) ).
cnf(c_556,plain,
( A != sK3(B,C,A)
| ~ member(A,C)
| max(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_max]) ).
cnf(c_557,plain,
( sK3(B,C,A) != A
| ~ member(A,C)
| max(A,B,C) ),
inference(copy,[status(thm)],[c_556]) ).
cnf(c_558,plain,
( apply(B,A,sK3(B,C,A))
| ~ member(A,C)
| max(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_max]) ).
cnf(c_559,plain,
( member(sK3(B,C,A),C)
| ~ member(A,C)
| max(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_max]) ).
cnf(c_1083,plain,
( sK3(A,sK1,sK2) != sK2
| max(sK2,A,sK1) ),
inference(resolve,[status(thm)],[c_557,c_368]) ).
cnf(c_1084,plain,
( apply(A,sK2,sK3(A,sK1,sK2))
| max(sK2,A,sK1) ),
inference(resolve,[status(thm)],[c_558,c_368]) ).
cnf(c_1085,plain,
( member(sK3(A,sK1,sK2),sK1)
| max(sK2,A,sK1) ),
inference(resolve,[status(thm)],[c_559,c_368]) ).
cnf(c_1166,plain,
member(sK3(sK0,sK1,sK2),sK1),
inference(resolve,[status(thm)],[c_1085,c_555]) ).
cnf(c_1225,plain,
apply(sK0,sK3(sK0,sK1,sK2),sK2),
inference(resolve,[status(thm)],[c_1166,c_369]) ).
cnf(c_1308,negated_conjecture,
( sK2 = sK3(sK0,sK1,sK2)
| ~ apply(sK0,sK3(sK0,sK1,sK2),sK2)
| ~ member(sK2,sK1)
| ~ member(sK3(sK0,sK1,sK2),sK1)
| max(sK2,sK0,sK1) ),
inference(resolve,[status(thm)],[c_1084,c_373]) ).
cnf(c_1309,negated_conjecture,
( sK3(sK0,sK1,sK2) = sK2
| ~ apply(sK0,sK3(sK0,sK1,sK2),sK2)
| ~ member(sK2,sK1)
| ~ member(sK3(sK0,sK1,sK2),sK1)
| max(sK2,sK0,sK1) ),
inference(copy,[status(thm)],[c_1308]) ).
cnf(c_1310,negated_conjecture,
( sK3(sK0,sK1,sK2) = sK2
| ~ apply(sK0,sK3(sK0,sK1,sK2),sK2)
| ~ member(sK2,sK1)
| ~ member(sK3(sK0,sK1,sK2),sK1) ),
inference(resolve,[status(thm)],[c_555,c_1309]) ).
cnf(c_1311,negated_conjecture,
( sK3(sK0,sK1,sK2) = sK2
| ~ apply(sK0,sK3(sK0,sK1,sK2),sK2)
| ~ member(sK2,sK1) ),
inference(resolve,[status(thm)],[c_1166,c_1310]) ).
cnf(c_1312,negated_conjecture,
( sK3(sK0,sK1,sK2) = sK2
| ~ apply(sK0,sK3(sK0,sK1,sK2),sK2) ),
inference(resolve,[status(thm)],[c_368,c_1311]) ).
cnf(c_1306,negated_conjecture,
sK3(sK0,sK1,sK2) = sK2,
inference(resolve,[status(thm)],[c_1225,c_1312]) ).
cnf(c_1313,plain,
max(sK2,sK0,sK1),
inference(resolve,[status(thm)],[c_1306,c_1083]) ).
cnf(c_1307,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_555,c_1313]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET791+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 08:18:08 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2419046 was started by sandbox2 on n003,
% 0.11/0.37 % Sat Sep 26 08:18:08 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 6.61/1.37
% 6.61/1.37 % given #500 (I,wt=47): 861 member(f1(A,B),B) | apply(A,f3(A,B),f2(A,B)) | member(f5(A,B),B) | -member(f3(A,B),B) | -member(C,B) | -member(f2(A,B),B) | -apply(A,f3(A,B),C) | -apply(A,C,f2(A,B)). [factor(497,b,i)].
% 6.61/1.37
% 6.61/1.37 % SZS status Theorem for theBenchmark
% 6.61/1.37
% 6.61/1.37 % Proof 1 at 0.82 (+ 0.09) seconds.
% 6.61/1.37 % Length of proof is 24.
% 6.61/1.37 % Level of proof is 7.
% 6.61/1.37 % Maximum clause weight is 19.000.
% 6.61/1.37 % Given clauses 673.
% 6.61/1.37
% 6.61/1.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------