%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET793+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 : n005.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 9.61s 1.68s
% Output : CNFRefutation 9.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 38 ( 11 unt; 0 def)
% Number of atoms : 112 ( 6 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 115 ( 41 ~; 46 |; 20 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 67 ( 1 sgn 39 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(total_order,axiom,
! [R,E] :
( total_order(R,E)
<=> ( ! [X,Y] :
( ( member(Y,E)
& member(X,E) )
=> ( apply(R,Y,X)
| apply(R,X,Y) ) )
& order(R,E) ) ),
file('theBenchmark.p',total_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(thIV5,conjecture,
! [R,E,M] :
( ( max(M,R,E)
& total_order(R,E) )
=> greatest(M,R,E) ),
file('theBenchmark.p',thIV5) ).
fof(thIV5_neg,negated_conjecture,
~ ! [R,E,M] :
( ( max(M,R,E)
& total_order(R,E) )
=> greatest(M,R,E) ),
inference(assume_negation,[status(cth)],[thIV5]) ).
fof(nnf_11,plain,
? [R,E,M] :
( ~ greatest(M,R,E)
& max(M,R,E)
& total_order(R,E) ),
inference(fof_nnf,[status(thm)],[thIV5_neg]) ).
fof(sk_thIV5_neg,plain,
( ~ greatest(sK2,sK0,sK1)
& max(sK2,sK0,sK1)
& total_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_322,negated_conjecture,
total_order(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thIV5_neg]) ).
cnf(c_323,plain,
( apply(A,D,C)
| apply(A,C,D)
| ~ member(D,B)
| ~ member(C,B)
| ~ total_order(A,B) ),
inference(clausify,[status(thm)],[total_order]) ).
cnf(c_328,plain,
( A = D
| ~ apply(B,A,D)
| ~ member(D,C)
| ~ max(A,B,C) ),
inference(clausify,[status(thm)],[max]) ).
cnf(c_332,negated_conjecture,
max(sK2,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thIV5_neg]) ).
cnf(c_333,plain,
( member(A,C)
| ~ max(A,B,C) ),
inference(clausify,[status(thm)],[max]) ).
cnf(c_547,negated_conjecture,
~ greatest(sK2,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thIV5_neg]) ).
fof(nnf_5,plain,
! [R,E,M] :
( ( ? [X] :
( ~ apply(R,X,M)
& member(X,E) )
| ~ member(M,E)
| greatest(M,R,E) )
& ( ( ! [X0] :
( apply(R,X0,M)
| ~ member(X0,E) )
& member(M,E) )
| ~ greatest(M,R,E) ) ),
inference(fof_nnf,[status(thm)],[greatest]) ).
fof(sk_greatest_sk,plain,
! [R,E,M] :
( ( ( ~ apply(R,sK3(R,E,M),M)
& member(sK3(R,E,M),E) )
| ~ member(M,E)
| greatest(M,R,E) )
& ( ( ! [X0] :
( apply(R,X0,M)
| ~ member(X0,E) )
& member(M,E) )
| ~ greatest(M,R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X,sK3(R,E,M))],[nnf_5]) ).
fof(sk_greatest,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ apply(VAR_1,sK3(VAR_1,VAR_2,VAR_0),VAR_0)
| ~ member(VAR_0,VAR_2)
| greatest(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)
| greatest(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( apply(VAR_1,VAR_3,VAR_0)
| ~ member(VAR_3,VAR_2)
| ~ greatest(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_2)
| ~ greatest(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_greatest_sk]) ).
cnf(c_548,plain,
( ~ apply(B,sK3(B,C,A),A)
| ~ member(A,C)
| greatest(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_greatest]) ).
cnf(c_549,plain,
( member(sK3(B,C,A),C)
| ~ member(A,C)
| greatest(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_greatest]) ).
cnf(c_554,negated_conjecture,
( apply(sK0,B,A)
| apply(sK0,A,B)
| ~ member(B,sK1)
| ~ member(A,sK1) ),
inference(resolve,[status(thm)],[c_323,c_322]) ).
cnf(c_799,negated_conjecture,
( sK2 = A
| ~ apply(sK0,sK2,A)
| ~ member(A,sK1) ),
inference(resolve,[status(thm)],[c_328,c_332]) ).
cnf(c_800,negated_conjecture,
member(sK2,sK1),
inference(resolve,[status(thm)],[c_333,c_332]) ).
cnf(c_5575,plain,
( apply(sK0,A,A)
| apply(sK0,A,A)
| ~ member(A,sK1) ),
inference(factor,[status(thm)],[c_554]) ).
cnf(c_878,plain,
( apply(sK0,A,A)
| ~ member(A,sK1) ),
inference(copy,[status(thm)],[c_5575]) ).
cnf(c_1057,plain,
( apply(sK0,sK2,A)
| apply(sK0,A,sK2)
| ~ member(A,sK1) ),
inference(resolve,[status(thm)],[c_800,c_554]) ).
cnf(c_1058,plain,
( member(sK3(A,sK1,sK2),sK1)
| greatest(sK2,A,sK1) ),
inference(resolve,[status(thm)],[c_800,c_549]) ).
cnf(c_1091,plain,
member(sK3(sK0,sK1,sK2),sK1),
inference(resolve,[status(thm)],[c_1058,c_547]) ).
cnf(c_1179,plain,
( apply(sK0,sK2,sK3(sK0,sK1,sK2))
| apply(sK0,sK3(sK0,sK1,sK2),sK2) ),
inference(resolve,[status(thm)],[c_1091,c_1057]) ).
cnf(c_1183,plain,
apply(sK0,sK3(sK0,sK1,sK2),sK3(sK0,sK1,sK2)),
inference(resolve,[status(thm)],[c_1091,c_878]) ).
cnf(c_5576,plain,
( ~ member(sK2,sK1)
| greatest(sK2,sK0,sK1)
| apply(sK0,sK2,sK3(sK0,sK1,sK2)) ),
inference(resolve,[status(thm)],[c_1179,c_548]) ).
cnf(c_5577,negated_conjecture,
( ~ member(sK2,sK1)
| apply(sK0,sK2,sK3(sK0,sK1,sK2)) ),
inference(resolve,[status(thm)],[c_547,c_5576]) ).
cnf(c_5273,negated_conjecture,
apply(sK0,sK2,sK3(sK0,sK1,sK2)),
inference(resolve,[status(thm)],[c_800,c_5577]) ).
cnf(c_5578,negated_conjecture,
( sK2 = sK3(sK0,sK1,sK2)
| ~ member(sK3(sK0,sK1,sK2),sK1) ),
inference(resolve,[status(thm)],[c_5273,c_799]) ).
cnf(c_5579,negated_conjecture,
( sK3(sK0,sK1,sK2) = sK2
| ~ member(sK3(sK0,sK1,sK2),sK1) ),
inference(copy,[status(thm)],[c_5578]) ).
cnf(c_5397,negated_conjecture,
sK3(sK0,sK1,sK2) = sK2,
inference(resolve,[status(thm)],[c_1091,c_5579]) ).
cnf(c_5571,plain,
apply(sK0,sK3(sK0,sK1,sK2),sK2),
inference(paramod,[status(thm)],[c_5397,c_1183]) ).
cnf(c_5580,plain,
( ~ member(sK2,sK1)
| greatest(sK2,sK0,sK1) ),
inference(resolve,[status(thm)],[c_5571,c_548]) ).
cnf(c_5581,negated_conjecture,
~ member(sK2,sK1),
inference(resolve,[status(thm)],[c_547,c_5580]) ).
cnf(c_5574,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_800,c_5581]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET793+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:16:01 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 1671837 was started by sandbox2 on n005,
% 0.08/0.35 % Sat Sep 26 08:16:01 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 9.61/1.68
% 9.61/1.68 % given #500 (I,wt=56): 858 member(f1(A,B),B) | apply(A,f2(A,B),f3(A,B)) | -apply(A,f4(A,B),f6(A,B)) | -member(f4(A,B),B) | -member(f6(A,B),B) | -member(C,B) | -apply(A,f6(A,B),C) | apply(A,f4(A,B),C). [factor(495,c,g)].
% 9.61/1.68
% 9.61/1.68 % SZS status Theorem for theBenchmark
% 9.61/1.68
% 9.61/1.68 % Proof 1 at 1.13 (+ 0.15) seconds.
% 9.61/1.68 % Length of proof is 25.
% 9.61/1.68 % Level of proof is 9.
% 9.61/1.68 % Maximum clause weight is 24.000.
% 9.61/1.68 % Given clauses 697.
% 9.61/1.68
% 9.61/1.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------