%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET804+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 02:43:59 PM UTC 2026
% Result : Theorem 0.13s 10.98s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 24 unt; 0 def)
% Number of atoms : 100 ( 30 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 98 ( 36 ~; 25 |; 29 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 69 ( 4 sgn 32 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [R,E,M] :
( min(M,R,E)
<=> ( ! [X] :
( ( apply(R,X,M)
& member(X,E) )
=> M = X )
& member(M,E) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',min) ).
fof(f7_nnf,plain,
! [R,E,M] :
( ( ? [X] :
( M != X
& apply(R,X,M)
& member(X,E) )
| ~ member(M,E)
| min(M,R,E) )
& ( ( ! [X] :
( M = X
| ~ apply(R,X,M)
| ~ member(X,E) )
& member(M,E) )
| ~ min(M,R,E) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [M,R,E,X] :
( ( ( M != sk13(R,E,M)
& apply(R,sk13(R,E,M),M)
& member(sk13(R,E,M),E) )
| ~ member(M,E)
| min(M,R,E) )
& ( ( ( M = X
| ~ apply(R,X,M)
| ~ member(X,E) )
& member(M,E) )
| ~ min(M,R,E) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13])],[f7_nnf]) ).
cnf(c88,plain,
( member(X2,X1)
| ~ min(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi88,axiom,
ifeq(min(X0,X1,X2),true,member(X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c88]) ).
fof(f10,conjecture,
! [R,E] :
( order(R,E)
=> ! [M1,M2] :
( ( M1 != M2
& min(M2,R,E)
& min(M1,R,E) )
=> ~ ? [M] : least(M,R,E) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV16) ).
fof(f10_neg,negated_conjecture,
~ ! [R,E] :
( order(R,E)
=> ! [M1,M2] :
( ( M1 != M2
& min(M2,R,E)
& min(M1,R,E) )
=> ~ ? [M] : least(M,R,E) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f10_nnf,plain,
? [R,E] :
( ? [M1,M2] :
( ? [M] : least(M,R,E)
& M1 != M2
& min(M2,R,E)
& min(M1,R,E) )
& order(R,E) ),
inference(nnf_transformation,[status(thm)],[f10_neg]) ).
fof(f10_sk,plain,
( least(sk20,sk16,sk17)
& sk18 != sk19
& min(sk19,sk16,sk17)
& min(sk18,sk16,sk17)
& order(sk16,sk17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16,sk17,sk18,sk19,sk20])],[f10_nnf]) ).
cnf(c107,plain,
min(sk19,sk16,sk17),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi107,negated_conjecture,
min(sk19,sk16,sk17) = true,
inference(equality_encoding,[status(esa)],[c107]) ).
cnf(h10,plain,
member(sk19,sk17) = true,
inference(hyper_resolution,[status(thm)],[hi88,hi107]) ).
fof(f5,axiom,
! [R,E,M] :
( least(M,R,E)
<=> ( ! [X] :
( member(X,E)
=> apply(R,M,X) )
& member(M,E) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',least) ).
fof(f5_nnf,plain,
! [R,E,M] :
( ( ? [X] :
( ~ apply(R,M,X)
& member(X,E) )
| ~ member(M,E)
| least(M,R,E) )
& ( ( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
& member(M,E) )
| ~ least(M,R,E) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [M,R,E,X] :
( ( ( ~ apply(R,M,sk11(R,E,M))
& member(sk11(R,E,M),E) )
| ~ member(M,E)
| least(M,R,E) )
& ( ( ( apply(R,M,X)
| ~ member(X,E) )
& member(M,E) )
| ~ least(M,R,E) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f5_nnf]) ).
cnf(c80,plain,
( apply(X0,X2,X3)
| ~ member(X3,X1)
| ~ least(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi80,axiom,
ifeq(least(X0,X1,X2),true,ifeq(member(X3,X2),true,apply(X1,X0,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c80]) ).
cnf(c109,plain,
least(sk20,sk16,sk17),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi108,negated_conjecture,
least(sk20,sk16,sk17) = true,
inference(equality_encoding,[status(esa)],[c109]) ).
cnf(h18,plain,
apply(sk16,sk20,sk19) = true,
inference(hyper_resolution,[status(thm)],[hi80,hi108,h10]) ).
cnf(c79,plain,
( member(X2,X1)
| ~ least(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi79,axiom,
ifeq(least(X0,X1,X2),true,member(X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c79]) ).
cnf(h20,plain,
member(sk20,sk17) = true,
inference(hyper_resolution,[status(thm)],[hi79,hi108]) ).
cnf(c89,plain,
( X2 = X3
| ~ apply(X0,X3,X2)
| ~ member(X3,X1)
| ~ min(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi89,axiom,
ifeq(min(X0,X1,X2),true,ifeq(member(X3,X2),true,ifeq(apply(X1,X3,X0),true,X0,X3),X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c89]) ).
cnf(t1,plain,
sk20 = sk19,
inference(hyper_resolution,[status(thm)],[hi89,hi107,h20,h18]) ).
cnf(t521,plain,
sk19 = sk20,
inference(orient,[status(thm)],[t1]) ).
cnf(c106,plain,
min(sk18,sk16,sk17),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi106,negated_conjecture,
min(sk18,sk16,sk17) = true,
inference(equality_encoding,[status(esa)],[c106]) ).
cnf(h2,plain,
member(sk18,sk17) = true,
inference(hyper_resolution,[status(thm)],[hi88,hi106]) ).
cnf(h19,plain,
apply(sk16,sk20,sk18) = true,
inference(hyper_resolution,[status(thm)],[hi80,hi108,h2]) ).
cnf(t0,plain,
sk20 = sk18,
inference(hyper_resolution,[status(thm)],[hi89,hi106,h20,h19]) ).
cnf(t519,plain,
sk18 = sk20,
inference(orient,[status(thm)],[t0]) ).
cnf(c108,plain,
sk18 != sk19,
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(goal_0,negated_conjecture,
sk19 != sk18,
inference(equality_encoding,[status(esa)],[c108]) ).
cnf(g0_0,plain,
sk20 != sk18,
inference(rw,[status(thm)],[goal_0,t521]) ).
cnf(g0_1,plain,
sk20 != sk20,
inference(rw,[status(thm)],[g0_0,t519]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET804+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/10.38 % Computer : n013.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Thu Sep 24 11:59:49 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/10.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/10.98 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------