%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV372+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 03:13:06 PM UTC 2026
% Result : Theorem 89.62s 13.41s
% Output : Proof 89.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 15 unt; 0 def)
% Number of atoms : 129 ( 29 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 108 ( 40 ~; 50 |; 9 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 129 ( 25 sgn 85 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f45,axiom,
! [U,V] : findmin_cpq_eff(triple(U,create_slb,V)) = triple(U,create_slb,bad),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
fof(f45_nnf,plain,
! [U,V] : findmin_cpq_eff(triple(U,create_slb,V)) = triple(U,create_slb,bad),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
! [U,V] : findmin_cpq_eff(triple(U,create_slb,V)) = triple(U,create_slb,bad),
inference(skolemisation,[status(esa)],[f45_nnf]) ).
cnf(c60,plain,
findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
fof(f63,lemma,
! [U,V,W] :
( ~ contains_cpq(triple(U,V,W),findmin_cpq_res(triple(U,V,W)))
=> ~ ok(findmin_cpq_eff(triple(U,V,W))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l8_l9) ).
fof(f63_nnf,plain,
! [U,V,W] :
( ~ ok(findmin_cpq_eff(triple(U,V,W)))
| contains_cpq(triple(U,V,W),findmin_cpq_res(triple(U,V,W))) ),
inference(nnf_transformation,[status(thm)],[f63]) ).
fof(f63_sk,plain,
! [U,V,W] :
( ~ ok(findmin_cpq_eff(triple(U,V,W)))
| contains_cpq(triple(U,V,W),findmin_cpq_res(triple(U,V,W))) ),
inference(skolemisation,[status(esa)],[f63_nnf]) ).
cnf(c90,plain,
( ~ ok(findmin_cpq_eff(triple(X0,X1,X2)))
| contains_cpq(triple(X0,X1,X2),findmin_cpq_res(triple(X0,X1,X2))) ),
inference(cnf_transformation,[status(esa)],[f63_sk]) ).
cnf(p1414,plain,
( ~ ok(triple(X0,create_slb,bad))
| contains_cpq(triple(X0,create_slb,X1),bottom) ),
inference(superposition,[status(thm)],[c60,c90]) ).
fof(f46,axiom,
! [U,V,W,X] :
( ( ~ contains_slb(V,findmin_pqp_res(U))
& V != create_slb )
=> findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47) ).
fof(f46_nnf,plain,
! [U,V,W,X] :
( findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad)
| contains_slb(V,findmin_pqp_res(U))
| V = create_slb ),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
! [V,U,W] :
( findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad)
| contains_slb(V,findmin_pqp_res(U))
| V = create_slb ),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c61,plain,
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| contains_slb(X1,findmin_pqp_res(X0))
| X1 = create_slb ),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
fof(f65,conjecture,
! [U,V,W] :
( phi(findmin_cpq_eff(triple(U,V,W)))
=> contains_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l8_co) ).
fof(f65_neg,negated_conjecture,
~ ! [U,V,W] :
( phi(findmin_cpq_eff(triple(U,V,W)))
=> contains_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))) ),
inference(negated_conjecture,[status(cth)],[f65]) ).
fof(f65_nnf,plain,
? [U,V,W] :
( ~ contains_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W)))
& phi(findmin_cpq_eff(triple(U,V,W))) ),
inference(nnf_transformation,[status(thm)],[f65_neg]) ).
fof(f65_sk,plain,
( ~ contains_pq(i(triple(sk4,sk5,sk6)),findmin_cpq_res(triple(sk4,sk5,sk6)))
& phi(findmin_cpq_eff(triple(sk4,sk5,sk6))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6])],[f65_nnf]) ).
cnf(c92,plain,
phi(findmin_cpq_eff(triple(sk4,sk5,sk6))),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
cnf(p747,plain,
( phi(triple(sk4,update_slb(sk5,findmin_pqp_res(sk4)),bad))
| contains_slb(sk5,findmin_pqp_res(sk4))
| sk5 = create_slb ),
inference(superposition,[status(thm)],[c61,c92]) ).
fof(f64,lemma,
! [U,V,W] :
( ~ ok(triple(U,V,W))
=> ~ phi(triple(U,V,W)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l8_lX) ).
fof(f64_nnf,plain,
! [U,V,W] :
( ~ phi(triple(U,V,W))
| ok(triple(U,V,W)) ),
inference(nnf_transformation,[status(thm)],[f64]) ).
fof(f64_sk,plain,
! [U,V,W] :
( ~ phi(triple(U,V,W))
| ok(triple(U,V,W)) ),
inference(skolemisation,[status(esa)],[f64_nnf]) ).
cnf(c91,plain,
( ~ phi(triple(X0,X1,X2))
| ok(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(p1815,plain,
( ok(triple(sk4,update_slb(sk5,findmin_pqp_res(sk4)),bad))
| contains_slb(sk5,findmin_pqp_res(sk4))
| sk5 = create_slb ),
inference(resolution,[status(thm)],[p747,c91]) ).
fof(f39,axiom,
! [U,V] :
( ok(triple(U,V,bad))
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).
fof(f39_nnf,plain,
! [U,V] :
( ( ~ $false
| ok(triple(U,V,bad)) )
& ( $false
| ~ ok(triple(U,V,bad)) ) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [U,V] :
( ( ~ $false
| ok(triple(U,V,bad)) )
& ( $false
| ~ ok(triple(U,V,bad)) ) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c53,plain,
( $false
| ~ ok(triple(X0,X1,bad)) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(p1869,plain,
( $false
| contains_slb(sk5,findmin_pqp_res(sk4))
| sk5 = create_slb ),
inference(resolution,[status(thm)],[p1815,c53]) ).
fof(f38,axiom,
! [U,V,W,X] :
( contains_cpq(triple(U,V,W),X)
<=> contains_slb(V,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
fof(f38_nnf,plain,
! [U,V,W,X] :
( ( ~ contains_slb(V,X)
| contains_cpq(triple(U,V,W),X) )
& ( contains_slb(V,X)
| ~ contains_cpq(triple(U,V,W),X) ) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [U,V,W,X] :
( ( ~ contains_slb(V,X)
| contains_cpq(triple(U,V,W),X) )
& ( contains_slb(V,X)
| ~ contains_cpq(triple(U,V,W),X) ) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c52,plain,
( ~ contains_slb(X1,X3)
| contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(p1874,plain,
( contains_cpq(triple(X0,sk5,X1),findmin_pqp_res(sk4))
| $false
| sk5 = create_slb ),
inference(resolution,[status(thm)],[p1869,c52]) ).
fof(f62,lemma,
! [U,V,W,X] :
( contains_cpq(triple(U,V,W),X)
<=> contains_pq(i(triple(U,V,W)),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l8_li56) ).
fof(f62_nnf,plain,
! [U,V,W,X] :
( ( ~ contains_pq(i(triple(U,V,W)),X)
| contains_cpq(triple(U,V,W),X) )
& ( contains_pq(i(triple(U,V,W)),X)
| ~ contains_cpq(triple(U,V,W),X) ) ),
inference(nnf_transformation,[status(thm)],[f62]) ).
fof(f62_sk,plain,
! [U,V,W,X] :
( ( ~ contains_pq(i(triple(U,V,W)),X)
| contains_cpq(triple(U,V,W),X) )
& ( contains_pq(i(triple(U,V,W)),X)
| ~ contains_cpq(triple(U,V,W),X) ) ),
inference(skolemisation,[status(esa)],[f62_nnf]) ).
cnf(c88,plain,
( contains_pq(i(triple(X0,X1,X2)),X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[status(esa)],[f62_sk]) ).
cnf(p1879,plain,
( contains_pq(i(triple(X0,sk5,X1)),findmin_pqp_res(sk4))
| $false
| sk5 = create_slb ),
inference(resolution,[status(thm)],[p1874,c88]) ).
fof(f50,axiom,
! [U,V,W,X] :
( V != create_slb
=> findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
fof(f50_nnf,plain,
! [U,V,W,X] :
( findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U)
| V = create_slb ),
inference(nnf_transformation,[status(thm)],[f50]) ).
fof(f50_sk,plain,
! [V,U,W] :
( findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U)
| V = create_slb ),
inference(skolemisation,[status(esa)],[f50_nnf]) ).
cnf(c65,plain,
( findmin_cpq_res(triple(X0,X1,X2)) = findmin_pqp_res(X0)
| X1 = create_slb ),
inference(cnf_transformation,[status(esa)],[f50_sk]) ).
cnf(c93,plain,
~ contains_pq(i(triple(sk4,sk5,sk6)),findmin_cpq_res(triple(sk4,sk5,sk6))),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
cnf(p1099,plain,
( ~ contains_pq(i(triple(sk4,sk5,sk6)),findmin_pqp_res(sk4))
| sk5 = create_slb ),
inference(superposition,[status(thm)],[c65,c93]) ).
cnf(p1896,plain,
( sk5 = create_slb
| $false
| sk5 = create_slb ),
inference(resolution,[status(thm)],[p1879,p1099]) ).
cnf(p1899,plain,
( $false
| sk5 = create_slb ),
inference(factoring,[status(thm)],[p1896]) ).
cnf(p1901,plain,
( phi(triple(sk4,create_slb,bad))
| $false ),
inference(superposition,[status(thm)],[p1899,c92]) ).
cnf(p2422,plain,
( ok(triple(sk4,create_slb,bad))
| $false ),
inference(resolution,[status(thm)],[p1901,c91]) ).
cnf(p2432,plain,
( $false
| $false ),
inference(resolution,[status(thm)],[p2422,c53]) ).
cnf(p2433,plain,
$false,
inference(factoring,[status(thm)],[p2432]) ).
cnf(c54,plain,
( ~ $false
| ok(triple(X0,X1,bad)) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(p2437,plain,
ok(triple(X0,X1,bad)),
inference(resolution,[status(thm)],[p2433,c54]) ).
cnf(p11469,plain,
contains_cpq(triple(X0,create_slb,X1),bottom),
inference(resolution,[status(thm)],[p1414,p2437]) ).
cnf(c51,plain,
( contains_slb(X1,X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(p11470,plain,
contains_slb(create_slb,bottom),
inference(resolution,[status(thm)],[p11469,c51]) ).
fof(f19,axiom,
! [U] : ~ contains_slb(create_slb,U),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
fof(f19_nnf,plain,
! [U] : ~ contains_slb(create_slb,U),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [U] : ~ contains_slb(create_slb,U),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c25,plain,
~ contains_slb(create_slb,X0),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p11472,plain,
$false,
inference(resolution,[status(thm)],[p11470,c25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV372+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 19:23:29 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 89.62/13.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 89.62/13.41 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------