%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV373+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 : n012.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 54.62s 8.19s
% Output : Proof 54.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 8 unt; 0 def)
% Number of atoms : 54 ( 16 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 53 ( 25 ~; 13 |; 10 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 56 ( 10 sgn 38 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f41,lemma,
! [U,V,W] :
( ok(findmin_cpq_eff(triple(U,V,W)))
=> ( less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U))
& contains_slb(V,findmin_pqp_res(U))
& V != create_slb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l9_l10) ).
fof(f41_nnf,plain,
! [U,V,W] :
( ( less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U))
& contains_slb(V,findmin_pqp_res(U))
& V != create_slb )
| ~ ok(findmin_cpq_eff(triple(U,V,W))) ),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
! [U,V,W] :
( ( less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U))
& contains_slb(V,findmin_pqp_res(U))
& V != create_slb )
| ~ ok(findmin_cpq_eff(triple(U,V,W))) ),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c53,plain,
( contains_slb(X1,findmin_pqp_res(X0))
| ~ ok(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
fof(f42,conjecture,
! [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',l9_co) ).
fof(f42_neg,negated_conjecture,
~ ! [U,V,W] :
( ~ contains_cpq(triple(U,V,W),findmin_cpq_res(triple(U,V,W)))
=> ~ ok(findmin_cpq_eff(triple(U,V,W))) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f42_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)],[f42_neg]) ).
fof(f42_sk,plain,
( ok(findmin_cpq_eff(triple(sk0,sk1,sk2)))
& ~ contains_cpq(triple(sk0,sk1,sk2),findmin_cpq_res(triple(sk0,sk1,sk2))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f42_nnf]) ).
cnf(c56,plain,
ok(findmin_cpq_eff(triple(sk0,sk1,sk2))),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(p692,plain,
contains_slb(sk1,findmin_pqp_res(sk0)),
inference(resolution,[status(thm)],[c53,c56]) ).
fof(f26,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(f26_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)],[f26]) ).
fof(f26_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)],[f26_nnf]) ).
cnf(c36,plain,
( ~ contains_slb(X1,X3)
| contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p699,plain,
contains_cpq(triple(X0,sk1,X1),findmin_pqp_res(sk0)),
inference(resolution,[status(thm)],[p692,c36]) ).
fof(f38,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(f38_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)],[f38]) ).
fof(f38_sk,plain,
! [V,U,W] :
( findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U)
| V = create_slb ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c49,plain,
( findmin_cpq_res(triple(X0,X1,X2)) = findmin_pqp_res(X0)
| X1 = create_slb ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(c55,plain,
~ contains_cpq(triple(sk0,sk1,sk2),findmin_cpq_res(triple(sk0,sk1,sk2))),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(p670,plain,
( ~ contains_cpq(triple(sk0,sk1,sk2),findmin_pqp_res(sk0))
| sk1 = create_slb ),
inference(superposition,[status(thm)],[c49,c55]) ).
cnf(p706,plain,
sk1 = create_slb,
inference(resolution,[status(thm)],[p699,p670]) ).
cnf(c52,plain,
( X1 != create_slb
| ~ ok(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(p685,plain,
sk1 != create_slb,
inference(resolution,[status(thm)],[c52,c56]) ).
cnf(p709,plain,
create_slb != create_slb,
inference(demodulation,[status(thm)],[p706,p685]) ).
cnf(p720,plain,
$false,
inference(equality_resolution,[status(thm)],[p709]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV373+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Thu Sep 24 19:24:53 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 54.62/8.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 54.62/8.19 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------