%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV390+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 : n014.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 03:13:08 PM UTC 2026
% Result : Theorem 110.23s 16.52s
% Output : Proof 110.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 70 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 67 ( 29 ~; 24 |; 8 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 100 ( 10 sgn 53 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f29,axiom,
! [U,V,W,X] : insert_cpq(triple(U,V,W),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
fof(f29_nnf,plain,
! [U,V,W,X] : insert_cpq(triple(U,V,W),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [U,V,W,X] : insert_cpq(triple(U,V,W),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c40,plain,
insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
fof(f41,lemma,
! [U,V,W] :
( check_cpq(triple(U,V,W))
<=> ! [X,Y] :
( pair_in_list(V,X,Y)
=> less_than(Y,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l26_li4142) ).
fof(f41_nnf,plain,
! [U,V,W] :
( ( ? [X,Y] :
( ~ less_than(Y,X)
& pair_in_list(V,X,Y) )
| check_cpq(triple(U,V,W)) )
& ( ! [X,Y] :
( less_than(Y,X)
| ~ pair_in_list(V,X,Y) )
| ~ check_cpq(triple(U,V,W)) ) ),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
! [U,V,W,X,Y] :
( ( ( ~ less_than(sk1(U,V,W),sk0(U,V,W))
& pair_in_list(V,sk0(U,V,W),sk1(U,V,W)) )
| check_cpq(triple(U,V,W)) )
& ( less_than(Y,X)
| ~ pair_in_list(V,X,Y)
| ~ check_cpq(triple(U,V,W)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f41_nnf]) ).
cnf(c52,plain,
( less_than(X4,X3)
| ~ pair_in_list(X1,X3,X4)
| ~ check_cpq(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(p712,plain,
( less_than(X5,X4)
| ~ pair_in_list(insert_slb(X1,pair(X3,bottom)),X4,X5)
| ~ check_cpq(insert_cpq(triple(X0,X1,X2),X3)) ),
inference(superposition,[status(thm)],[c40,c52]) ).
fof(f42,conjecture,
! [U,V,W] :
( ~ check_cpq(triple(U,V,W))
=> ! [X] : ~ check_cpq(insert_cpq(triple(U,V,W),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l26_co) ).
fof(f42_neg,negated_conjecture,
~ ! [U,V,W] :
( ~ check_cpq(triple(U,V,W))
=> ! [X] : ~ check_cpq(insert_cpq(triple(U,V,W),X)) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f42_nnf,plain,
? [U,V,W] :
( ? [X] : check_cpq(insert_cpq(triple(U,V,W),X))
& ~ check_cpq(triple(U,V,W)) ),
inference(nnf_transformation,[status(thm)],[f42_neg]) ).
fof(f42_sk,plain,
( check_cpq(insert_cpq(triple(sk2,sk3,sk4),sk5))
& ~ check_cpq(triple(sk2,sk3,sk4)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4,sk5])],[f42_nnf]) ).
cnf(c56,plain,
check_cpq(insert_cpq(triple(sk2,sk3,sk4),sk5)),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(p8562,plain,
( less_than(X1,X0)
| ~ pair_in_list(insert_slb(sk3,pair(sk5,bottom)),X0,X1) ),
inference(resolution,[status(thm)],[p712,c56]) ).
cnf(c53,plain,
( pair_in_list(X1,sk0(X0,X1,X2),sk1(X0,X1,X2))
| check_cpq(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(p8568,plain,
( check_cpq(triple(X0,insert_slb(sk3,pair(sk5,bottom)),X1))
| less_than(sk1(X0,insert_slb(sk3,pair(sk5,bottom)),X1),sk0(X0,insert_slb(sk3,pair(sk5,bottom)),X1)) ),
inference(resolution,[status(thm)],[p8562,c53]) ).
cnf(c54,plain,
( ~ less_than(sk1(X0,X1,X2),sk0(X0,X1,X2))
| check_cpq(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(p8573,plain,
( check_cpq(triple(X0,insert_slb(sk3,pair(sk5,bottom)),X1))
| check_cpq(triple(X0,insert_slb(sk3,pair(sk5,bottom)),X1)) ),
inference(resolution,[status(thm)],[p8568,c54]) ).
cnf(p8576,plain,
check_cpq(triple(X0,insert_slb(sk3,pair(sk5,bottom)),X1)),
inference(factoring,[status(thm)],[p8573]) ).
fof(f24,axiom,
! [U,V,W,X,Y] :
( less_than(Y,X)
=> ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
<=> check_cpq(triple(U,V,W)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).
fof(f24_nnf,plain,
! [U,V,W,X,Y] :
( ( ( ~ check_cpq(triple(U,V,W))
| check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) )
& ( check_cpq(triple(U,V,W))
| ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) ) )
| ~ less_than(Y,X) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [Y,X,U,V,W] :
( ( ( ~ check_cpq(triple(U,V,W))
| check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) )
& ( check_cpq(triple(U,V,W))
| ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) ) )
| ~ less_than(Y,X) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c31,plain,
( check_cpq(triple(X0,X1,X2))
| ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ less_than(X4,X3) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
fof(f4,axiom,
! [U] : less_than(bottom,U),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bottom_smallest) ).
fof(f4_nnf,plain,
! [U] : less_than(bottom,U),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [U] : less_than(bottom,U),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c6,plain,
less_than(bottom,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p316,plain,
( check_cpq(triple(X0,X1,X3))
| ~ check_cpq(triple(X0,insert_slb(X1,pair(X2,bottom)),X3)) ),
inference(resolution,[status(thm)],[c31,c6]) ).
cnf(p8578,plain,
check_cpq(triple(X0,sk3,X1)),
inference(resolution,[status(thm)],[p8576,p316]) ).
cnf(c55,plain,
~ check_cpq(triple(sk2,sk3,sk4)),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(p8589,plain,
$false,
inference(resolution,[status(thm)],[p8578,c55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV390+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 19:27:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 110.23/16.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 110.23/16.52 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------