%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV416+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 : n010.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 03:13:13 PM UTC 2026
% Result : Theorem 108.37s 14.15s
% Output : Proof 108.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 13 unt; 0 def)
% Number of atoms : 65 ( 18 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 58 ( 24 ~; 17 |; 10 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 78 ( 12 sgn 47 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f62,lemma,
! [U,V,W,X,Y] : i(triple(U,W,X)) = i(triple(V,W,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main3_li12) ).
fof(f62_nnf,plain,
! [U,V,W,X,Y] : i(triple(U,W,X)) = i(triple(V,W,Y)),
inference(nnf_transformation,[status(thm)],[f62]) ).
fof(f62_sk,plain,
! [U,W,X,V,Y] : i(triple(U,W,X)) = i(triple(V,W,Y)),
inference(skolemisation,[status(esa)],[f62_nnf]) ).
cnf(c88,plain,
i(triple(X0,X2,X3)) = i(triple(X1,X2,X4)),
inference(cnf_transformation,[status(esa)],[f62_sk]) ).
fof(f63,lemma,
! [U,V,W,X] :
( contains_pq(i(triple(U,V,W)),X)
=> i(remove_cpq(triple(U,V,W),X)) = remove_pq(i(triple(U,V,W)),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main3_li34) ).
fof(f63_nnf,plain,
! [U,V,W,X] :
( i(remove_cpq(triple(U,V,W),X)) = remove_pq(i(triple(U,V,W)),X)
| ~ contains_pq(i(triple(U,V,W)),X) ),
inference(nnf_transformation,[status(thm)],[f63]) ).
fof(f63_sk,plain,
! [U,V,W,X] :
( i(remove_cpq(triple(U,V,W),X)) = remove_pq(i(triple(U,V,W)),X)
| ~ contains_pq(i(triple(U,V,W)),X) ),
inference(skolemisation,[status(esa)],[f63_nnf]) ).
cnf(c89,plain,
( i(remove_cpq(triple(X0,X1,X2),X3)) = remove_pq(i(triple(X0,X1,X2)),X3)
| ~ contains_pq(i(triple(X0,X1,X2)),X3) ),
inference(cnf_transformation,[status(esa)],[f63_sk]) ).
cnf(p1248,plain,
( i(remove_cpq(triple(X4,X1,X5),X3)) = remove_pq(i(triple(X4,X1,X5)),X3)
| ~ contains_pq(i(triple(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c88,c89]) ).
fof(f56,axiom,
! [U,V] :
( pi_remove(U,V)
<=> pi_sharp_remove(i(U),V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
fof(f56_nnf,plain,
! [U,V] :
( ( ~ pi_sharp_remove(i(U),V)
| pi_remove(U,V) )
& ( pi_sharp_remove(i(U),V)
| ~ pi_remove(U,V) ) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [U,V] :
( ( ~ pi_sharp_remove(i(U),V)
| pi_remove(U,V) )
& ( pi_sharp_remove(i(U),V)
| ~ pi_remove(U,V) ) ),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c72,plain,
( pi_sharp_remove(i(X0),X1)
| ~ pi_remove(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
fof(f64,conjecture,
! [U,V,W,X] :
( pi_remove(triple(U,V,W),X)
=> ( phi(remove_cpq(triple(U,V,W),X))
=> ( i(remove_cpq(triple(U,V,W),X)) = remove_pq(i(triple(U,V,W)),X)
& pi_sharp_remove(i(triple(U,V,W)),X) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co3) ).
fof(f64_neg,negated_conjecture,
~ ! [U,V,W,X] :
( pi_remove(triple(U,V,W),X)
=> ( phi(remove_cpq(triple(U,V,W),X))
=> ( i(remove_cpq(triple(U,V,W),X)) = remove_pq(i(triple(U,V,W)),X)
& pi_sharp_remove(i(triple(U,V,W)),X) ) ) ),
inference(negated_conjecture,[status(cth)],[f64]) ).
fof(f64_nnf,plain,
? [U,V,W,X] :
( ( i(remove_cpq(triple(U,V,W),X)) != remove_pq(i(triple(U,V,W)),X)
| ~ pi_sharp_remove(i(triple(U,V,W)),X) )
& phi(remove_cpq(triple(U,V,W),X))
& pi_remove(triple(U,V,W),X) ),
inference(nnf_transformation,[status(thm)],[f64_neg]) ).
fof(f64_sk,plain,
( ( i(remove_cpq(triple(sk4,sk5,sk6),sk7)) != remove_pq(i(triple(sk4,sk5,sk6)),sk7)
| ~ pi_sharp_remove(i(triple(sk4,sk5,sk6)),sk7) )
& phi(remove_cpq(triple(sk4,sk5,sk6),sk7))
& pi_remove(triple(sk4,sk5,sk6),sk7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6,sk7])],[f64_nnf]) ).
cnf(c90,plain,
pi_remove(triple(sk4,sk5,sk6),sk7),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(p1073,plain,
pi_sharp_remove(i(triple(sk4,sk5,sk6)),sk7),
inference(resolution,[status(thm)],[c72,c90]) ).
fof(f55,axiom,
! [U,V] :
( pi_sharp_remove(U,V)
<=> contains_pq(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax56) ).
fof(f55_nnf,plain,
! [U,V] :
( ( ~ contains_pq(U,V)
| pi_sharp_remove(U,V) )
& ( contains_pq(U,V)
| ~ pi_sharp_remove(U,V) ) ),
inference(nnf_transformation,[status(thm)],[f55]) ).
fof(f55_sk,plain,
! [U,V] :
( ( ~ contains_pq(U,V)
| pi_sharp_remove(U,V) )
& ( contains_pq(U,V)
| ~ pi_sharp_remove(U,V) ) ),
inference(skolemisation,[status(esa)],[f55_nnf]) ).
cnf(c70,plain,
( contains_pq(X0,X1)
| ~ pi_sharp_remove(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(p1075,plain,
contains_pq(i(triple(sk4,sk5,sk6)),sk7),
inference(resolution,[status(thm)],[p1073,c70]) ).
cnf(p1210,plain,
contains_pq(i(triple(X0,sk5,X1)),sk7),
inference(superposition,[status(thm)],[c88,p1075]) ).
cnf(p11358,plain,
i(remove_cpq(triple(X0,sk5,X1),sk7)) = remove_pq(i(triple(X0,sk5,X1)),sk7),
inference(resolution,[status(thm)],[p1248,p1210]) ).
cnf(c92,plain,
( i(remove_cpq(triple(sk4,sk5,sk6),sk7)) != remove_pq(i(triple(sk4,sk5,sk6)),sk7)
| ~ pi_sharp_remove(i(triple(sk4,sk5,sk6)),sk7) ),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(p1074,plain,
i(remove_cpq(triple(sk4,sk5,sk6),sk7)) != remove_pq(i(triple(sk4,sk5,sk6)),sk7),
inference(resolution,[status(thm)],[p1073,c92]) ).
cnf(p1218,plain,
i(remove_cpq(triple(sk4,sk5,sk6),sk7)) != remove_pq(i(triple(X0,sk5,X1)),sk7),
inference(superposition,[status(thm)],[c88,p1074]) ).
cnf(p11359,plain,
remove_pq(i(triple(sk4,sk5,sk6)),sk7) != remove_pq(i(triple(X0,sk5,X1)),sk7),
inference(demodulation,[status(thm)],[p11358,p1218]) ).
cnf(p11370,plain,
$false,
inference(equality_resolution,[status(thm)],[p11359]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV416+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 : n010.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 19:31:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 108.37/14.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 108.37/14.15 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------