%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV378+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 : n026.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 03:13:07 PM UTC 2026
% Result : Theorem 95.53s 12.64s
% Output : Proof 95.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 9 unt; 0 def)
% Number of atoms : 132 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 120 ( 44 ~; 57 |; 11 &)
% ( 2 <=>; 6 =>; 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 : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 117 ( 19 sgn 71 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f31,axiom,
! [U,V,W,X] :
( ( less_than(lookup_slb(V,X),X)
& contains_slb(V,X) )
=> remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax44) ).
fof(f31_nnf,plain,
! [U,V,W,X] :
( remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),W)
| ~ less_than(lookup_slb(V,X),X)
| ~ contains_slb(V,X) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [V,X,U,W] :
( remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),W)
| ~ less_than(lookup_slb(V,X),X)
| ~ contains_slb(V,X) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c42,plain,
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
| ~ less_than(lookup_slb(X1,X3),X3)
| ~ contains_slb(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
fof(f30,axiom,
! [U,V,W,X] :
( ~ contains_slb(V,X)
=> remove_cpq(triple(U,V,W),X) = triple(U,V,bad) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax43) ).
fof(f30_nnf,plain,
! [U,V,W,X] :
( remove_cpq(triple(U,V,W),X) = triple(U,V,bad)
| contains_slb(V,X) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [V,X,U,W] :
( remove_cpq(triple(U,V,W),X) = triple(U,V,bad)
| contains_slb(V,X) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c41,plain,
( remove_cpq(triple(X0,X1,X2),X3) = triple(X0,X1,bad)
| contains_slb(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f28,axiom,
! [U,V,W] :
( ~ ok(triple(U,V,W))
=> W = bad ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).
fof(f28_nnf,plain,
! [U,V,W] :
( W = bad
| ok(triple(U,V,W)) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [U,V,W] :
( W = bad
| ok(triple(U,V,W)) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c39,plain,
( X2 = bad
| ok(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
fof(f41,conjecture,
! [U,V,W,X] :
( ~ ok(triple(U,V,W))
=> ~ ok(remove_cpq(triple(U,V,W),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l14_co) ).
fof(f41_neg,negated_conjecture,
~ ! [U,V,W,X] :
( ~ ok(triple(U,V,W))
=> ~ ok(remove_cpq(triple(U,V,W),X)) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f41_nnf,plain,
? [U,V,W,X] :
( ok(remove_cpq(triple(U,V,W),X))
& ~ ok(triple(U,V,W)) ),
inference(nnf_transformation,[status(thm)],[f41_neg]) ).
fof(f41_sk,plain,
( ok(remove_cpq(triple(sk0,sk1,sk2),sk3))
& ~ ok(triple(sk0,sk1,sk2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f41_nnf]) ).
cnf(c52,plain,
~ ok(triple(sk0,sk1,sk2)),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(p417,plain,
sk2 = bad,
inference(resolution,[status(thm)],[c39,c52]) ).
cnf(c53,plain,
ok(remove_cpq(triple(sk0,sk1,sk2),sk3)),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(p419,plain,
ok(remove_cpq(triple(sk0,sk1,bad),sk3)),
inference(demodulation,[status(thm)],[p417,c53]) ).
cnf(p452,plain,
( ok(triple(sk0,sk1,bad))
| contains_slb(sk1,sk3) ),
inference(superposition,[status(thm)],[c41,p419]) ).
cnf(p418,plain,
~ ok(triple(sk0,sk1,bad)),
inference(demodulation,[status(thm)],[p417,c52]) ).
cnf(p456,plain,
contains_slb(sk1,sk3),
inference(resolution,[status(thm)],[p452,p418]) ).
cnf(p466,plain,
( remove_cpq(triple(X0,sk1,X1),sk3) = triple(remove_pqp(X0,sk3),remove_slb(sk1,sk3),X1)
| ~ less_than(lookup_slb(sk1,sk3),sk3) ),
inference(resolution,[status(thm)],[c42,p456]) ).
fof(f1,axiom,
! [U,V] :
( less_than(V,U)
| less_than(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
fof(f1_nnf,plain,
! [U,V] :
( less_than(V,U)
| less_than(U,V) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [U,V] :
( less_than(V,U)
| less_than(U,V) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p590,plain,
( less_than(sk3,lookup_slb(sk1,sk3))
| remove_cpq(triple(X0,sk1,X1),sk3) = triple(remove_pqp(X0,sk3),remove_slb(sk1,sk3),X1) ),
inference(resolution,[status(thm)],[p466,c1]) ).
fof(f27,axiom,
! [U,V] :
( ok(triple(U,V,bad))
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).
fof(f27_nnf,plain,
! [U,V] :
( ( ~ $false
| ok(triple(U,V,bad)) )
& ( $false
| ~ ok(triple(U,V,bad)) ) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [U,V] :
( ( ~ $false
| ok(triple(U,V,bad)) )
& ( $false
| ~ ok(triple(U,V,bad)) ) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c37,plain,
( $false
| ~ ok(triple(X0,X1,bad)) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p592,plain,
( $false
| ~ ok(remove_cpq(triple(X0,sk1,bad),sk3))
| less_than(sk3,lookup_slb(sk1,sk3)) ),
inference(superposition,[status(thm)],[p590,c37]) ).
cnf(p601,plain,
( $false
| less_than(sk3,lookup_slb(sk1,sk3)) ),
inference(resolution,[status(thm)],[p592,p419]) ).
fof(f3,axiom,
! [U,V] :
( strictly_less_than(U,V)
<=> ( ~ less_than(V,U)
& less_than(U,V) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
fof(f3_nnf,plain,
! [U,V] :
( ( less_than(V,U)
| ~ less_than(U,V)
| strictly_less_than(U,V) )
& ( ( ~ less_than(V,U)
& less_than(U,V) )
| ~ strictly_less_than(U,V) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [U,V] :
( ( less_than(V,U)
| ~ less_than(U,V)
| strictly_less_than(U,V) )
& ( ( ~ less_than(V,U)
& less_than(U,V) )
| ~ strictly_less_than(U,V) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c5,plain,
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p603,plain,
( less_than(lookup_slb(sk1,sk3),sk3)
| strictly_less_than(sk3,lookup_slb(sk1,sk3))
| $false ),
inference(resolution,[status(thm)],[p601,c5]) ).
fof(f32,axiom,
! [U,V,W,X] :
( ( strictly_less_than(X,lookup_slb(V,X))
& contains_slb(V,X) )
=> remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),bad) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
fof(f32_nnf,plain,
! [U,V,W,X] :
( remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),bad)
| ~ strictly_less_than(X,lookup_slb(V,X))
| ~ contains_slb(V,X) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [V,X,U,W] :
( remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),bad)
| ~ strictly_less_than(X,lookup_slb(V,X))
| ~ contains_slb(V,X) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c43,plain,
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
| ~ strictly_less_than(X3,lookup_slb(X1,X3))
| ~ contains_slb(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p476,plain,
( remove_cpq(triple(X0,sk1,X1),sk3) = triple(remove_pqp(X0,sk3),remove_slb(sk1,sk3),bad)
| ~ strictly_less_than(sk3,lookup_slb(sk1,sk3)) ),
inference(resolution,[status(thm)],[c43,p456]) ).
cnf(p616,plain,
( remove_cpq(triple(X0,sk1,X1),sk3) = triple(remove_pqp(X0,sk3),remove_slb(sk1,sk3),bad)
| less_than(lookup_slb(sk1,sk3),sk3)
| $false ),
inference(resolution,[status(thm)],[p603,p476]) ).
cnf(p1195,plain,
( $false
| ~ ok(remove_cpq(triple(X0,sk1,X1),sk3))
| less_than(lookup_slb(sk1,sk3),sk3)
| $false ),
inference(superposition,[status(thm)],[p616,c37]) ).
cnf(p1253,plain,
( ~ ok(remove_cpq(triple(X0,sk1,X1),sk3))
| less_than(lookup_slb(sk1,sk3),sk3)
| $false ),
inference(factoring,[status(thm)],[p1195]) ).
cnf(p1254,plain,
( less_than(lookup_slb(sk1,sk3),sk3)
| $false ),
inference(resolution,[status(thm)],[p1253,p419]) ).
cnf(p1263,plain,
( remove_cpq(triple(X0,sk1,X1),sk3) = triple(remove_pqp(X0,sk3),remove_slb(sk1,sk3),X1)
| $false ),
inference(resolution,[status(thm)],[p1254,p466]) ).
cnf(p1306,plain,
( $false
| ~ ok(remove_cpq(triple(X0,sk1,bad),sk3))
| $false ),
inference(superposition,[status(thm)],[p1263,c37]) ).
cnf(p1359,plain,
( ~ ok(remove_cpq(triple(X0,sk1,bad),sk3))
| $false ),
inference(factoring,[status(thm)],[p1306]) ).
cnf(p1360,plain,
$false,
inference(resolution,[status(thm)],[p1359,p419]) ).
cnf(c38,plain,
( ~ $false
| ok(triple(X0,X1,bad)) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p1366,plain,
ok(triple(X0,X1,bad)),
inference(resolution,[status(thm)],[p1360,c38]) ).
cnf(p1367,plain,
$false,
inference(resolution,[status(thm)],[p1366,p418]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV378+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.44 % Computer : n026.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Thu Sep 24 19:28:27 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 95.53/12.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 95.53/12.64 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------