%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWW101+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 03:26:46 PM UTC 2026
% Result : Theorem 28.63s 4.58s
% Output : Proof 28.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 34 unt; 0 def)
% Number of atoms : 142 ( 72 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 137 ( 54 ~; 47 |; 32 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 37 ( 1 sgn 23 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y] :
( forallprefers(X,Y)
<=> ( ( Y = true
& X = false )
| ( bool(Y)
& ~ bool(X)
& d(Y)
& d(X) )
| ( d(Y)
& ~ d(X) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_forallprefers) ).
fof(f3_nnf,plain,
! [X,Y] :
( ( ( ( Y != true
| X != false )
& ( ~ bool(Y)
| bool(X)
| ~ d(Y)
| ~ d(X) )
& ( ~ d(Y)
| d(X) ) )
| forallprefers(X,Y) )
& ( ( Y = true
& X = false )
| ( bool(Y)
& ~ bool(X)
& d(Y)
& d(X) )
| ( d(Y)
& ~ d(X) )
| ~ forallprefers(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] :
( ( ( ( Y != true
| X != false )
& ( ~ bool(Y)
| bool(X)
| ~ d(Y)
| ~ d(X) )
& ( ~ d(Y)
| d(X) ) )
| forallprefers(X,Y) )
& ( ( Y = true
& X = false )
| ( bool(Y)
& ~ bool(X)
& d(Y)
& d(X) )
| ( d(Y)
& ~ d(X) )
| ~ forallprefers(X,Y) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c27,plain,
( X1 != true
| X0 != false
| forallprefers(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p189,plain,
( X0 != true
| forallprefers(false,X0) ),
inference(equality_resolution,[status(thm)],[c27]) ).
cnf(p192,plain,
forallprefers(false,true),
inference(equality_resolution,[status(thm)],[p189]) ).
fof(f7,axiom,
! [X] :
( prop(X) = false
<=> ~ bool(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop_false) ).
fof(f7_nnf,plain,
! [X] :
( ( bool(X)
| prop(X) = false )
& ( ~ bool(X)
| prop(X) != false ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X] :
( ( bool(X)
| prop(X) = false )
& ( ~ bool(X)
| prop(X) != false ) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c54,plain,
( bool(X0)
| prop(X0) = false ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f38,axiom,
! [P] : f7(P) = lazy_impl(prop(P),P),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f7) ).
fof(f38_nnf,plain,
! [P] : f7(P) = lazy_impl(prop(P),P),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [P] : f7(P) = lazy_impl(prop(P),P),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c91,plain,
f7(X0) = lazy_impl(prop(X0),X0),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(p116,plain,
( f7(X0) = true
| bool(X0) ),
inference(superposition,[status(thm)],[c54,c91]) ).
fof(f6,axiom,
! [X] :
( prop(X) = true
<=> bool(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop_true) ).
fof(f6_nnf,plain,
! [X] :
( ( ~ bool(X)
| prop(X) = true )
& ( bool(X)
| prop(X) != true ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X] :
( ( ~ bool(X)
| prop(X) = true )
& ( bool(X)
| prop(X) != true ) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c52,plain,
( ~ bool(X0)
| prop(X0) = true ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
fof(f0,axiom,
! [X] :
( bool(X)
<=> ( X = true
| X = false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_bool) ).
fof(f0_nnf,plain,
! [X] :
( ( ( X != true
& X != false )
| bool(X) )
& ( X = true
| X = false
| ~ bool(X) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] :
( ( ( X != true
& X != false )
| bool(X) )
& ( X = true
| X = false
| ~ bool(X) ) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c1,plain,
( X0 != false
| bool(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p101,plain,
bool(false),
inference(equality_resolution,[status(thm)],[c1]) ).
cnf(p109,plain,
prop(false) = true,
inference(resolution,[status(thm)],[c52,p101]) ).
cnf(p114,plain,
f7(false) = false,
inference(superposition,[status(thm)],[p109,c91]) ).
fof(f39,axiom,
? [P] :
( ~ ? [P1] : forallprefers(f7(P1),f7(P))
& false2 = phi(f7(P)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_false2) ).
fof(f39_nnf,plain,
? [P] :
( ! [P1] : ~ forallprefers(f7(P1),f7(P))
& false2 = phi(f7(P)) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [P1] :
( ~ forallprefers(f7(P1),f7(sk6))
& false2 = phi(f7(sk6)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk6])],[f39_nnf]) ).
cnf(c93,plain,
~ forallprefers(f7(X1),f7(sk6)),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(p117,plain,
~ forallprefers(false,f7(sk6)),
inference(superposition,[status(thm)],[p114,c93]) ).
cnf(p125,plain,
( ~ forallprefers(false,true)
| bool(sk6) ),
inference(superposition,[status(thm)],[p116,p117]) ).
cnf(p196,plain,
bool(sk6),
inference(resolution,[status(thm)],[p192,p125]) ).
cnf(c0,plain,
( X0 = true
| X0 = false
| ~ bool(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p197,plain,
( sk6 = true
| sk6 = false ),
inference(resolution,[status(thm)],[p196,c0]) ).
cnf(p198,plain,
prop(sk6) = true,
inference(resolution,[status(thm)],[p196,c52]) ).
cnf(p205,plain,
f7(sk6) = phi(sk6),
inference(superposition,[status(thm)],[p198,c91]) ).
cnf(p210,plain,
~ forallprefers(false,phi(sk6)),
inference(demodulation,[status(thm)],[p205,p117]) ).
cnf(p230,plain,
( ~ forallprefers(false,true)
| sk6 = false ),
inference(superposition,[status(thm)],[p197,p210]) ).
cnf(p248,plain,
sk6 = false,
inference(resolution,[status(thm)],[p230,p192]) ).
cnf(c92,plain,
false2 = phi(f7(sk6)),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
fof(f14,axiom,
! [B] : lazy_impl(true,B) = phi(B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lazy_impl_axiom3) ).
fof(f14_nnf,plain,
! [B] : lazy_impl(true,B) = phi(B),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [B] : lazy_impl(true,B) = phi(B),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c61,plain,
lazy_impl(true,X0) = phi(X0),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p103,plain,
phi(f7(sk6)) = false2,
inference(superposition,[status(thm)],[c92,c61]) ).
cnf(p207,plain,
phi(phi(sk6)) = false2,
inference(demodulation,[status(thm)],[p205,p103]) ).
cnf(p251,plain,
phi(phi(false)) = false2,
inference(demodulation,[status(thm)],[p248,p207]) ).
cnf(p273,plain,
false = false2,
inference(superposition,[status(thm)],[p251,c61]) ).
fof(f37,axiom,
false1 = false,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_false1) ).
fof(f37_nnf,plain,
false1 = false,
inference(nnf_transformation,[status(thm)],[f37]) ).
cnf(c90,plain,
false1 = false,
inference(cnf_transformation,[status(esa)],[f37_nnf]) ).
fof(f44,conjecture,
false1 = false2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',false1_false2) ).
fof(f44_neg,negated_conjecture,
false1 != false2,
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f44_nnf,plain,
false1 != false2,
inference(nnf_transformation,[status(thm)],[f44_neg]) ).
fof(f44_sk,plain,
false1 != false2,
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c98,plain,
false1 != false2,
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(p100,plain,
false != false2,
inference(superposition,[status(thm)],[c90,c98]) ).
cnf(p275,plain,
$false,
inference(resolution,[status(thm)],[p273,p100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW101+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 21:39:33 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 28.63/4.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.63/4.58 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------