%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV377+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 : n016.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 99.83s 13.56s
% Output : Proof 99.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 71 ( 51 unt; 0 def)
% Number of atoms : 112 ( 40 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 86 ( 45 ~; 23 |; 11 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-4 aty)
% Number of variables : 130 ( 32 sgn 65 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f41,conjecture,
! [U,V,W,X] :
( ~ ok(triple(U,V,W))
=> ~ ok(insert_cpq(triple(U,V,W),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l13_co) ).
fof(f41_neg,negated_conjecture,
~ ! [U,V,W,X] :
( ~ ok(triple(U,V,W))
=> ~ ok(insert_cpq(triple(U,V,W),X)) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f41_nnf,plain,
? [U,V,W,X] :
( ok(insert_cpq(triple(U,V,W),X))
& ~ ok(triple(U,V,W)) ),
inference(nnf_transformation,[status(thm)],[f41_neg]) ).
fof(f41_sk,plain,
( ok(insert_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(c53,plain,
ok(insert_cpq(triple(sk0,sk1,sk2),sk3)),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(t51,plain,
ok(insert_cpq(triple(sk0,sk1,sk2),sk3)) = true,
inference(equality_encoding,[status(esa)],[c53]) ).
cnf(t824,plain,
ok(insert_cpq(triple(sk0,sk1,sk2),sk3)) = true,
inference(orient,[status(thm)],[t51]) ).
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(t20,plain,
ok(triple(X1,X2,bad)) = false,
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(t872,plain,
ok(triple(X1,X2,bad)) = false,
inference(orient,[status(thm)],[t20]) ).
cnf(t49,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t259,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t49]) ).
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]) ).
cnf(t97,plain,
or(ok(triple(X1,X2,X3)),eq(X3,bad)) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t340,plain,
or(ok(triple(X1,X2,X3)),eq(X3,bad)) = true,
inference(orient,[status(thm)],[t97]) ).
cnf(c52,plain,
~ ok(triple(sk0,sk1,sk2)),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(t21,plain,
ok(triple(sk0,sk1,sk2)) = false,
inference(equality_encoding,[status(esa)],[c52]) ).
cnf(t874,plain,
ok(triple(sk0,sk1,sk2)) = false,
inference(orient,[status(thm)],[t21]) ).
cnf(t875,plain,
true = or(false,eq(sk2,bad)),
inference(cp,[status(thm)],[t340,t874]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t257,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t1284,plain,
true = eq(sk2,bad),
inference(step,[status(thm)],[t875,t257]) ).
cnf(t1002,plain,
eq(sk2,bad) = true,
inference(orient,[status(thm)],[t1284]) ).
cnf(t1003,plain,
bad = ifeq(true,true,sk2,bad),
inference(cp,[status(thm)],[t259,t1002]) ).
cnf(t19,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t258,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t19]) ).
cnf(t1285,plain,
bad = sk2,
inference(step,[status(thm)],[t1003,t258]) ).
cnf(t1009,plain,
bad = sk2,
inference(orient,[status(thm)],[t1285]) ).
cnf(t1288,plain,
ok(triple(X1,X2,sk2)) = false,
inference(step,[status(thm)],[t872,t1009]) ).
cnf(t1012,plain,
ok(triple(X1,X2,sk2)) = false,
inference(rw,[status(thm)],[t1288]) ).
cnf(t1022,plain,
ok(triple(X1,X2,sk2)) = false,
inference(orient,[status(thm)],[t1012]) ).
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]) ).
cnf(t204,plain,
triple(insert_pqp(X1,X2),insert_slb(X3,pair(X2,bottom)),X4) = insert_cpq(triple(X1,X3,X4),X2),
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t966,plain,
triple(insert_pqp(X1,X2),insert_slb(X3,pair(X2,bottom)),X4) = insert_cpq(triple(X1,X3,X4),X2),
inference(orient,[status(thm)],[t204]) ).
cnf(t1023,plain,
false = ok(insert_cpq(triple(X1,X2,sk2),X3)),
inference(cp,[status(thm)],[t1022,t966]) ).
cnf(t1200,plain,
ok(insert_cpq(triple(X1,X2,sk2),X3)) = false,
inference(orient,[status(thm)],[t1023]) ).
cnf(t1328,plain,
false = true,
inference(step,[status(thm)],[t824,t1200]) ).
cnf(t1202,plain,
false = true,
inference(rw,[status(thm)],[t1328]) ).
cnf(t1203,plain,
false = true,
inference(orient,[status(thm)],[t1202]) ).
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(c4,plain,
( ~ less_than(X1,X0)
| ~ strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f5,axiom,
~ isnonempty_slb(create_slb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
fof(f5_nnf,plain,
~ isnonempty_slb(create_slb),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
~ isnonempty_slb(create_slb),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c7,plain,
~ isnonempty_slb(create_slb),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f7,axiom,
! [U] : ~ contains_slb(create_slb,U),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
fof(f7_nnf,plain,
! [U] : ~ contains_slb(create_slb,U),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [U] : ~ contains_slb(create_slb,U),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c9,plain,
~ contains_slb(create_slb,X0),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f9,axiom,
! [U,V] : ~ pair_in_list(create_slb,U,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
fof(f9_nnf,plain,
! [U,V] : ~ pair_in_list(create_slb,U,V),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [U,V] : ~ pair_in_list(create_slb,U,V),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c13,plain,
~ pair_in_list(create_slb,X0,X1),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
fof(f25,axiom,
! [U,V,W,X,Y] :
( strictly_less_than(X,Y)
=> ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
fof(f25_nnf,plain,
! [U,V,W,X,Y] :
( ( ( ~ $false
| check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) )
& ( $false
| ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) ) )
| ~ strictly_less_than(X,Y) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [X,Y,U,V,W] :
( ( ( ~ $false
| check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) )
& ( $false
| ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) ) )
| ~ strictly_less_than(X,Y) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c33,plain,
( $false
| ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ strictly_less_than(X3,X4) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c4,c7,c9,c13,c33,c37,c52]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1203]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV377+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.79 % Computer : n016.cluster.edu
% 0.12/0.79 % Model : x86_64 x86_64
% 0.12/0.79 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.79 % Memory : 8046.5625MB
% 0.12/0.79 % OS : Linux 6.8.0-71-generic
% 0.12/0.80 % CPULimit : 300
% 0.12/0.80 % WCLimit : 300
% 0.12/0.80 % DateTime : Thu Sep 24 19:29:29 UTC 2026
% 0.14/0.80 % CPUTime :
% 0.14/0.80 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 99.83/13.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 99.83/13.56 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------