%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV389+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 03:13:08 PM UTC 2026
% Result : Theorem 4.09s 0.97s
% Output : Proof 4.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 35 unt; 0 def)
% Number of atoms : 104 ( 19 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 101 ( 52 ~; 28 |; 14 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-4 aty)
% Number of variables : 82 ( 8 sgn 57 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f41,lemma,
! [U,V,W] :
( ( ok(removemin_cpq_eff(triple(U,V,W)))
& check_cpq(removemin_cpq_eff(triple(U,V,W))) )
=> check_cpq(triple(U,V,W)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_l40) ).
fof(f41_nnf,plain,
! [U,V,W] :
( check_cpq(triple(U,V,W))
| ~ ok(removemin_cpq_eff(triple(U,V,W)))
| ~ check_cpq(removemin_cpq_eff(triple(U,V,W))) ),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
! [U,V,W] :
( check_cpq(triple(U,V,W))
| ~ ok(removemin_cpq_eff(triple(U,V,W)))
| ~ check_cpq(removemin_cpq_eff(triple(U,V,W))) ),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c52,plain,
( check_cpq(triple(X0,X1,X2))
| ~ ok(removemin_cpq_eff(triple(X0,X1,X2)))
| ~ check_cpq(removemin_cpq_eff(triple(X0,X1,X2))) ),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(hi44,axiom,
ifeq(check_cpq(removemin_cpq_eff(triple(X0,X1,X2))),true,ifeq(ok(removemin_cpq_eff(triple(X0,X1,X2))),true,check_cpq(triple(X0,X1,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c52]) ).
fof(f42,conjecture,
! [U,V,W] :
( ~ check_cpq(triple(U,V,W))
=> ( ~ ok(removemin_cpq_eff(triple(U,V,W)))
| ~ check_cpq(removemin_cpq_eff(triple(U,V,W))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_co) ).
fof(f42_neg,negated_conjecture,
~ ! [U,V,W] :
( ~ check_cpq(triple(U,V,W))
=> ( ~ ok(removemin_cpq_eff(triple(U,V,W)))
| ~ check_cpq(removemin_cpq_eff(triple(U,V,W))) ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f42_nnf,plain,
? [U,V,W] :
( ok(removemin_cpq_eff(triple(U,V,W)))
& check_cpq(removemin_cpq_eff(triple(U,V,W)))
& ~ check_cpq(triple(U,V,W)) ),
inference(nnf_transformation,[status(thm)],[f42_neg]) ).
fof(f42_sk,plain,
( ok(removemin_cpq_eff(triple(sk0,sk1,sk2)))
& check_cpq(removemin_cpq_eff(triple(sk0,sk1,sk2)))
& ~ check_cpq(triple(sk0,sk1,sk2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f42_nnf]) ).
cnf(c54,plain,
check_cpq(removemin_cpq_eff(triple(sk0,sk1,sk2))),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi45,negated_conjecture,
check_cpq(removemin_cpq_eff(triple(sk0,sk1,sk2))) = true,
inference(equality_encoding,[status(esa)],[c54]) ).
cnf(c55,plain,
ok(removemin_cpq_eff(triple(sk0,sk1,sk2))),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi46,negated_conjecture,
ok(removemin_cpq_eff(triple(sk0,sk1,sk2))) = true,
inference(equality_encoding,[status(esa)],[c55]) ).
fof(f39,axiom,
! [U] : removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U),findmin_cpq_res(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
fof(f39_nnf,plain,
! [U] : removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U),findmin_cpq_res(U)),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [U] : removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U),findmin_cpq_res(U)),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c50,plain,
removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),findmin_cpq_res(X0)),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi26,axiom,
removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),findmin_cpq_res(X0)),
inference(equality_encoding,[status(esa)],[c50]) ).
fof(f40,axiom,
! [U] : removemin_cpq_res(U) = findmin_cpq_res(U),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
fof(f40_nnf,plain,
! [U] : removemin_cpq_res(U) = findmin_cpq_res(U),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [U] : removemin_cpq_res(U) = findmin_cpq_res(U),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c51,plain,
removemin_cpq_res(X0) = findmin_cpq_res(X0),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(hi27,axiom,
removemin_cpq_res(X0) = findmin_cpq_res(X0),
inference(equality_encoding,[status(esa)],[c51]) ).
cnf(h3650,plain,
check_cpq(triple(sk0,sk1,sk2)) = true,
inference(hyper_resolution,[status(thm)],[hi44,hi45,hi46,hi26,hi27]) ).
cnf(c53,plain,
~ check_cpq(triple(sk0,sk1,sk2)),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi53,negated_conjecture,
ifeq(check_cpq(triple(sk0,sk1,sk2)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c53]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi53,h3650]) ).
cnf(t262,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
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]) ).
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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c4,c7,c9,c13,c33,c37,c53]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t262]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV389+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 : n026.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 19:30:09 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.09/0.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.09/0.97 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------