%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV385+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 9.12s 1.65s
% Output : Proof 9.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 26 unt; 0 def)
% Number of atoms : 109 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 123 ( 65 ~; 37 |; 13 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 87 ( 8 sgn 60 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f41,lemma,
! [U,V,W] :
( ~ ok(triple(U,V,W))
=> ~ ok(im_succ_cpq(triple(U,V,W))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l21_li1316) ).
fof(f41_nnf,plain,
! [U,V,W] :
( ~ ok(im_succ_cpq(triple(U,V,W)))
| ok(triple(U,V,W)) ),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
! [U,V,W] :
( ~ ok(im_succ_cpq(triple(U,V,W)))
| ok(triple(U,V,W)) ),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c52,plain,
( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
| ok(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(hi44,axiom,
ifeq(ok(im_succ_cpq(triple(X0,X1,X2))),true,ok(triple(X0,X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c52]) ).
fof(f43,conjecture,
! [U,V,W] :
( ( ~ ok(triple(U,V,W))
| ~ check_cpq(triple(U,V,W)) )
=> ( ~ ok(im_succ_cpq(triple(U,V,W)))
| ~ check_cpq(im_succ_cpq(triple(U,V,W))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l21_co) ).
fof(f43_neg,negated_conjecture,
~ ! [U,V,W] :
( ( ~ ok(triple(U,V,W))
| ~ check_cpq(triple(U,V,W)) )
=> ( ~ ok(im_succ_cpq(triple(U,V,W)))
| ~ check_cpq(im_succ_cpq(triple(U,V,W))) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f43_nnf,plain,
? [U,V,W] :
( ok(im_succ_cpq(triple(U,V,W)))
& check_cpq(im_succ_cpq(triple(U,V,W)))
& ( ~ ok(triple(U,V,W))
| ~ check_cpq(triple(U,V,W)) ) ),
inference(nnf_transformation,[status(thm)],[f43_neg]) ).
fof(f43_sk,plain,
( ok(im_succ_cpq(triple(sk0,sk1,sk2)))
& check_cpq(im_succ_cpq(triple(sk0,sk1,sk2)))
& ( ~ ok(triple(sk0,sk1,sk2))
| ~ check_cpq(triple(sk0,sk1,sk2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f43_nnf]) ).
cnf(c56,plain,
ok(im_succ_cpq(triple(sk0,sk1,sk2))),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(hi47,negated_conjecture,
ok(im_succ_cpq(triple(sk0,sk1,sk2))) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(h3413,plain,
ok(triple(sk0,sk1,sk2)) = true,
inference(hyper_resolution,[status(thm)],[hi44,hi47]) ).
fof(f42,lemma,
! [U,V,W] :
( ~ check_cpq(triple(U,V,W))
=> ( ~ ok(im_succ_cpq(triple(U,V,W)))
| ~ check_cpq(im_succ_cpq(triple(U,V,W))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l21_li2225) ).
fof(f42_nnf,plain,
! [U,V,W] :
( ~ ok(im_succ_cpq(triple(U,V,W)))
| ~ check_cpq(im_succ_cpq(triple(U,V,W)))
| check_cpq(triple(U,V,W)) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [U,V,W] :
( ~ ok(im_succ_cpq(triple(U,V,W)))
| ~ check_cpq(im_succ_cpq(triple(U,V,W)))
| check_cpq(triple(U,V,W)) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c53,plain,
( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
| ~ check_cpq(im_succ_cpq(triple(X0,X1,X2)))
| check_cpq(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi45,axiom,
ifeq(check_cpq(im_succ_cpq(triple(X0,X1,X2))),true,ifeq(ok(im_succ_cpq(triple(X0,X1,X2))),true,check_cpq(triple(X0,X1,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c53]) ).
cnf(c55,plain,
check_cpq(im_succ_cpq(triple(sk0,sk1,sk2))),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(hi46,negated_conjecture,
check_cpq(im_succ_cpq(triple(sk0,sk1,sk2))) = true,
inference(equality_encoding,[status(esa)],[c55]) ).
cnf(h3412,plain,
check_cpq(triple(sk0,sk1,sk2)) = true,
inference(hyper_resolution,[status(thm)],[hi45,hi46,hi47]) ).
cnf(c54,plain,
( ~ ok(triple(sk0,sk1,sk2))
| ~ check_cpq(triple(sk0,sk1,sk2)) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(hi54,negated_conjecture,
ifeq(check_cpq(triple(sk0,sk1,sk2)),true,ifeq(ok(triple(sk0,sk1,sk2)),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c54]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi54,h3412,h3413]) ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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,c54]) ).
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
% 0.00/0.03 % Problem : SWV385+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n013.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 19:26:12 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.12/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.12/1.65 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------