%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV412+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 : n018.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 03:13:12 PM UTC 2026
% Result : Theorem 6.48s 1.29s
% Output : Proof 6.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 25 unt; 0 def)
% Number of atoms : 70 ( 9 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 66 ( 33 ~; 13 |; 16 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 52 ( 3 sgn 35 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,lemma,
! [U,V,W,X] :
( ( strictly_less_than(W,X)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l48_li3839) ).
fof(f18_nnf,plain,
! [U,V,W,X] :
( pair_in_list(update_slb(U,X),V,X)
| ~ strictly_less_than(W,X)
| ~ pair_in_list(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [U,V,W,X] :
( pair_in_list(update_slb(U,X),V,X)
| ~ strictly_less_than(W,X)
| ~ pair_in_list(U,V,W) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c25,plain,
( pair_in_list(update_slb(X0,X3),X1,X3)
| ~ strictly_less_than(X2,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi21,axiom,
ifeq(pair_in_list(X0,X1,X2),true,ifeq(strictly_less_than(X2,X3),true,pair_in_list(update_slb(X0,X3),X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
fof(f19,conjecture,
! [U,V,W,X] :
( ( strictly_less_than(W,X)
& strictly_less_than(V,X)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l48_co) ).
fof(f19_neg,negated_conjecture,
~ ! [U,V,W,X] :
( ( strictly_less_than(W,X)
& strictly_less_than(V,X)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,X) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f19_nnf,plain,
? [U,V,W,X] :
( ~ pair_in_list(update_slb(U,X),V,X)
& strictly_less_than(W,X)
& strictly_less_than(V,X)
& pair_in_list(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f19_neg]) ).
fof(f19_sk,plain,
( ~ pair_in_list(update_slb(sk0,sk3),sk1,sk3)
& strictly_less_than(sk2,sk3)
& strictly_less_than(sk1,sk3)
& pair_in_list(sk0,sk1,sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f19_nnf]) ).
cnf(c26,plain,
pair_in_list(sk0,sk1,sk2),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi22,negated_conjecture,
pair_in_list(sk0,sk1,sk2) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(c28,plain,
strictly_less_than(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi24,negated_conjecture,
strictly_less_than(sk2,sk3) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(h386,plain,
pair_in_list(update_slb(sk0,sk3),sk1,sk3) = true,
inference(hyper_resolution,[status(thm)],[hi21,hi22,hi24]) ).
cnf(c29,plain,
~ pair_in_list(update_slb(sk0,sk3),sk1,sk3),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi29,negated_conjecture,
ifeq(pair_in_list(update_slb(sk0,sk3),sk1,sk3),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi29,h386]) ).
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]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c4,c7,c9,c13,c29]) ).
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 : SWV412+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.34 % Computer : n018.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Thu Sep 24 19:33:18 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.48/1.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.48/1.29 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------