%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV381+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Sun Sep 27 09:07:35 AM UTC 2026
% Result : Theorem 2.87s 0.82s
% Output : CNFRefutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 7 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 68 ( 27 ~; 24 |; 10 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 60 ( 0 sgn 33 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(totality,axiom,
! [U,V] :
( less_than(V,U)
| less_than(U,V) ),
file('theBenchmark.p',totality) ).
fof(stricly_smaller_definition,axiom,
! [U,V] :
( strictly_less_than(U,V)
<=> ( ~ less_than(V,U)
& less_than(U,V) ) ),
file('theBenchmark.p',stricly_smaller_definition) ).
fof(ax10,axiom,
! [U,V] :
( issmallestelement_pq(U,V)
<=> ! [W] :
( contains_pq(U,W)
=> less_than(V,W) ) ),
file('theBenchmark.p',ax10) ).
fof(l17_li56,axiom,
! [U,V,W,X] :
( contains_cpq(triple(U,V,W),X)
<=> contains_pq(i(triple(U,V,W)),X) ),
file('theBenchmark.p',l17_li56) ).
fof(l17_l18,axiom,
! [U,V,W] :
( ? [X] :
( strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& contains_cpq(triple(U,V,W),X) )
=> ~ phi(findmin_cpq_eff(triple(U,V,W))) ),
file('theBenchmark.p',l17_l18) ).
fof(l17_co,conjecture,
! [U,V,W] :
( phi(findmin_cpq_eff(triple(U,V,W)))
=> issmallestelement_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))) ),
file('theBenchmark.p',l17_co) ).
fof(l17_co_neg,negated_conjecture,
~ ! [U,V,W] :
( phi(findmin_cpq_eff(triple(U,V,W)))
=> issmallestelement_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))) ),
inference(assume_negation,[status(cth)],[l17_co]) ).
fof(nnf_63,plain,
? [U,V,W] :
( ~ issmallestelement_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W)))
& phi(findmin_cpq_eff(triple(U,V,W))) ),
inference(fof_nnf,[status(thm)],[l17_co_neg]) ).
fof(sk_l17_co_neg,plain,
( ~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))
& phi(findmin_cpq_eff(triple(sK0,sK1,sK2))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK2)],[nnf_63]) ).
cnf(c_77,negated_conjecture,
~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))),
inference(split_conjunct,[status(thm)],[sk_l17_co_neg]) ).
cnf(c_78,negated_conjecture,
phi(findmin_cpq_eff(triple(sK0,sK1,sK2))),
inference(split_conjunct,[status(thm)],[sk_l17_co_neg]) ).
cnf(c_79,plain,
( ~ phi(findmin_cpq_eff(triple(A,B,C)))
| ~ strictly_less_than(D,findmin_cpq_res(triple(A,B,C)))
| ~ contains_cpq(triple(A,B,C),D) ),
inference(clausify,[status(thm)],[l17_l18]) ).
cnf(c_80,plain,
( ~ contains_pq(i(triple(A,B,C)),D)
| contains_cpq(triple(A,B,C),D) ),
inference(clausify,[status(thm)],[l17_li56]) ).
fof(nnf_9,plain,
! [U,V] :
( ( ? [W] :
( ~ less_than(V,W)
& contains_pq(U,W) )
| issmallestelement_pq(U,V) )
& ( ! [X0] :
( less_than(V,X0)
| ~ contains_pq(U,X0) )
| ~ issmallestelement_pq(U,V) ) ),
inference(fof_nnf,[status(thm)],[ax10]) ).
fof(sk_ax10_sk,plain,
! [U,V] :
( ( ( ~ less_than(V,sK3(U,V))
& contains_pq(U,sK3(U,V)) )
| issmallestelement_pq(U,V) )
& ( ! [X0] :
( less_than(V,X0)
| ~ contains_pq(U,X0) )
| ~ issmallestelement_pq(U,V) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(W,sK3(U,V))],[nnf_9]) ).
fof(sk_ax10,plain,
( ! [VAR_0,VAR_1] :
( ~ less_than(VAR_1,sK3(VAR_0,VAR_1))
| issmallestelement_pq(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( contains_pq(VAR_0,sK3(VAR_0,VAR_1))
| issmallestelement_pq(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( less_than(VAR_1,VAR_2)
| ~ contains_pq(VAR_0,VAR_2)
| ~ issmallestelement_pq(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_ax10_sk]) ).
cnf(c_144,plain,
( ~ less_than(B,sK3(A,B))
| issmallestelement_pq(A,B) ),
inference(split_conjunct,[status(thm)],[sk_ax10]) ).
cnf(c_145,plain,
( contains_pq(A,sK3(A,B))
| issmallestelement_pq(A,B) ),
inference(split_conjunct,[status(thm)],[sk_ax10]) ).
cnf(c_154,plain,
( less_than(B,A)
| ~ less_than(A,B)
| strictly_less_than(A,B) ),
inference(clausify,[status(thm)],[stricly_smaller_definition]) ).
cnf(c_158,plain,
( less_than(B,A)
| less_than(A,B) ),
inference(clausify,[status(thm)],[totality]) ).
cnf(c_161,plain,
( ~ strictly_less_than(A,findmin_cpq_res(triple(sK0,sK1,sK2)))
| ~ contains_cpq(triple(sK0,sK1,sK2),A) ),
inference(resolve,[status(thm)],[c_79,c_78]) ).
cnf(c_210,negated_conjecture,
~ less_than(findmin_cpq_res(triple(sK0,sK1,sK2)),sK3(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))),
inference(resolve,[status(thm)],[c_144,c_77]) ).
cnf(c_216,plain,
contains_pq(i(triple(sK0,sK1,sK2)),sK3(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))),
inference(resolve,[status(thm)],[c_145,c_77]) ).
cnf(c_1184,plain,
( less_than(A,B)
| strictly_less_than(B,A)
| less_than(A,B) ),
inference(resolve,[status(thm)],[c_158,c_154]) ).
cnf(c_233,plain,
( strictly_less_than(B,A)
| less_than(A,B) ),
inference(copy,[status(thm)],[c_1184]) ).
cnf(c_253,plain,
( ~ contains_cpq(triple(sK0,sK1,sK2),A)
| less_than(findmin_cpq_res(triple(sK0,sK1,sK2)),A) ),
inference(resolve,[status(thm)],[c_233,c_161]) ).
cnf(c_999,plain,
~ contains_cpq(triple(sK0,sK1,sK2),sK3(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))),
inference(resolve,[status(thm)],[c_253,c_210]) ).
cnf(c_1185,plain,
~ contains_pq(i(triple(sK0,sK1,sK2)),sK3(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))),
inference(resolve,[status(thm)],[c_80,c_999]) ).
cnf(c_1183,plain,
$false,
inference(resolve,[status(thm)],[c_216,c_1185]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV381+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.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 : Sat Sep 26 13:42:07 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 576177 was started by sandbox2 on n018,
% 0.09/0.36 % Sat Sep 26 13:42:07 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.38
% 0.14/0.38 % From the command line: assign(max_seconds, 300).
% 2.87/0.82
% 2.87/0.82 % SZS status Theorem for theBenchmark
% 2.87/0.82
% 2.87/0.82 % Proof 1 at 0.28 (+ 0.07) seconds.
% 2.87/0.82 % Length of proof is 21.
% 2.87/0.82 % Level of proof is 5.
% 2.87/0.82 % Maximum clause weight is 37.000.
% 2.87/0.82 % Given clauses 306.
% 2.87/0.82
% 2.87/0.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------