%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV408+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 : n001.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 09:07:39 AM UTC 2026
% Result : Theorem 0.16s 11.53s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 50 ( 16 unt; 0 def)
% Number of atoms : 127 ( 9 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 117 ( 40 ~; 54 |; 17 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 81 ( 6 sgn 40 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(transitivity,axiom,
! [U,V,W] :
( ( less_than(V,W)
& less_than(U,V) )
=> less_than(U,W) ),
file('theBenchmark.p',transitivity) ).
fof(totality,axiom,
! [U,V] :
( less_than(V,U)
| less_than(U,V) ),
file('theBenchmark.p',totality) ).
fof(reflexivity,axiom,
! [U] : less_than(U,U),
file('theBenchmark.p',reflexivity) ).
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(bottom_smallest,axiom,
! [U] : less_than(bottom,U),
file('theBenchmark.p',bottom_smallest) ).
fof(ax50,axiom,
! [U,V] : findmin_cpq_res(triple(U,create_slb,V)) = bottom,
file('theBenchmark.p',ax50) ).
fof(ax51,axiom,
! [U,V,W,X] :
( V != create_slb
=> findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U) ),
file('theBenchmark.p',ax51) ).
fof(l44_l45,axiom,
! [U,V,W] :
( ( strictly_less_than(V,W)
& contains_slb(U,V) )
=> ( ? [X] :
( less_than(W,X)
& pair_in_list(update_slb(U,W),V,X) )
| pair_in_list(update_slb(U,W),V,W) ) ),
file('theBenchmark.p',l44_l45) ).
fof(l44_co,conjecture,
! [U,V,W,X] :
( ( strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& contains_slb(V,X) )
=> ( ? [Y] :
( less_than(findmin_pqp_res(U),Y)
& pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y) )
| pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U)) ) ),
file('theBenchmark.p',l44_co) ).
fof(l44_co_neg,negated_conjecture,
~ ! [U,V,W,X] :
( ( strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& contains_slb(V,X) )
=> ( ? [Y] :
( less_than(findmin_pqp_res(U),Y)
& pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y) )
| pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U)) ) ),
inference(assume_negation,[status(cth)],[l44_co]) ).
cnf(c_43,plain,
( less_than(A,C)
| ~ less_than(B,C)
| ~ less_than(A,B) ),
inference(clausify,[status(thm)],[transitivity]) ).
cnf(c_44,plain,
( less_than(B,A)
| less_than(A,B) ),
inference(clausify,[status(thm)],[totality]) ).
cnf(c_45,plain,
less_than(A,A),
inference(clausify,[status(thm)],[reflexivity]) ).
cnf(c_47,plain,
( ~ less_than(B,A)
| ~ strictly_less_than(A,B) ),
inference(clausify,[status(thm)],[stricly_smaller_definition]) ).
cnf(c_48,plain,
( less_than(B,A)
| ~ less_than(A,B)
| strictly_less_than(A,B) ),
inference(clausify,[status(thm)],[stricly_smaller_definition]) ).
cnf(c_49,plain,
less_than(bottom,A),
inference(clausify,[status(thm)],[bottom_smallest]) ).
cnf(c_91,plain,
findmin_cpq_res(triple(A,create_slb,B)) = bottom,
inference(clausify,[status(thm)],[ax50]) ).
cnf(c_92,plain,
( findmin_cpq_res(triple(B,A,C)) = findmin_pqp_res(B)
| create_slb = A ),
inference(clausify,[status(thm)],[ax51]) ).
fof(nnf_41,plain,
! [U,V,W] :
( ? [X] :
( less_than(W,X)
& pair_in_list(update_slb(U,W),V,X) )
| pair_in_list(update_slb(U,W),V,W)
| ~ strictly_less_than(V,W)
| ~ contains_slb(U,V) ),
inference(fof_nnf,[status(thm)],[l44_l45]) ).
fof(sk_l44_l45_sk,plain,
! [U,V,W] :
( ( less_than(W,sK0(U,V,W))
& pair_in_list(update_slb(U,W),V,sK0(U,V,W)) )
| pair_in_list(update_slb(U,W),V,W)
| ~ strictly_less_than(V,W)
| ~ contains_slb(U,V) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0(U,V,W))],[nnf_41]) ).
fof(sk_l44_l45,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( less_than(VAR_2,sK0(VAR_0,VAR_1,VAR_2))
| pair_in_list(update_slb(VAR_0,VAR_2),VAR_1,VAR_2)
| ~ strictly_less_than(VAR_1,VAR_2)
| ~ contains_slb(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( pair_in_list(update_slb(VAR_0,VAR_2),VAR_1,sK0(VAR_0,VAR_1,VAR_2))
| pair_in_list(update_slb(VAR_0,VAR_2),VAR_1,VAR_2)
| ~ strictly_less_than(VAR_1,VAR_2)
| ~ contains_slb(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_l44_l45_sk]) ).
cnf(c_95,plain,
( pair_in_list(update_slb(A,C),B,sK0(A,B,C))
| pair_in_list(update_slb(A,C),B,C)
| ~ strictly_less_than(B,C)
| ~ contains_slb(A,B) ),
inference(split_conjunct,[status(thm)],[sk_l44_l45]) ).
cnf(c_96,plain,
( less_than(C,sK0(A,B,C))
| pair_in_list(update_slb(A,C),B,C)
| ~ strictly_less_than(B,C)
| ~ contains_slb(A,B) ),
inference(split_conjunct,[status(thm)],[sk_l44_l45]) ).
fof(nnf_42,plain,
? [U,V,W,X] :
( ! [Y] :
( ~ less_than(findmin_pqp_res(U),Y)
| ~ pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y) )
& ~ pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U))
& strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& contains_slb(V,X) ),
inference(fof_nnf,[status(thm)],[l44_co_neg]) ).
fof(sk_l44_co_neg,plain,
( ! [Y] :
( ~ less_than(findmin_pqp_res(sK3),Y)
| ~ pair_in_list(update_slb(sK1,findmin_pqp_res(sK3)),sK2,Y) )
& ~ pair_in_list(update_slb(sK1,findmin_pqp_res(sK3)),sK2,findmin_pqp_res(sK3))
& strictly_less_than(sK2,findmin_cpq_res(triple(sK3,sK1,sK4)))
& contains_slb(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(U,sK3),skolemize(V,sK1),skolemize(W,sK4),skolemize(X,sK2)],[nnf_42]) ).
cnf(c_97,negated_conjecture,
contains_slb(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_l44_co_neg]) ).
cnf(c_98,negated_conjecture,
strictly_less_than(sK2,findmin_cpq_res(triple(sK3,sK1,sK4))),
inference(split_conjunct,[status(thm)],[sk_l44_co_neg]) ).
cnf(c_99,negated_conjecture,
~ pair_in_list(update_slb(sK1,findmin_pqp_res(sK3)),sK2,findmin_pqp_res(sK3)),
inference(split_conjunct,[status(thm)],[sk_l44_co_neg]) ).
cnf(c_100,negated_conjecture,
( ~ less_than(findmin_pqp_res(sK3),A)
| ~ pair_in_list(update_slb(sK1,findmin_pqp_res(sK3)),sK2,A) ),
inference(split_conjunct,[status(thm)],[sk_l44_co_neg]) ).
cnf(c_844,plain,
( less_than(B,A)
| less_than(B,A)
| strictly_less_than(A,B) ),
inference(resolve,[status(thm)],[c_48,c_44]) ).
cnf(c_106,plain,
( less_than(B,A)
| strictly_less_than(A,B) ),
inference(copy,[status(thm)],[c_844]) ).
cnf(c_107,plain,
( less_than(A,B)
| ~ less_than(A,bottom) ),
inference(resolve,[status(thm)],[c_49,c_43]) ).
cnf(c_199,plain,
~ less_than(findmin_cpq_res(triple(sK3,sK1,sK4)),sK2),
inference(resolve,[status(thm)],[c_98,c_47]) ).
cnf(c_845,negated_conjecture,
( less_than(A,sK0(sK1,sK2,A))
| pair_in_list(update_slb(sK1,A),sK2,A)
| ~ strictly_less_than(sK2,A) ),
inference(resolve,[status(thm)],[c_96,c_97]) ).
cnf(c_214,negated_conjecture,
( less_than(A,sK2)
| less_than(A,sK0(sK1,sK2,A))
| pair_in_list(update_slb(sK1,A),sK2,A) ),
inference(resolve,[status(thm)],[c_845,c_106]) ).
cnf(c_846,negated_conjecture,
( pair_in_list(update_slb(sK1,A),sK2,sK0(sK1,sK2,A))
| pair_in_list(update_slb(sK1,A),sK2,A)
| ~ strictly_less_than(sK2,A) ),
inference(resolve,[status(thm)],[c_95,c_97]) ).
cnf(c_217,negated_conjecture,
( less_than(A,sK2)
| pair_in_list(update_slb(sK1,A),sK2,sK0(sK1,sK2,A))
| pair_in_list(update_slb(sK1,A),sK2,A) ),
inference(resolve,[status(thm)],[c_846,c_106]) ).
cnf(c_269,plain,
~ less_than(findmin_cpq_res(triple(sK3,sK1,sK4)),bottom),
inference(resolve,[status(thm)],[c_107,c_199]) ).
cnf(c_847,plain,
( ~ less_than(findmin_pqp_res(sK3),sK2)
| create_slb = sK1 ),
inference(paramod,[status(thm)],[c_92,c_199]) ).
cnf(c_271,plain,
( ~ less_than(findmin_pqp_res(sK3),sK2)
| sK1 = create_slb ),
inference(copy,[status(thm)],[c_847]) ).
cnf(c_848,negated_conjecture,
( ~ less_than(findmin_pqp_res(sK3),findmin_pqp_res(sK3))
| less_than(findmin_pqp_res(sK3),sK2)
| less_than(findmin_pqp_res(sK3),sK0(sK1,sK2,findmin_pqp_res(sK3))) ),
inference(resolve,[status(thm)],[c_214,c_100]) ).
cnf(c_500,negated_conjecture,
( less_than(findmin_pqp_res(sK3),sK2)
| less_than(findmin_pqp_res(sK3),sK0(sK1,sK2,findmin_pqp_res(sK3))) ),
inference(resolve,[status(thm)],[c_45,c_848]) ).
cnf(c_849,negated_conjecture,
( less_than(findmin_pqp_res(sK3),sK2)
| pair_in_list(update_slb(sK1,findmin_pqp_res(sK3)),sK2,findmin_pqp_res(sK3))
| ~ less_than(findmin_pqp_res(sK3),sK0(sK1,sK2,findmin_pqp_res(sK3))) ),
inference(resolve,[status(thm)],[c_100,c_217]) ).
cnf(c_850,negated_conjecture,
( less_than(findmin_pqp_res(sK3),sK2)
| less_than(findmin_pqp_res(sK3),sK2)
| pair_in_list(update_slb(sK1,findmin_pqp_res(sK3)),sK2,findmin_pqp_res(sK3)) ),
inference(resolve,[status(thm)],[c_849,c_500]) ).
cnf(c_851,negated_conjecture,
( less_than(findmin_pqp_res(sK3),sK2)
| pair_in_list(update_slb(sK1,findmin_pqp_res(sK3)),sK2,findmin_pqp_res(sK3)) ),
inference(copy,[status(thm)],[c_850]) ).
cnf(c_746,negated_conjecture,
less_than(findmin_pqp_res(sK3),sK2),
inference(resolve,[status(thm)],[c_99,c_851]) ).
cnf(c_747,plain,
sK1 = create_slb,
inference(resolve,[status(thm)],[c_746,c_271]) ).
cnf(c_852,plain,
~ less_than(findmin_cpq_res(triple(sK3,create_slb,sK4)),bottom),
inference(paramod,[status(thm)],[c_747,c_269]) ).
cnf(c_853,plain,
~ less_than(bottom,bottom),
inference(paramod,[status(thm)],[c_91,c_852]) ).
cnf(c_843,plain,
$false,
inference(resolve,[status(thm)],[c_45,c_853]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV408+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/11.00 % Computer : n001.cluster.edu
% 0.10/11.00 % Model : x86_64 x86_64
% 0.10/11.00 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/11.00 % Memory : 8046.5625MB
% 0.10/11.00 % OS : Linux 6.8.0-71-generic
% 0.10/11.00 % CPULimit : 300
% 0.10/11.00 % WCLimit : 300
% 0.10/11.00 % DateTime : Sat Sep 26 13:47:55 UTC 2026
% 0.10/11.01 % CPUTime :
% 0.10/11.01 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/11.01 % Process 1941219 was started by sandbox2 on n001,
% 0.10/11.01 % Sat Sep 26 13:47:55 2026
% 0.10/11.01 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/11.02
% 0.10/11.02 % From the command line: assign(max_seconds, 300).
% 0.16/11.53
% 0.16/11.53 % SZS status Theorem for theBenchmark
% 0.16/11.53
% 0.16/11.53 % Proof 1 at 0.44 (+ 0.04) seconds.
% 0.16/11.53 % Length of proof is 34.
% 0.16/11.53 % Level of proof is 7.
% 0.16/11.53 % Maximum clause weight is 31.000.
% 0.16/11.53 % Given clauses 166.
% 0.16/11.53
% 0.16/11.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------