%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU080+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 08:44:59 AM UTC 2026
% Result : Theorem 0.17s 0.51s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 13 unt; 0 def)
% Number of atoms : 69 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 65 ( 23 ~; 16 |; 19 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 1 sgn 13 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t158_funct_1,axiom,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( ( subset(A,relation_rng(C))
& subset(relation_inverse_image(C,A),relation_inverse_image(C,B)) )
=> subset(A,B) ) ),
file('theBenchmark.p',t158_funct_1) ).
fof(t161_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( ( subset(B,relation_rng(C))
& subset(A,relation_rng(C))
& relation_inverse_image(C,A) = relation_inverse_image(C,B) )
=> A = B ) ),
file('theBenchmark.p',t161_funct_1) ).
fof(t161_funct_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( ( subset(B,relation_rng(C))
& subset(A,relation_rng(C))
& relation_inverse_image(C,A) = relation_inverse_image(C,B) )
=> A = B ) ),
inference(assume_negation,[status(cth)],[t161_funct_1]) ).
cnf(c_38,plain,
( subset(B,C)
| ~ subset(B,relation_rng(A))
| ~ subset(relation_inverse_image(A,B),relation_inverse_image(A,C))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t158_funct_1]) ).
fof(nnf_32,plain,
? [A,B,C] :
( B != A
& subset(B,relation_rng(C))
& subset(A,relation_rng(C))
& relation_inverse_image(C,B) = relation_inverse_image(C,A)
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[t161_funct_1_neg]) ).
fof(sk_t161_funct_1_neg,plain,
( sK1 != sK2
& subset(sK1,relation_rng(sK0))
& subset(sK2,relation_rng(sK0))
& relation_inverse_image(sK0,sK1) = relation_inverse_image(sK0,sK2)
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK2),skolemize(B,sK1),skolemize(C,sK0)],[nnf_32]) ).
cnf(c_39,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t161_funct_1_neg]) ).
cnf(c_40,negated_conjecture,
( subset(A,B)
| ~ subset(A,relation_rng(sK0))
| ~ subset(relation_inverse_image(sK0,A),relation_inverse_image(sK0,B))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_39,c_38]) ).
cnf(c_45,negated_conjecture,
sK1 != sK2,
inference(split_conjunct,[status(thm)],[sk_t161_funct_1_neg]) ).
cnf(c_46,negated_conjecture,
subset(sK1,relation_rng(sK0)),
inference(split_conjunct,[status(thm)],[sk_t161_funct_1_neg]) ).
cnf(c_47,negated_conjecture,
subset(sK2,relation_rng(sK0)),
inference(split_conjunct,[status(thm)],[sk_t161_funct_1_neg]) ).
cnf(c_48,negated_conjecture,
relation_inverse_image(sK0,sK1) = relation_inverse_image(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_t161_funct_1_neg]) ).
cnf(c_49,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t161_funct_1_neg]) ).
cnf(c_59,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_82,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(clausify,[status(thm)],[d10_xboole_0]) ).
cnf(c_87,negated_conjecture,
( subset(A,B)
| ~ subset(A,relation_rng(sK0))
| ~ subset(relation_inverse_image(sK0,A),relation_inverse_image(sK0,B)) ),
inference(resolve,[status(thm)],[c_49,c_40]) ).
cnf(c_241,plain,
( subset(sK1,A)
| ~ subset(sK1,relation_rng(sK0))
| ~ subset(relation_inverse_image(sK0,sK2),relation_inverse_image(sK0,A)) ),
inference(paramod,[status(thm)],[c_48,c_87]) ).
cnf(c_121,negated_conjecture,
( subset(sK1,A)
| ~ subset(relation_inverse_image(sK0,sK2),relation_inverse_image(sK0,A)) ),
inference(resolve,[status(thm)],[c_46,c_241]) ).
cnf(c_227,plain,
subset(sK1,sK2),
inference(resolve,[status(thm)],[c_121,c_59]) ).
cnf(c_242,plain,
( ~ subset(sK2,sK1)
| sK1 = sK2 ),
inference(resolve,[status(thm)],[c_227,c_82]) ).
cnf(c_233,negated_conjecture,
~ subset(sK2,sK1),
inference(resolve,[status(thm)],[c_45,c_242]) ).
cnf(c_243,negated_conjecture,
( subset(sK2,A)
| ~ subset(relation_inverse_image(sK0,sK2),relation_inverse_image(sK0,A)) ),
inference(resolve,[status(thm)],[c_87,c_47]) ).
cnf(c_244,negated_conjecture,
~ subset(relation_inverse_image(sK0,sK2),relation_inverse_image(sK0,sK1)),
inference(resolve,[status(thm)],[c_243,c_233]) ).
cnf(c_245,negated_conjecture,
~ subset(relation_inverse_image(sK0,sK2),relation_inverse_image(sK0,sK2)),
inference(paramod,[status(thm)],[c_48,c_244]) ).
cnf(c_240,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_59,c_245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU080+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n002.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 08:37:51 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 1273341 was started by sandbox2 on n002,
% 0.17/0.45 % Sat Sep 26 08:37:51 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.47
% 0.17/0.47 % From the command line: assign(max_seconds, 300).
% 0.17/0.51
% 0.17/0.51 % SZS status Theorem for theBenchmark
% 0.17/0.51
% 0.17/0.51 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.17/0.51 % Length of proof is 19.
% 0.17/0.51 % Level of proof is 7.
% 0.17/0.51 % Maximum clause weight is 26.000.
% 0.17/0.51 % Given clauses 121.
% 0.17/0.51
% 0.17/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------