%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 09:06:37 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 8 unt; 0 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 87 ( 45 ~; 42 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 34 ( 2 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause_2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( q3(VAR_0,VAR_1,VAR_2)
| less_or_equalish(VAR_0,VAR_1)
| ~ q1(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',clause_2) ).
cnf(c_5,plain,
( q3(A,B,C)
| less_or_equalish(A,B)
| ~ q1(A,B,C) ),
inference(clausify,[status(thm)],[clause_2]) ).
fof(clause_5,axiom,
q1(a,b,c),
file('theBenchmark.p',clause_5) ).
cnf(c_6,plain,
q1(a,b,c),
inference(clausify,[status(thm)],[clause_5]) ).
fof(clause_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( q2(VAR_0,VAR_1,VAR_2)
| ~ less_or_equalish(VAR_0,VAR_1)
| ~ q1(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',clause_1) ).
cnf(c_7,plain,
( q2(A,B,C)
| ~ less_or_equalish(A,B)
| ~ q1(A,B,C) ),
inference(clausify,[status(thm)],[clause_1]) ).
fof(clause_3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( q4(VAR_0,VAR_1,VAR_1)
| ~ q2(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',clause_3) ).
cnf(c_8,plain,
( q4(A,B,B)
| ~ q2(A,B,C) ),
inference(clausify,[status(thm)],[clause_3]) ).
cnf(c_9,plain,
( q2(a,b,c)
| ~ less_or_equalish(a,b) ),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_10,plain,
( q3(a,b,c)
| less_or_equalish(a,b) ),
inference(resolve,[status(thm)],[c_5,c_6]) ).
fof(clause_4,axiom,
! [VAR_0,VAR_1,VAR_2] :
( q4(VAR_0,VAR_1,VAR_0)
| ~ q3(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',clause_4) ).
cnf(c_11,plain,
( q4(A,B,A)
| ~ q3(A,B,C) ),
inference(clausify,[status(thm)],[clause_4]) ).
fof(clause_6,axiom,
! [VAR_0] :
( ~ less_or_equalish(VAR_0,a)
| ~ less_or_equalish(b,VAR_0)
| ~ less_or_equalish(a,VAR_0)
| ~ q4(a,b,VAR_0) ),
file('theBenchmark.p',clause_6) ).
cnf(c_12,plain,
( ~ less_or_equalish(A,a)
| ~ less_or_equalish(b,A)
| ~ less_or_equalish(a,A)
| ~ q4(a,b,A) ),
inference(clausify,[status(thm)],[clause_6]) ).
cnf(c_13,plain,
( q4(a,b,a)
| less_or_equalish(a,b) ),
inference(resolve,[status(thm)],[c_10,c_11]) ).
fof(clause_7,axiom,
! [VAR_0] :
( ~ less_or_equalish(VAR_0,b)
| ~ less_or_equalish(b,VAR_0)
| ~ less_or_equalish(a,VAR_0)
| ~ q4(a,b,VAR_0) ),
file('theBenchmark.p',clause_7) ).
cnf(c_14,plain,
( ~ less_or_equalish(A,b)
| ~ less_or_equalish(b,A)
| ~ less_or_equalish(a,A)
| ~ q4(a,b,A) ),
inference(clausify,[status(thm)],[clause_7]) ).
cnf(c_15,plain,
( ~ less_or_equalish(a,b)
| q4(a,b,b) ),
inference(resolve,[status(thm)],[c_8,c_9]) ).
cnf(c_16,plain,
( ~ less_or_equalish(b,b)
| ~ less_or_equalish(b,b)
| ~ less_or_equalish(a,b)
| ~ less_or_equalish(a,b) ),
inference(resolve,[status(thm)],[c_15,c_14]) ).
cnf(c_28,plain,
( ~ less_or_equalish(b,b)
| ~ less_or_equalish(b,b)
| ~ less_or_equalish(a,b) ),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_17,plain,
( ~ less_or_equalish(b,b)
| ~ less_or_equalish(a,b) ),
inference(copy,[status(thm)],[c_28]) ).
cnf(c_18,plain,
( less_or_equalish(a,b)
| ~ less_or_equalish(a,a)
| ~ less_or_equalish(b,a)
| ~ less_or_equalish(a,a) ),
inference(resolve,[status(thm)],[c_12,c_13]) ).
cnf(c_19,plain,
( less_or_equalish(a,b)
| ~ less_or_equalish(b,a)
| ~ less_or_equalish(a,a) ),
inference(copy,[status(thm)],[c_18]) ).
fof(all_less_or_equal,axiom,
! [VAR_0,VAR_1] :
( less_or_equalish(VAR_1,VAR_0)
| less_or_equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',all_less_or_equal) ).
cnf(c_20,plain,
( less_or_equalish(B,A)
| less_or_equalish(A,B) ),
inference(clausify,[status(thm)],[all_less_or_equal]) ).
fof(less_or_equal_reflexivity,axiom,
! [VAR_0] : less_or_equalish(VAR_0,VAR_0),
file('theBenchmark.p',less_or_equal_reflexivity) ).
cnf(c_22,plain,
less_or_equalish(A,A),
inference(clausify,[status(thm)],[less_or_equal_reflexivity]) ).
cnf(c_23,plain,
( less_or_equalish(a,b)
| ~ less_or_equalish(b,a) ),
inference(resolve,[status(thm)],[c_22,c_19]) ).
cnf(c_24,plain,
~ less_or_equalish(a,b),
inference(resolve,[status(thm)],[c_22,c_17]) ).
cnf(c_25,plain,
~ less_or_equalish(b,a),
inference(resolve,[status(thm)],[c_24,c_23]) ).
cnf(c_29,plain,
less_or_equalish(b,a),
inference(resolve,[status(thm)],[c_24,c_20]) ).
cnf(c_27,plain,
$false,
inference(resolve,[status(thm)],[c_25,c_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 13:04:49 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 1389301 was started by sandbox2 on n019,
% 0.13/0.36 % Sat Sep 26 13:04:49 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 21.
% 0.13/0.37 % Level of proof is 7.
% 0.13/0.37 % Maximum clause weight is 9.000.
% 0.13/0.37 % Given clauses 4.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------