%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN631-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 09:39:00 AM UTC 2026
% Result : Unsatisfiable 0.37s 0.47s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 17 unt; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 84 ( 47 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 78 ( 8 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p10_1,axiom,
! [VAR_0] : p10(VAR_0,VAR_0),
file('theBenchmark.p',p10_1) ).
cnf(c_1,plain,
p10(A,A),
inference(clausify,[status(thm)],[p10_1]) ).
fof(p5_5,axiom,
! [VAR_0] : p5(VAR_0,VAR_0),
file('theBenchmark.p',p5_5) ).
cnf(c_5,plain,
p5(A,A),
inference(clausify,[status(thm)],[p5_5]) ).
fof(p5_11,axiom,
! [VAR_0,VAR_1] : p5(f16(f18(VAR_0,VAR_1)),VAR_1),
file('theBenchmark.p',p5_11) ).
cnf(c_11,plain,
p5(f16(f18(A,B)),B),
inference(clausify,[status(thm)],[p5_11]) ).
fof(p23_12,axiom,
p23(f13(c27,f14(c28)),f11(f15(c24))),
file('theBenchmark.p',p23_12) ).
cnf(c_12,plain,
p23(f13(c27,f14(c28)),f11(f15(c24))),
inference(clausify,[status(thm)],[p23_12]) ).
fof(not_p23_13,axiom,
~ p23(f13(f16(c27),f14(c28)),f11(c24)),
file('theBenchmark.p',not_p23_13) ).
cnf(c_13,plain,
~ p23(f13(f16(c27),f14(c28)),f11(c24)),
inference(clausify,[status(thm)],[not_p23_13]) ).
fof(p5_18,axiom,
! [VAR_0,VAR_1] :
( ~ p5(VAR_0,VAR_1)
| p5(f16(VAR_0),f16(VAR_1)) ),
file('theBenchmark.p',p5_18) ).
cnf(c_18,plain,
( ~ p5(A,B)
| p5(f16(A),f16(B)) ),
inference(clausify,[status(thm)],[p5_18]) ).
fof(p5_25,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p5(VAR_2,VAR_1)
| ~ p5(VAR_2,VAR_0)
| p5(VAR_0,VAR_1) ),
file('theBenchmark.p',p5_25) ).
cnf(c_25,plain,
( ~ p5(C,B)
| ~ p5(C,A)
| p5(A,B) ),
inference(clausify,[status(thm)],[p5_25]) ).
fof(p23_29,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ p10(VAR_3,VAR_1)
| ~ p23(VAR_2,VAR_3)
| ~ p12(VAR_2,VAR_0)
| p23(VAR_0,VAR_1) ),
file('theBenchmark.p',p23_29) ).
cnf(c_29,plain,
( ~ p10(D,B)
| ~ p23(C,D)
| ~ p12(C,A)
| p23(A,B) ),
inference(clausify,[status(thm)],[p23_29]) ).
fof(p12_32,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ p5(VAR_1,VAR_3)
| ~ p5(VAR_0,VAR_2)
| p12(f13(VAR_0,VAR_1),f13(VAR_2,VAR_3)) ),
file('theBenchmark.p',p12_32) ).
cnf(c_32,plain,
( ~ p5(B,D)
| ~ p5(A,C)
| p12(f13(A,B),f13(C,D)) ),
inference(clausify,[status(thm)],[p12_32]) ).
fof(p5_34,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p23(f13(VAR_0,VAR_2),f11(f15(VAR_1)))
| p5(VAR_0,f18(f20(c29),f19(VAR_1,VAR_0,VAR_2))) ),
file('theBenchmark.p',p5_34) ).
cnf(c_34,plain,
( ~ p23(f13(A,C),f11(f15(B)))
| p5(A,f18(f20(c29),f19(B,A,C))) ),
inference(clausify,[status(thm)],[p5_34]) ).
fof(p23_35,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p23(f13(VAR_1,VAR_2),f11(f15(VAR_0)))
| p23(f13(f19(VAR_0,VAR_1,VAR_2),VAR_2),f11(VAR_0)) ),
file('theBenchmark.p',p23_35) ).
cnf(c_35,plain,
( ~ p23(f13(B,C),f11(f15(A)))
| p23(f13(f19(A,B,C),C),f11(A)) ),
inference(clausify,[status(thm)],[p23_35]) ).
cnf(c_3364,plain,
( ~ p5(f16(f18(C,A)),B)
| p5(A,B) ),
inference(resolve,[status(thm)],[c_25,c_11]) ).
cnf(c_45,plain,
p5(A,f16(f18(B,A))),
inference(resolve,[status(thm)],[c_3364,c_5]) ).
cnf(c_47,plain,
( ~ p10(B,f11(c24))
| ~ p23(A,B)
| ~ p12(A,f13(f16(c27),f14(c28))) ),
inference(resolve,[status(thm)],[c_29,c_13]) ).
cnf(c_64,plain,
p5(c27,f18(f20(c29),f19(c24,c27,f14(c28)))),
inference(resolve,[status(thm)],[c_34,c_12]) ).
cnf(c_65,plain,
p23(f13(f19(c24,c27,f14(c28)),f14(c28)),f11(c24)),
inference(resolve,[status(thm)],[c_35,c_12]) ).
cnf(c_180,plain,
( ~ p23(A,f11(c24))
| ~ p12(A,f13(f16(c27),f14(c28))) ),
inference(resolve,[status(thm)],[c_47,c_1]) ).
cnf(c_184,plain,
( ~ p5(B,f14(c28))
| ~ p5(A,f16(c27))
| ~ p23(f13(A,B),f11(c24)) ),
inference(resolve,[status(thm)],[c_180,c_32]) ).
cnf(c_192,plain,
( ~ p5(C,f16(c27))
| ~ p5(C,A)
| ~ p5(B,f14(c28))
| ~ p23(f13(A,B),f11(c24)) ),
inference(resolve,[status(thm)],[c_184,c_25]) ).
cnf(c_3365,plain,
( ~ p5(B,D)
| p12(f13(A,B),f13(f16(f18(C,A)),D)) ),
inference(resolve,[status(thm)],[c_32,c_45]) ).
cnf(c_255,plain,
p12(f13(A,B),f13(f16(f18(C,A)),B)),
inference(resolve,[status(thm)],[c_3365,c_5]) ).
cnf(c_1407,plain,
( ~ p5(f16(c27),A)
| ~ p5(B,f14(c28))
| ~ p23(f13(A,B),f11(c24)) ),
inference(resolve,[status(thm)],[c_192,c_5]) ).
cnf(c_1450,plain,
( ~ p5(f16(c27),A)
| ~ p23(f13(A,f14(c28)),f11(c24)) ),
inference(resolve,[status(thm)],[c_1407,c_5]) ).
cnf(c_1456,plain,
( ~ p5(c27,A)
| ~ p23(f13(f16(A),f14(c28)),f11(c24)) ),
inference(resolve,[status(thm)],[c_1450,c_18]) ).
cnf(c_2253,plain,
~ p23(f13(f16(f18(f20(c29),f19(c24,c27,f14(c28)))),f14(c28)),f11(c24)),
inference(resolve,[status(thm)],[c_64,c_1456]) ).
cnf(c_3366,plain,
( ~ p10(E,D)
| ~ p23(f13(B,C),E)
| p23(f13(f16(f18(A,B)),C),D) ),
inference(resolve,[status(thm)],[c_29,c_255]) ).
cnf(c_3367,plain,
( ~ p10(f11(c24),B)
| p23(f13(f16(f18(A,f19(c24,c27,f14(c28)))),f14(c28)),B) ),
inference(resolve,[status(thm)],[c_3366,c_65]) ).
cnf(c_3362,plain,
p23(f13(f16(f18(A,f19(c24,c27,f14(c28)))),f14(c28)),f11(c24)),
inference(resolve,[status(thm)],[c_3367,c_1]) ).
cnf(c_3363,plain,
$false,
inference(resolve,[status(thm)],[c_3362,c_2253]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN631-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Sat Sep 26 18:17:20 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.30 % Process 1226672 was started by sandbox2 on n012,
% 0.02/0.30 % Sat Sep 26 18:17:20 2026
% 0.02/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/0.31
% 0.02/0.31 % From the command line: assign(max_seconds, 300).
% 0.37/0.47
% 0.37/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.37/0.47
% 0.37/0.47 % Proof 1 at 0.10 (+ 0.05) seconds.
% 0.37/0.47 % Length of proof is 25.
% 0.37/0.47 % Level of proof is 9.
% 0.37/0.47 % Maximum clause weight is 45.000.
% 0.37/0.47 % Given clauses 104.
% 0.37/0.47
% 0.37/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------