%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWX204-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 09:16:20 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 33 unt; 0 def)
% Number of atoms : 33 ( 32 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 12 ( 12 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 5 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom,axiom,
! [VAR_0] : x2(z,VAR_0) = VAR_0,
file('theBenchmark.p',axiom) ).
cnf(c_1,plain,
x2(z,A) = A,
inference(clausify,[status(thm)],[axiom]) ).
fof(axiom_001,axiom,
! [VAR_0,VAR_1] : x2(s(VAR_0),VAR_1) = s(x2(VAR_0,VAR_1)),
file('theBenchmark.p',axiom_001) ).
cnf(c_2,plain,
x2(s(A),B) = s(x2(A,B)),
inference(clausify,[status(thm)],[axiom_001]) ).
cnf(c_3,plain,
s(x2(A,B)) = x2(s(A),B),
inference(copy,[status(thm)],[c_2]) ).
fof(axiom_002,axiom,
! [VAR_0] : x22(z,VAR_0) = z,
file('theBenchmark.p',axiom_002) ).
cnf(c_4,plain,
x22(z,A) = z,
inference(clausify,[status(thm)],[axiom_002]) ).
fof(axiom_003,axiom,
! [VAR_0,VAR_1] : x22(s(VAR_0),VAR_1) = x2(VAR_1,x22(VAR_0,VAR_1)),
file('theBenchmark.p',axiom_003) ).
cnf(c_5,plain,
x22(s(A),B) = x2(B,x22(A,B)),
inference(clausify,[status(thm)],[axiom_003]) ).
fof(axiom_004,axiom,
! [VAR_0] : mul_idem(VAR_0) = eq(x22(VAR_0,VAR_0),VAR_0),
file('theBenchmark.p',axiom_004) ).
cnf(c_6,plain,
mul_idem(A) = eq(x22(A,A),A),
inference(clausify,[status(thm)],[axiom_004]) ).
fof(axiom_007,axiom,
! [VAR_0,VAR_1] : eq(s(VAR_0),s(VAR_1)) = eq(VAR_0,VAR_1),
file('theBenchmark.p',axiom_007) ).
cnf(c_9,plain,
eq(s(A),s(B)) = eq(A,B),
inference(clausify,[status(thm)],[axiom_007]) ).
fof(axiom_009,axiom,
! [VAR_0] : eq(s(VAR_0),z) = bfalse,
file('theBenchmark.p',axiom_009) ).
cnf(c_11,plain,
eq(s(A),z) = bfalse,
inference(clausify,[status(thm)],[axiom_009]) ).
fof(axiom_011,axiom,
! [VAR_0] : eq2(VAR_0,VAR_0) = btrue,
file('theBenchmark.p',axiom_011) ).
cnf(c_13,plain,
eq2(A,A) = btrue,
inference(clausify,[status(thm)],[axiom_011]) ).
fof(goal,axiom,
! [VAR_0] : eq2(mul_idem(VAR_0),bfalse) != btrue,
file('theBenchmark.p',goal) ).
cnf(c_14,plain,
eq2(mul_idem(A),bfalse) != btrue,
inference(clausify,[status(thm)],[goal]) ).
cnf(c_15,plain,
eq2(eq(x22(A,A),A),bfalse) != btrue,
inference(paramod,[status(thm)],[c_6,c_14]) ).
cnf(c_16,plain,
s(A) = x2(s(z),A),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_18,plain,
eq(x2(s(A),B),s(C)) = eq(x2(A,B),C),
inference(paramod,[status(thm)],[c_3,c_9]) ).
cnf(c_21,plain,
eq(x2(s(A),B),z) = bfalse,
inference(paramod,[status(thm)],[c_3,c_11]) ).
cnf(c_32,plain,
eq2(eq(x2(s(A),x22(A,s(A))),s(A)),bfalse) != btrue,
inference(paramod,[status(thm)],[c_5,c_15]) ).
cnf(c_23,plain,
eq2(eq(x2(A,x22(A,s(A))),A),bfalse) != btrue,
inference(paramod,[status(thm)],[c_18,c_32]) ).
cnf(c_33,plain,
eq2(eq(s(x22(s(z),s(s(z)))),s(z)),bfalse) != btrue,
inference(paramod,[status(thm)],[c_16,c_23]) ).
cnf(c_34,plain,
eq2(eq(s(x2(s(s(z)),x22(z,s(s(z))))),s(z)),bfalse) != btrue,
inference(paramod,[status(thm)],[c_5,c_33]) ).
cnf(c_35,plain,
eq2(eq(s(x2(s(s(z)),z)),s(z)),bfalse) != btrue,
inference(paramod,[status(thm)],[c_4,c_34]) ).
cnf(c_36,plain,
eq2(eq(x2(s(s(s(z))),z),s(z)),bfalse) != btrue,
inference(paramod,[status(thm)],[c_3,c_35]) ).
cnf(c_37,plain,
eq2(eq(x2(s(s(z)),z),z),bfalse) != btrue,
inference(paramod,[status(thm)],[c_18,c_36]) ).
cnf(c_38,plain,
eq2(bfalse,bfalse) != btrue,
inference(paramod,[status(thm)],[c_21,c_37]) ).
cnf(c_39,plain,
btrue != btrue,
inference(paramod,[status(thm)],[c_13,c_38]) ).
cnf(c_31,plain,
$false,
inference(copy,[status(thm)],[c_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX204-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 16:58:25 UTC 2026
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.37 % Process 1501928 was started by sandbox2 on n026,
% 0.15/0.37 % Sat Sep 26 16:58:25 2026
% 0.15/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.38
% 0.15/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.39
% 0.15/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.39
% 0.15/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/0.39 % Length of proof is 16.
% 0.15/0.39 % Level of proof is 4.
% 0.15/0.39 % Maximum clause weight is 13.000.
% 0.15/0.39 % Given clauses 16.
% 0.15/0.39
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------