%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWX206-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 07:07:25 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.40s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 13 RR)
% Number of literals : 13 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(impl(btrue,u),u),
file('SWX206-1.p',unknown),
[] ).
cnf(3,axiom,
equal(x2__dfg(z__dfg,u),u),
file('SWX206-1.p',unknown),
[] ).
cnf(5,axiom,
equal(impl(eq(x2__dfg(u,u),u),eq2(btrue,bfalse)),plus_not_idem(u)),
file('SWX206-1.p',unknown),
[] ).
cnf(7,axiom,
equal(eq2(btrue,bfalse),bfalse),
file('SWX206-1.p',unknown),
[] ).
cnf(11,axiom,
equal(eq(u,u),btrue),
file('SWX206-1.p',unknown),
[] ).
cnf(12,axiom,
equal(eq2(u,u),btrue),
file('SWX206-1.p',unknown),
[] ).
cnf(13,axiom,
~ equal(eq2(plus_not_idem(u),bfalse),btrue),
file('SWX206-1.p',unknown),
[] ).
cnf(14,plain,
equal(impl(eq(x2__dfg(u,u),u),bfalse),plus_not_idem(u)),
inference(rew,[status(thm),theory(equality)],[7,5]),
[iquote('0:Rew:7.0,5.0')] ).
cnf(28,plain,
equal(impl(eq(z__dfg,z__dfg),bfalse),plus_not_idem(z__dfg)),
inference(spr,[status(thm),theory(equality)],[3,14]),
[iquote('0:SpR:3.0,14.0')] ).
cnf(30,plain,
equal(plus_not_idem(z__dfg),bfalse),
inference(rew,[status(thm),theory(equality)],[1,28,11]),
[iquote('0:Rew:1.0,28.0,11.0,28.0')] ).
cnf(33,plain,
~ equal(eq2(bfalse,bfalse),btrue),
inference(spl,[status(thm),theory(equality)],[30,13]),
[iquote('0:SpL:30.0,13.0')] ).
cnf(34,plain,
~ equal(btrue,btrue),
inference(rew,[status(thm),theory(equality)],[12,33]),
[iquote('0:Rew:12.0,33.0')] ).
cnf(35,plain,
$false,
inference(obv,[status(thm),theory(equality)],[34]),
[iquote('0:Obv:34.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX206-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.16/0.33 % Computer : n029.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 11:34:44 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.19/0.40
% 0.19/0.40 SPASS V 3.9
% 0.19/0.40 SPASS beiseite: Proof found.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.40 SPASS derived 17 clauses, backtracked 0 clauses, performed 0 splits and kept 16 clauses.
% 0.19/0.40 SPASS allocated 63111 KBytes.
% 0.19/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.40 0:00:00.03 for the input.
% 0.19/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.40 0:00:00.00 for inferences.
% 0.19/0.40 0:00:00.00 for the backtracking.
% 0.19/0.40 0:00:00.00 for the reduction.
% 0.19/0.40
% 0.19/0.40
% 0.19/0.40 Here is a proof with depth 2, length 13 :
% 0.19/0.40 % SZS output start Refutation
% See solution above
% 0.19/0.40 Formulae used in the proof : axiom axiom_002 axiom_004 axiom_006 axiom_010 axiom_011 goal
% 0.19/0.40
%------------------------------------------------------------------------------