%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWX228-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 07:07:28 PM UTC 2026
% Result : Unsatisfiable 0.85s 1.04s
% Output : Refutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of clauses : 29 ( 25 unt; 0 nHn; 29 RR)
% Number of literals : 33 ( 0 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(aux(u,v,w,bfalse),cons(v,union(w,u))),
file('SWX228-1.p',unknown),
[] ).
cnf(4,axiom,
equal(barbar(bfalse,u),u),
file('SWX228-1.p',unknown),
[] ).
cnf(6,axiom,
equal(eqNat(s(u),z__dfg),bfalse),
file('SWX228-1.p',unknown),
[] ).
cnf(7,axiom,
equal(eqNat(z__dfg,s(u)),bfalse),
file('SWX228-1.p',unknown),
[] ).
cnf(9,axiom,
equal(elem(u,nil),bfalse),
file('SWX228-1.p',unknown),
[] ).
cnf(10,axiom,
equal(barbar(eqNat(u,v),elem(u,w)),elem(u,cons(v,w))),
file('SWX228-1.p',unknown),
[] ).
cnf(12,axiom,
equal(aux(u,v,w,elem(v,u)),union(cons(v,w),u)),
file('SWX228-1.p',unknown),
[] ).
cnf(13,axiom,
equal(eq(union(u,v),union(v,u)),prop_union_comm(u,v)),
file('SWX228-1.p',unknown),
[] ).
cnf(18,axiom,
equal(eq2(z__dfg,s(u)),bfalse),
file('SWX228-1.p',unknown),
[] ).
cnf(21,axiom,
equal(eq3(u,u),btrue),
file('SWX228-1.p',unknown),
[] ).
cnf(22,axiom,
( ~ equal(eq2(u,v),bfalse)
| equal(eq(cons(u,w),cons(v,x)),bfalse) ),
file('SWX228-1.p',unknown),
[] ).
cnf(26,axiom,
~ equal(eq3(prop_union_comm(u,v),bfalse),btrue),
file('SWX228-1.p',unknown),
[] ).
cnf(62,plain,
equal(elem(u,cons(v,nil)),barbar(eqNat(u,v),bfalse)),
inference(spr,[status(thm),theory(equality)],[9,10]),
[iquote('0:SpR:9.0,10.0')] ).
cnf(65,plain,
equal(elem(z__dfg,cons(s(u),v)),barbar(bfalse,elem(z__dfg,v))),
inference(spr,[status(thm),theory(equality)],[7,10]),
[iquote('0:SpR:7.0,10.0')] ).
cnf(68,plain,
equal(elem(z__dfg,cons(s(u),v)),elem(z__dfg,v)),
inference(rew,[status(thm),theory(equality)],[4,65]),
[iquote('0:Rew:4.0,65.0')] ).
cnf(78,plain,
equal(aux(cons(s(u),v),z__dfg,w,elem(z__dfg,v)),union(cons(z__dfg,w),cons(s(u),v))),
inference(spr,[status(thm),theory(equality)],[68,12]),
[iquote('0:SpR:68.0,12.0')] ).
cnf(85,plain,
equal(aux(cons(u,nil),v,w,barbar(eqNat(v,u),bfalse)),union(cons(v,w),cons(u,nil))),
inference(spr,[status(thm),theory(equality)],[62,12]),
[iquote('0:SpR:62.0,12.0')] ).
cnf(538,plain,
equal(aux(cons(s(u),nil),z__dfg,v,bfalse),union(cons(z__dfg,v),cons(s(u),nil))),
inference(spr,[status(thm),theory(equality)],[9,78]),
[iquote('0:SpR:9.0,78.0')] ).
cnf(553,plain,
equal(cons(z__dfg,union(u,cons(s(v),nil))),union(cons(z__dfg,u),cons(s(v),nil))),
inference(rew,[status(thm),theory(equality)],[2,538]),
[iquote('0:Rew:2.0,538.0')] ).
cnf(601,plain,
( ~ equal(eq2(z__dfg,u),bfalse)
| equal(eq(union(cons(z__dfg,v),cons(s(w),nil)),cons(u,x)),bfalse) ),
inference(spr,[status(thm),theory(equality)],[553,22]),
[iquote('0:SpR:553.0,22.1')] ).
cnf(665,plain,
equal(aux(cons(z__dfg,nil),s(u),v,barbar(bfalse,bfalse)),union(cons(s(u),v),cons(z__dfg,nil))),
inference(spr,[status(thm),theory(equality)],[6,85]),
[iquote('0:SpR:6.0,85.0')] ).
cnf(669,plain,
equal(cons(s(u),union(v,cons(z__dfg,nil))),union(cons(s(u),v),cons(z__dfg,nil))),
inference(rew,[status(thm),theory(equality)],[2,665,4]),
[iquote('0:Rew:2.0,665.0,4.0,665.0')] ).
cnf(2921,plain,
( ~ equal(eq2(z__dfg,s(u)),bfalse)
| equal(eq(union(cons(z__dfg,v),cons(s(w),nil)),union(cons(s(u),x),cons(z__dfg,nil))),bfalse) ),
inference(spr,[status(thm),theory(equality)],[669,601]),
[iquote('0:SpR:669.0,601.1')] ).
cnf(2928,plain,
( ~ equal(bfalse,bfalse)
| equal(eq(union(cons(z__dfg,u),cons(s(v),nil)),union(cons(s(w),x),cons(z__dfg,nil))),bfalse) ),
inference(rew,[status(thm),theory(equality)],[18,2921]),
[iquote('0:Rew:18.0,2921.0')] ).
cnf(2929,plain,
equal(eq(union(cons(z__dfg,u),cons(s(v),nil)),union(cons(s(w),x),cons(z__dfg,nil))),bfalse),
inference(obv,[status(thm),theory(equality)],[2928]),
[iquote('0:Obv:2928.0')] ).
cnf(2930,plain,
equal(prop_union_comm(cons(z__dfg,nil),cons(s(u),nil)),bfalse),
inference(spr,[status(thm),theory(equality)],[2929,13]),
[iquote('0:SpR:2929.0,13.0')] ).
cnf(2944,plain,
~ equal(eq3(bfalse,bfalse),btrue),
inference(spl,[status(thm),theory(equality)],[2930,26]),
[iquote('0:SpL:2930.0,26.0')] ).
cnf(2945,plain,
~ equal(btrue,btrue),
inference(rew,[status(thm),theory(equality)],[21,2944]),
[iquote('0:Rew:21.0,2944.0')] ).
cnf(2946,plain,
$false,
inference(obv,[status(thm),theory(equality)],[2945]),
[iquote('0:Obv:2945.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX228-1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.17/0.34 % Computer : n019.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 12:55:59 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.85/1.04
% 0.85/1.04 SPASS V 3.9
% 0.85/1.04 SPASS beiseite: Proof found.
% 0.85/1.04 % SZS status Theorem
% 0.85/1.04 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.85/1.04 SPASS derived 2220 clauses, backtracked 0 clauses, performed 0 splits and kept 1068 clauses.
% 0.85/1.04 SPASS allocated 68846 KBytes.
% 0.85/1.04 SPASS spent 0:00:00.65 on the problem.
% 0.85/1.04 0:00:00.03 for the input.
% 0.85/1.04 0:00:00.00 for the FLOTTER CNF translation.
% 0.85/1.04 0:00:00.05 for inferences.
% 0.85/1.04 0:00:00.00 for the backtracking.
% 0.85/1.04 0:00:00.54 for the reduction.
% 0.85/1.04
% 0.85/1.04
% 0.85/1.04 Here is a proof with depth 7, length 29 :
% 0.85/1.04 % SZS output start Refutation
% See solution above
% 0.85/1.04 Formulae used in the proof : axiom_001 axiom_003 axiom_005 axiom_006 axiom_008 axiom_009 axiom_011 axiom_012 axiom_017 axiom_020 axiom_021 goal
% 0.85/1.04
%------------------------------------------------------------------------------