%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWX222-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 07:07:27 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 23 RR)
% Number of literals : 23 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 10 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(aux(u,v,w,just(x)),eq(x,v)),
file('SWX222-1.p',unknown),
[] ).
cnf(3,axiom,
equal(notb(btrue),bfalse),
file('SWX222-1.p',unknown),
[] ).
cnf(6,axiom,
equal(index(cons(u,v),zero),just(u)),
file('SWX222-1.p',unknown),
[] ).
cnf(8,axiom,
equal(andb(btrue,u),u),
file('SWX222-1.p',unknown),
[] ).
cnf(13,axiom,
equal(nf(lam(u)),nf(u)),
file('SWX222-1.p',unknown),
[] ).
cnf(14,axiom,
equal(nf(var(u)),btrue),
file('SWX222-1.p',unknown),
[] ).
cnf(16,axiom,
equal(tc(u,lam(v),arr(w,x)),tc(cons(w,u),v,x)),
file('SWX222-1.p',unknown),
[] ).
cnf(20,axiom,
equal(aux(u,v,w,index(u,w)),tc(u,var(w),v)),
file('SWX222-1.p',unknown),
[] ).
cnf(21,axiom,
equal(notb(andb(nf(u),tc(nil,u,arr(a,arr(b,b))))),sat_synth_nf_k(u)),
file('SWX222-1.p',unknown),
[] ).
cnf(52,axiom,
equal(eq(u,u),btrue),
file('SWX222-1.p',unknown),
[] ).
cnf(55,axiom,
equal(eq4(u,u),btrue),
file('SWX222-1.p',unknown),
[] ).
cnf(56,axiom,
~ equal(eq4(sat_synth_nf_k(u),bfalse),btrue),
file('SWX222-1.p',unknown),
[] ).
cnf(108,plain,
equal(aux(cons(u,v),w,zero,just(u)),tc(cons(u,v),var(zero),w)),
inference(spr,[status(thm),theory(equality)],[6,20]),
[iquote('0:SpR:6.0,20.0')] ).
cnf(111,plain,
equal(tc(cons(u,v),var(zero),w),eq(u,w)),
inference(rew,[status(thm),theory(equality)],[2,108]),
[iquote('0:Rew:2.0,108.0')] ).
cnf(116,plain,
equal(notb(andb(nf(lam(u)),tc(cons(a,nil),u,arr(b,b)))),sat_synth_nf_k(lam(u))),
inference(spr,[status(thm),theory(equality)],[16,21]),
[iquote('0:SpR:16.0,21.0')] ).
cnf(124,plain,
equal(notb(andb(nf(u),tc(cons(a,nil),u,arr(b,b)))),sat_synth_nf_k(lam(u))),
inference(rew,[status(thm),theory(equality)],[13,116]),
[iquote('0:Rew:13.0,116.0')] ).
cnf(137,plain,
equal(notb(andb(nf(lam(u)),tc(cons(b,cons(a,nil)),u,b))),sat_synth_nf_k(lam(lam(u)))),
inference(spr,[status(thm),theory(equality)],[16,124]),
[iquote('0:SpR:16.0,124.0')] ).
cnf(145,plain,
equal(notb(andb(nf(u),tc(cons(b,cons(a,nil)),u,b))),sat_synth_nf_k(lam(lam(u)))),
inference(rew,[status(thm),theory(equality)],[13,137]),
[iquote('0:Rew:13.0,137.0')] ).
cnf(162,plain,
equal(notb(andb(nf(var(zero)),eq(b,b))),sat_synth_nf_k(lam(lam(var(zero))))),
inference(spr,[status(thm),theory(equality)],[111,145]),
[iquote('0:SpR:111.0,145.0')] ).
cnf(168,plain,
equal(sat_synth_nf_k(lam(lam(var(zero)))),bfalse),
inference(rew,[status(thm),theory(equality)],[3,162,8,14,52]),
[iquote('0:Rew:3.0,162.0,8.0,162.0,14.0,162.0,52.0,162.0')] ).
cnf(173,plain,
~ equal(eq4(bfalse,bfalse),btrue),
inference(spl,[status(thm),theory(equality)],[168,56]),
[iquote('0:SpL:168.0,56.0')] ).
cnf(174,plain,
~ equal(btrue,btrue),
inference(rew,[status(thm),theory(equality)],[55,173]),
[iquote('0:Rew:55.0,173.0')] ).
cnf(175,plain,
$false,
inference(obv,[status(thm),theory(equality)],[174]),
[iquote('0:Obv:174.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX222-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.13 % Command : run_spass %d %s
% 0.15/0.33 % Computer : n018.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 12:34:46 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.19/0.42
% 0.19/0.42 SPASS V 3.9
% 0.19/0.42 SPASS beiseite: Proof found.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 93 clauses, backtracked 0 clauses, performed 0 splits and kept 76 clauses.
% 0.19/0.42 SPASS allocated 63326 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.19/0.42 0:00:00.03 for the input.
% 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42 0:00:00.00 for inferences.
% 0.19/0.42 0:00:00.00 for the backtracking.
% 0.19/0.42 0:00:00.01 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 4, length 23 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : axiom_001 axiom_002 axiom_005 axiom_007 axiom_012 axiom_013 axiom_015 axiom_019 axiom_020 axiom_051 axiom_054 goal
% 0.19/0.42
%------------------------------------------------------------------------------