%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWX194+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 07:07:23 PM UTC 2026
% Result : Theorem 67.63s 67.86s
% Output : Refutation 67.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 29
% Syntax : Number of clauses : 83 ( 59 unt; 24 nHn; 83 RR)
% Number of literals : 118 ( 0 equ; 7 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(proj1Suc(suc(u)),u),
file('SWX194+1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(suc(u),zero),
file('SWX194+1.p',unknown),
[] ).
cnf(6,axiom,
equal(addNat(zero,u),u),
file('SWX194+1.p',unknown),
[] ).
cnf(7,axiom,
equal(mulNat(zero,u),zero),
file('SWX194+1.p',unknown),
[] ).
cnf(17,axiom,
~ equal(n(u),v__dfg(v)),
file('SWX194+1.p',unknown),
[] ).
cnf(19,axiom,
equal(eval(u,n(v)),v),
file('SWX194+1.p',unknown),
[] ).
cnf(23,axiom,
~ equal(add(u,v),v__dfg(w)),
file('SWX194+1.p',unknown),
[] ).
cnf(24,axiom,
~ equal(mul(u,v),v__dfg(w)),
file('SWX194+1.p',unknown),
[] ).
cnf(25,axiom,
~ equal(eq(u,v),v__dfg(w)),
file('SWX194+1.p',unknown),
[] ).
cnf(27,axiom,
equal(fail12(n(suc(zero)),u),u),
file('SWX194+1.p',unknown),
[] ).
cnf(30,axiom,
equal(fetch(cons(u,v),zero),u),
file('SWX194+1.p',unknown),
[] ).
cnf(31,axiom,
equal(eval(u,simp1(v)),eval(u,v)),
file('SWX194+1.p',unknown),
[] ).
cnf(36,axiom,
equal(step1(eq(u,u)),n(suc(zero))),
file('SWX194+1.p',unknown),
[] ).
cnf(37,axiom,
equal(eval(u,v__dfg(v)),fetch(u,v)),
file('SWX194+1.p',unknown),
[] ).
cnf(40,axiom,
equal(addNat(suc(u),v),suc(addNat(u,v))),
file('SWX194+1.p',unknown),
[] ).
cnf(42,axiom,
equal(fetch(cons(u,v),suc(w)),fetch(v,w)),
file('SWX194+1.p',unknown),
[] ).
cnf(43,axiom,
equal(addNat(u,mulNat(v,u)),mulNat(suc(v),u)),
file('SWX194+1.p',unknown),
[] ).
cnf(48,axiom,
equal(step1(add(simp1(u),simp1(v))),simp1(add(u,v))),
file('SWX194+1.p',unknown),
[] ).
cnf(49,axiom,
equal(step1(mul(simp1(u),simp1(v))),simp1(mul(u,v))),
file('SWX194+1.p',unknown),
[] ).
cnf(50,axiom,
equal(step1(eq(simp1(u),simp1(v))),simp1(eq(u,v))),
file('SWX194+1.p',unknown),
[] ).
cnf(51,axiom,
( equal(n(proj1N(u)),u)
| equal(fail1(v,u),fail(v,u)) ),
file('SWX194+1.p',unknown),
[] ).
cnf(54,axiom,
( equal(n(proj1N(u)),u)
| equal(fail12(v,u),fail2(v,u)) ),
file('SWX194+1.p',unknown),
[] ).
cnf(56,axiom,
equal(step1(mul(n(suc(u)),v)),fail2(n(suc(u)),v)),
file('SWX194+1.p',unknown),
[] ).
cnf(59,axiom,
( equal(n(proj1N(u)),u)
| equal(step1(add(u,v)),fail(u,v)) ),
file('SWX194+1.p',unknown),
[] ).
cnf(61,axiom,
equal(addNat(eval(u,v),eval(u,w)),eval(u,add(v,w))),
file('SWX194+1.p',unknown),
[] ).
cnf(62,axiom,
equal(mulNat(eval(u,v),eval(u,w)),eval(u,mul(v,w))),
file('SWX194+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ equal(u,u)
| equal(u,v)
| equal(fail1(v__dfg(u),v__dfg(v)),mul(n(suc(suc(zero))),v__dfg(u))) ),
file('SWX194+1.p',unknown),
[] ).
cnf(71,axiom,
( equal(step1(u),u)
| equal(eq(proj1Eq(u),proj2Eq(u)),u)
| equal(mul(proj1Mul(u),proj2Mul(u)),u)
| equal(add(proj1Add(u),proj2Add(u)),u) ),
file('SWX194+1.p',unknown),
[] ).
cnf(72,axiom,
( equal(add(proj1Add(u),proj2Add(u)),u)
| equal(mul(proj1Mul(u),proj2Mul(u)),u)
| equal(eq(proj1Eq(u),proj2Eq(u)),u)
| equal(step1(u),simp1(u)) ),
file('SWX194+1.p',unknown),
[] ).
cnf(73,plain,
( equal(u,v)
| equal(fail1(v__dfg(u),v__dfg(v)),mul(n(suc(suc(zero))),v__dfg(u))) ),
inference(obv,[status(thm),theory(equality)],[69]),
[iquote('0:Obv:69.0')] ).
cnf(74,plain,
( equal(simp1(u),u)
| equal(eq(proj1Eq(u),proj2Eq(u)),u)
| equal(mul(proj1Mul(u),proj2Mul(u)),u)
| equal(add(proj1Add(u),proj2Add(u)),u) ),
inference(rew,[status(thm),theory(equality)],[71,72]),
[iquote('0:Rew:71.3,72.3')] ).
cnf(123,plain,
equal(mulNat(suc(zero),u),addNat(u,zero)),
inference(spr,[status(thm),theory(equality)],[7,43]),
[iquote('0:SpR:7.0,43.0')] ).
cnf(129,plain,
equal(addNat(u,addNat(u,zero)),mulNat(suc(suc(zero)),u)),
inference(spr,[status(thm),theory(equality)],[123,43]),
[iquote('0:SpR:123.0,43.0')] ).
cnf(139,plain,
equal(suc(addNat(u,addNat(suc(u),zero))),mulNat(suc(suc(zero)),suc(u))),
inference(spr,[status(thm),theory(equality)],[129,40]),
[iquote('0:SpR:129.0,40.0')] ).
cnf(145,plain,
equal(suc(addNat(u,suc(addNat(u,zero)))),mulNat(suc(suc(zero)),suc(u))),
inference(rew,[status(thm),theory(equality)],[40,139]),
[iquote('0:Rew:40.0,139.0')] ).
cnf(158,plain,
equal(simp1(eq(u,u)),n(suc(zero))),
inference(spr,[status(thm),theory(equality)],[50,36]),
[iquote('0:SpR:50.0,36.0')] ).
cnf(160,plain,
equal(eval(u,eq(v,v)),eval(u,n(suc(zero)))),
inference(spr,[status(thm),theory(equality)],[158,31]),
[iquote('0:SpR:158.0,31.0')] ).
cnf(164,plain,
equal(eval(u,eq(v,v)),suc(zero)),
inference(rew,[status(thm),theory(equality)],[19,160]),
[iquote('0:Rew:19.0,160.0')] ).
cnf(168,plain,
equal(step1(mul(n(suc(zero)),simp1(u))),simp1(mul(eq(v,v),u))),
inference(spr,[status(thm),theory(equality)],[158,49]),
[iquote('0:SpR:158.0,49.0')] ).
cnf(169,plain,
equal(fail2(n(suc(zero)),simp1(u)),simp1(mul(eq(v,v),u))),
inference(rew,[status(thm),theory(equality)],[56,168]),
[iquote('0:Rew:56.0,168.0')] ).
cnf(189,plain,
( equal(n(proj1N(u)),u)
| equal(fail2(n(suc(zero)),u),u) ),
inference(spr,[status(thm),theory(equality)],[54,27]),
[iquote('0:SpR:54.1,27.0')] ).
cnf(255,plain,
equal(eval(u,fail2(n(suc(zero)),simp1(v))),eval(u,mul(eq(w,w),v))),
inference(spr,[status(thm),theory(equality)],[169,31]),
[iquote('0:SpR:169.0,31.0')] ).
cnf(348,plain,
( equal(n(proj1N(simp1(u))),simp1(u))
| equal(fail(simp1(u),simp1(v)),simp1(add(u,v))) ),
inference(spr,[status(thm),theory(equality)],[59,48]),
[iquote('0:SpR:59.1,48.0')] ).
cnf(406,plain,
equal(eval(u,mul(n(v),w)),mulNat(v,eval(u,w))),
inference(spr,[status(thm),theory(equality)],[19,62]),
[iquote('0:SpR:19.0,62.0')] ).
cnf(409,plain,
equal(eval(u,mul(eq(v,v),w)),mulNat(suc(zero),eval(u,w))),
inference(spr,[status(thm),theory(equality)],[164,62]),
[iquote('0:SpR:164.0,62.0')] ).
cnf(415,plain,
equal(eval(u,mul(eq(v,v),w)),addNat(eval(u,w),zero)),
inference(rew,[status(thm),theory(equality)],[123,409]),
[iquote('0:Rew:123.0,409.0')] ).
cnf(416,plain,
equal(eval(u,fail2(n(suc(zero)),simp1(v))),addNat(eval(u,v),zero)),
inference(rew,[status(thm),theory(equality)],[415,255]),
[iquote('0:Rew:415.0,255.0')] ).
cnf(462,plain,
equal(addNat(eval(u,v),fetch(u,w)),eval(u,add(v,v__dfg(w)))),
inference(spr,[status(thm),theory(equality)],[37,61]),
[iquote('0:SpR:37.0,61.0')] ).
cnf(470,plain,
equal(addNat(fetch(u,v),eval(u,w)),eval(u,add(v__dfg(v),w))),
inference(spr,[status(thm),theory(equality)],[37,61]),
[iquote('0:SpR:37.0,61.0')] ).
cnf(472,plain,
equal(eval(u,add(eq(v,v),w)),addNat(suc(zero),eval(u,w))),
inference(spr,[status(thm),theory(equality)],[164,61]),
[iquote('0:SpR:164.0,61.0')] ).
cnf(479,plain,
equal(eval(u,add(eq(v,v),w)),suc(eval(u,w))),
inference(rew,[status(thm),theory(equality)],[6,472,40]),
[iquote('0:Rew:6.0,472.0,40.0,472.0')] ).
cnf(610,plain,
( equal(u,v)
| equal(n(proj1N(v__dfg(v))),v__dfg(v))
| equal(mul(n(suc(suc(zero))),v__dfg(u)),fail(v__dfg(u),v__dfg(v))) ),
inference(spr,[status(thm),theory(equality)],[73,51]),
[iquote('0:SpR:73.1,51.1')] ).
cnf(629,plain,
( equal(u,v)
| equal(mul(n(suc(suc(zero))),v__dfg(u)),fail(v__dfg(u),v__dfg(v))) ),
inference(mrr,[status(thm)],[610,17]),
[iquote('0:MRR:610.1,17.0')] ).
cnf(976,plain,
( ~ equal(u,v__dfg(v))
| equal(simp1(u),u)
| equal(mul(proj1Mul(u),proj2Mul(u)),u)
| equal(add(proj1Add(u),proj2Add(u)),u) ),
inference(spl,[status(thm),theory(equality)],[74,25]),
[iquote('0:SpL:74.1,25.0')] ).
cnf(2381,plain,
equal(addNat(u,eval(cons(u,v),w)),eval(cons(u,v),add(v__dfg(zero),w))),
inference(spr,[status(thm),theory(equality)],[30,470]),
[iquote('0:SpR:30.0,470.0')] ).
cnf(3475,plain,
( equal(u,v)
| equal(eval(w,fail(v__dfg(u),v__dfg(v))),mulNat(suc(suc(zero)),eval(w,v__dfg(u)))) ),
inference(spr,[status(thm),theory(equality)],[629,406]),
[iquote('0:SpR:629.1,406.0')] ).
cnf(3513,plain,
( equal(u,v)
| equal(eval(w,fail(v__dfg(u),v__dfg(v))),mulNat(suc(suc(zero)),fetch(w,u))) ),
inference(rew,[status(thm),theory(equality)],[37,3475]),
[iquote('0:Rew:37.0,3475.1')] ).
cnf(12493,plain,
( equal(simp1(v__dfg(u)),v__dfg(u))
| equal(mul(proj1Mul(v__dfg(u)),proj2Mul(v__dfg(u))),v__dfg(u))
| equal(add(proj1Add(v__dfg(u)),proj2Add(v__dfg(u))),v__dfg(u)) ),
inference(eqr,[status(thm),theory(equality)],[976]),
[iquote('0:EqR:976.0')] ).
cnf(12496,plain,
equal(simp1(v__dfg(u)),v__dfg(u)),
inference(mrr,[status(thm)],[12493,24,23]),
[iquote('0:MRR:12493.1,12493.2,24.0,23.0')] ).
cnf(12505,plain,
equal(eval(u,fail2(n(suc(zero)),v__dfg(v))),addNat(eval(u,v__dfg(v)),zero)),
inference(spr,[status(thm),theory(equality)],[12496,416]),
[iquote('0:SpR:12496.0,416.0')] ).
cnf(12522,plain,
( equal(n(proj1N(simp1(v__dfg(u)))),simp1(v__dfg(u)))
| equal(fail(v__dfg(u),simp1(v)),simp1(add(v__dfg(u),v))) ),
inference(spr,[status(thm),theory(equality)],[12496,348]),
[iquote('0:SpR:12496.0,348.1')] ).
cnf(12529,plain,
equal(eval(u,fail2(n(suc(zero)),v__dfg(v))),addNat(fetch(u,v),zero)),
inference(rew,[status(thm),theory(equality)],[37,12505]),
[iquote('0:Rew:37.0,12505.0')] ).
cnf(12534,plain,
( equal(n(proj1N(v__dfg(u))),v__dfg(u))
| equal(fail(v__dfg(u),simp1(v)),simp1(add(v__dfg(u),v))) ),
inference(rew,[status(thm),theory(equality)],[12496,12522]),
[iquote('0:Rew:12496.0,12522.0')] ).
cnf(12535,plain,
equal(fail(v__dfg(u),simp1(v)),simp1(add(v__dfg(u),v))),
inference(mrr,[status(thm)],[12534,17]),
[iquote('0:MRR:12534.0,17.0')] ).
cnf(12564,plain,
equal(simp1(add(v__dfg(u),v__dfg(v))),fail(v__dfg(u),v__dfg(v))),
inference(spr,[status(thm),theory(equality)],[12496,12535]),
[iquote('0:SpR:12496.0,12535.0')] ).
cnf(12950,plain,
equal(eval(u,fail(v__dfg(v),v__dfg(w))),eval(u,add(v__dfg(v),v__dfg(w)))),
inference(spr,[status(thm),theory(equality)],[12564,31]),
[iquote('0:SpR:12564.0,31.0')] ).
cnf(12997,plain,
( equal(u,v)
| equal(eval(w,add(v__dfg(u),v__dfg(v))),mulNat(suc(suc(zero)),fetch(w,u))) ),
inference(rew,[status(thm),theory(equality)],[12950,3513]),
[iquote('0:Rew:12950.0,3513.1')] ).
cnf(14093,plain,
( equal(n(proj1N(v__dfg(u))),v__dfg(u))
| equal(addNat(fetch(v,u),zero),eval(v,v__dfg(u))) ),
inference(spr,[status(thm),theory(equality)],[189,12529]),
[iquote('0:SpR:189.1,12529.0')] ).
cnf(14095,plain,
( equal(n(proj1N(v__dfg(u))),v__dfg(u))
| equal(addNat(fetch(v,u),zero),fetch(v,u)) ),
inference(rew,[status(thm),theory(equality)],[37,14093]),
[iquote('0:Rew:37.0,14093.1')] ).
cnf(14096,plain,
equal(addNat(fetch(u,v),zero),fetch(u,v)),
inference(mrr,[status(thm)],[14095,17]),
[iquote('0:MRR:14095.0,17.0')] ).
cnf(14138,plain,
equal(addNat(u,zero),u),
inference(spr,[status(thm),theory(equality)],[30,14096]),
[iquote('0:SpR:30.0,14096.0')] ).
cnf(14175,plain,
equal(suc(addNat(u,suc(u))),mulNat(suc(suc(zero)),suc(u))),
inference(rew,[status(thm),theory(equality)],[14138,145]),
[iquote('0:Rew:14138.0,145.0')] ).
cnf(35871,plain,
( equal(zero,u)
| equal(addNat(v,eval(cons(v,w),v__dfg(u))),mulNat(suc(suc(zero)),fetch(cons(v,w),zero))) ),
inference(spr,[status(thm),theory(equality)],[12997,2381]),
[iquote('0:SpR:12997.1,2381.0')] ).
cnf(35887,plain,
( equal(zero,u)
| equal(addNat(v,fetch(cons(v,w),u)),mulNat(suc(suc(zero)),v)) ),
inference(rew,[status(thm),theory(equality)],[37,35871,30]),
[iquote('0:Rew:37.0,35871.1,30.0,35871.1')] ).
cnf(37670,plain,
( equal(suc(u),zero)
| equal(addNat(v,fetch(w,u)),mulNat(suc(suc(zero)),v)) ),
inference(spr,[status(thm),theory(equality)],[42,35887]),
[iquote('0:SpR:42.0,35887.1')] ).
cnf(37714,plain,
equal(addNat(u,fetch(v,w)),mulNat(suc(suc(zero)),u)),
inference(mrr,[status(thm)],[37670,2]),
[iquote('0:MRR:37670.0,2.0')] ).
cnf(37716,plain,
equal(mulNat(suc(suc(zero)),eval(u,v)),eval(u,add(v,v__dfg(w)))),
inference(rew,[status(thm),theory(equality)],[37714,462]),
[iquote('0:Rew:37714.0,462.0')] ).
cnf(37890,plain,
equal(mulNat(suc(suc(zero)),eval(u,eq(v,v))),suc(eval(u,v__dfg(w)))),
inference(spr,[status(thm),theory(equality)],[37716,479]),
[iquote('0:SpR:37716.0,479.0')] ).
cnf(38107,plain,
equal(suc(fetch(u,v)),suc(suc(zero))),
inference(rew,[status(thm),theory(equality)],[6,37890,14175,164,37]),
[iquote('0:Rew:6.0,37890.0,14175.0,37890.0,164.0,37890.0,37.0,37890.0')] ).
cnf(38558,plain,
equal(proj1Suc(suc(suc(zero))),fetch(u,v)),
inference(spr,[status(thm),theory(equality)],[38107,1]),
[iquote('0:SpR:38107.0,1.0')] ).
cnf(41749,plain,
equal(fetch(u,v),suc(zero)),
inference(rew,[status(thm),theory(equality)],[1,38558]),
[iquote('0:Rew:1.0,38558.0')] ).
cnf(41762,plain,
equal(suc(zero),u),
inference(rew,[status(thm),theory(equality)],[41749,30]),
[iquote('0:Rew:41749.0,30.0')] ).
cnf(41939,plain,
$false,
inference(aed,[status(thm),theory(equality)],[2,41762]),
[iquote('0:AED:2.0,41762.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX194+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.15/0.33 % Computer : n019.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
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 10:19:14 EDT 2026
% 0.15/0.33 % CPUTime :
% 67.63/67.86
% 67.63/67.86 SPASS V 3.9
% 67.63/67.86 SPASS beiseite: Proof found.
% 67.63/67.86 % SZS status Theorem
% 67.63/67.86 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 67.63/67.86 SPASS derived 35838 clauses, backtracked 0 clauses, performed 0 splits and kept 13117 clauses.
% 67.63/67.86 SPASS allocated 150276 KBytes.
% 67.63/67.86 SPASS spent 0:01:07.47 on the problem.
% 67.63/67.86 0:00:00.04 for the input.
% 67.63/67.86 0:00:00.04 for the FLOTTER CNF translation.
% 67.63/67.86 0:00:00.42 for inferences.
% 67.63/67.86 0:00:00.00 for the backtracking.
% 67.63/67.86 0:01:06.81 for the reduction.
% 67.63/67.86
% 67.63/67.86
% 67.63/67.86 Here is a proof with depth 6, length 83 :
% 67.63/67.86 % SZS output start Refutation
% See solution above
% 67.63/67.86 Formulae used in the proof : axiom_004 axiom_005 axiom_062 axiom_064 axiom_017 axiom_066 axiom_020 axiom_022 axiom_023 axiom_041 axiom_060 goal_072 axiom_053 axiom_071 axiom_063 axiom_061 axiom_065 axiom_056 axiom_057 axiom_058 axiom_030 axiom_043 axiom_052 axiom_047 axiom_067 axiom_068 axiom_028 axiom_046 axiom_055
% 68.23/68.45
%------------------------------------------------------------------------------