%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYO038-1.003.003 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 : Fri Sep 25 03:47:39 PM UTC 2026
% Result : Unsatisfiable 18.18s 2.75s
% Output : Proof 18.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 64
% Number of leaves : 7
% Syntax : Number of formulae : 118 ( 114 unt; 0 def)
% Number of atoms : 122 ( 106 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 11 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-4 aty)
% Number of variables : 53 ( 6 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,axiom,
f(s(N),s(X)) = f(N,f(s(N),X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f2_nnf,plain,
! [N,X] : f(s(N),s(X)) = f(N,f(s(N),X)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [N,X] : f(s(N),s(X)) = f(N,f(s(N),X)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
f(s(X0),s(X1)) = f(X0,f(s(X0),X1)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t5,plain,
f(X1,f(s(X1),X2)) = f(s(X1),s(X2)),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t12,plain,
f(X1,f(s(X1),X2)) = f(s(X1),s(X2)),
inference(orient,[status(thm)],[t5]) ).
cnf(t16,plain,
f(s(X1),s(f(s(s(X1)),X2))) = f(X1,f(s(s(X1)),s(X2))),
inference(cp,[status(thm)],[t12,t12]) ).
cnf(t55,plain,
f(s(X1),s(f(s(s(X1)),X2))) = f(X1,f(s(s(X1)),s(X2))),
inference(orient,[status(thm)],[t16]) ).
cnf(f1,axiom,
f(one,s(X)) = s(s(f(one,X))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f1_nnf,plain,
! [X] : f(one,s(X)) = s(s(f(one,X))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : f(one,s(X)) = s(s(f(one,X))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
f(one,s(X0)) = s(s(f(one,X0))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t4,plain,
s(s(f(one,X1))) = f(one,s(X1)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t9,plain,
s(s(f(one,X1))) = f(one,s(X1)),
inference(orient,[status(thm)],[t4]) ).
cnf(f0,axiom,
f(N,one) = s(one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f0_nnf,plain,
! [N] : f(N,one) = s(one),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [N] : f(N,one) = s(one),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
f(X0,one) = s(one),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t1,plain,
f(X1,one) = s(one),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t7,plain,
f(X1,one) = s(one),
inference(orient,[status(thm)],[t1]) ).
cnf(t10,plain,
f(one,s(one)) = s(s(s(one))),
inference(cp,[status(thm)],[t9,t7]) ).
cnf(t11,plain,
s(s(s(one))) = f(one,s(one)),
inference(orient,[status(thm)],[t10]) ).
cnf(t59,plain,
f(s(one),f(s(s(s(one))),s(X1))) = f(s(s(one)),s(f(f(one,s(one)),X1))),
inference(cp,[status(thm)],[t55,t11]) ).
cnf(t217,plain,
f(s(one),f(f(one,s(one)),s(X1))) = f(s(s(one)),s(f(f(one,s(one)),X1))),
inference(step,[status(thm)],[t59,t11]) ).
cnf(t166,plain,
f(s(s(one)),s(f(f(one,s(one)),X1))) = f(s(one),f(f(one,s(one)),s(X1))),
inference(orient,[status(thm)],[t217]) ).
cnf(t167,plain,
f(s(one),f(f(one,s(one)),s(one))) = f(s(s(one)),s(s(one))),
inference(cp,[status(thm)],[t166,t7]) ).
cnf(t13,plain,
f(s(X1),s(one)) = f(X1,s(one)),
inference(cp,[status(thm)],[t12,t7]) ).
cnf(t18,plain,
f(s(X1),s(one)) = f(X1,s(one)),
inference(orient,[status(thm)],[t13]) ).
cnf(t19,plain,
f(s(f(one,X1)),s(one)) = f(f(one,s(X1)),s(one)),
inference(cp,[status(thm)],[t18,t9]) ).
cnf(t176,plain,
f(f(one,X1),s(one)) = f(f(one,s(X1)),s(one)),
inference(step,[status(thm)],[t19,t18]) ).
cnf(t28,plain,
f(f(one,s(X1)),s(one)) = f(f(one,X1),s(one)),
inference(orient,[status(thm)],[t176]) ).
cnf(t218,plain,
f(s(one),f(f(one,one),s(one))) = f(s(s(one)),s(s(one))),
inference(step,[status(thm)],[t167,t28]) ).
cnf(t219,plain,
f(s(one),f(s(one),s(one))) = f(s(s(one)),s(s(one))),
inference(step,[status(thm)],[t218,t7]) ).
cnf(t220,plain,
f(s(one),f(one,s(one))) = f(s(s(one)),s(s(one))),
inference(step,[status(thm)],[t219,t18]) ).
cnf(t174,plain,
f(s(s(one)),s(s(one))) = f(s(one),f(one,s(one))),
inference(orient,[status(thm)],[t220]) ).
cnf(f4,axiom,
( d(s(X))
| ~ d(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
fof(f4_nnf,plain,
! [X] :
( d(s(X))
| ~ d(X) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] :
( d(s(X))
| ~ d(X) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( d(s(X0))
| ~ d(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t3,plain,
ifeq(d(X1),true,d(s(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t32,plain,
ifeq(d(X1),true,d(s(X1)),true) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(f3,axiom,
d(one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f3_nnf,plain,
d(one),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
d(one),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(t0,plain,
d(one) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t6,plain,
d(one) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t33,plain,
true = ifeq(true,true,d(s(one)),true),
inference(cp,[status(thm)],[t32,t6]) ).
cnf(t2,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t8,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(t177,plain,
true = d(s(one)),
inference(step,[status(thm)],[t33,t8]) ).
cnf(t37,plain,
d(s(one)) = true,
inference(orient,[status(thm)],[t177]) ).
cnf(t38,plain,
true = ifeq(true,true,d(s(s(one))),true),
inference(cp,[status(thm)],[t32,t37]) ).
cnf(t178,plain,
true = d(s(s(one))),
inference(step,[status(thm)],[t38,t8]) ).
cnf(t39,plain,
d(s(s(one))) = true,
inference(orient,[status(thm)],[t178]) ).
cnf(t40,plain,
true = ifeq(true,true,d(s(s(s(one)))),true),
inference(cp,[status(thm)],[t32,t39]) ).
cnf(t179,plain,
true = d(s(s(s(one)))),
inference(step,[status(thm)],[t40,t8]) ).
cnf(t180,plain,
true = d(f(one,s(one))),
inference(step,[status(thm)],[t179,t11]) ).
cnf(t41,plain,
d(f(one,s(one))) = true,
inference(orient,[status(thm)],[t180]) ).
cnf(t42,plain,
true = ifeq(true,true,d(s(f(one,s(one)))),true),
inference(cp,[status(thm)],[t32,t41]) ).
cnf(t181,plain,
true = d(s(f(one,s(one)))),
inference(step,[status(thm)],[t42,t8]) ).
cnf(t43,plain,
d(s(f(one,s(one)))) = true,
inference(orient,[status(thm)],[t181]) ).
cnf(t44,plain,
true = ifeq(true,true,d(s(s(f(one,s(one))))),true),
inference(cp,[status(thm)],[t32,t43]) ).
cnf(t182,plain,
true = d(s(s(f(one,s(one))))),
inference(step,[status(thm)],[t44,t8]) ).
cnf(t183,plain,
true = d(f(one,s(s(one)))),
inference(step,[status(thm)],[t182,t9]) ).
cnf(t45,plain,
d(f(one,s(s(one)))) = true,
inference(orient,[status(thm)],[t183]) ).
cnf(t46,plain,
true = ifeq(true,true,d(s(f(one,s(s(one))))),true),
inference(cp,[status(thm)],[t32,t45]) ).
cnf(t184,plain,
true = d(s(f(one,s(s(one))))),
inference(step,[status(thm)],[t46,t8]) ).
cnf(t47,plain,
d(s(f(one,s(s(one))))) = true,
inference(orient,[status(thm)],[t184]) ).
cnf(t48,plain,
true = ifeq(true,true,d(s(s(f(one,s(s(one)))))),true),
inference(cp,[status(thm)],[t32,t47]) ).
cnf(t185,plain,
true = d(s(s(f(one,s(s(one)))))),
inference(step,[status(thm)],[t48,t8]) ).
cnf(t186,plain,
true = d(f(one,s(s(s(one))))),
inference(step,[status(thm)],[t185,t9]) ).
cnf(t187,plain,
true = d(f(one,f(one,s(one)))),
inference(step,[status(thm)],[t186,t11]) ).
cnf(t49,plain,
d(f(one,f(one,s(one)))) = true,
inference(orient,[status(thm)],[t187]) ).
cnf(t50,plain,
true = ifeq(true,true,d(s(f(one,f(one,s(one))))),true),
inference(cp,[status(thm)],[t32,t49]) ).
cnf(t188,plain,
true = d(s(f(one,f(one,s(one))))),
inference(step,[status(thm)],[t50,t8]) ).
cnf(t51,plain,
d(s(f(one,f(one,s(one))))) = true,
inference(orient,[status(thm)],[t188]) ).
cnf(t52,plain,
true = ifeq(true,true,d(s(s(f(one,f(one,s(one)))))),true),
inference(cp,[status(thm)],[t32,t51]) ).
cnf(t189,plain,
true = d(s(s(f(one,f(one,s(one)))))),
inference(step,[status(thm)],[t52,t8]) ).
cnf(t190,plain,
true = d(f(one,s(f(one,s(one))))),
inference(step,[status(thm)],[t189,t9]) ).
cnf(t53,plain,
d(f(one,s(f(one,s(one))))) = true,
inference(orient,[status(thm)],[t190]) ).
cnf(t54,plain,
true = ifeq(true,true,d(s(f(one,s(f(one,s(one)))))),true),
inference(cp,[status(thm)],[t32,t53]) ).
cnf(t193,plain,
true = d(s(f(one,s(f(one,s(one)))))),
inference(step,[status(thm)],[t54,t8]) ).
cnf(t83,plain,
d(s(f(one,s(f(one,s(one)))))) = true,
inference(orient,[status(thm)],[t193]) ).
cnf(t84,plain,
true = ifeq(true,true,d(s(s(f(one,s(f(one,s(one))))))),true),
inference(cp,[status(thm)],[t32,t83]) ).
cnf(t194,plain,
true = d(s(s(f(one,s(f(one,s(one))))))),
inference(step,[status(thm)],[t84,t8]) ).
cnf(t195,plain,
true = d(f(one,s(s(f(one,s(one)))))),
inference(step,[status(thm)],[t194,t9]) ).
cnf(t196,plain,
true = d(f(one,f(one,s(s(one))))),
inference(step,[status(thm)],[t195,t9]) ).
cnf(t85,plain,
d(f(one,f(one,s(s(one))))) = true,
inference(orient,[status(thm)],[t196]) ).
cnf(t86,plain,
true = ifeq(true,true,d(s(f(one,f(one,s(s(one)))))),true),
inference(cp,[status(thm)],[t32,t85]) ).
cnf(t198,plain,
true = d(s(f(one,f(one,s(s(one)))))),
inference(step,[status(thm)],[t86,t8]) ).
cnf(t101,plain,
d(s(f(one,f(one,s(s(one)))))) = true,
inference(orient,[status(thm)],[t198]) ).
cnf(t102,plain,
true = ifeq(true,true,d(s(s(f(one,f(one,s(s(one))))))),true),
inference(cp,[status(thm)],[t32,t101]) ).
cnf(t199,plain,
true = d(s(s(f(one,f(one,s(s(one))))))),
inference(step,[status(thm)],[t102,t8]) ).
cnf(t200,plain,
true = d(f(one,s(f(one,s(s(one)))))),
inference(step,[status(thm)],[t199,t9]) ).
cnf(t103,plain,
d(f(one,s(f(one,s(s(one)))))) = true,
inference(orient,[status(thm)],[t200]) ).
cnf(t104,plain,
true = ifeq(true,true,d(s(f(one,s(f(one,s(s(one))))))),true),
inference(cp,[status(thm)],[t32,t103]) ).
cnf(t208,plain,
true = d(s(f(one,s(f(one,s(s(one))))))),
inference(step,[status(thm)],[t104,t8]) ).
cnf(t137,plain,
d(s(f(one,s(f(one,s(s(one))))))) = true,
inference(orient,[status(thm)],[t208]) ).
cnf(t138,plain,
true = ifeq(true,true,d(s(s(f(one,s(f(one,s(s(one)))))))),true),
inference(cp,[status(thm)],[t32,t137]) ).
cnf(t209,plain,
true = d(s(s(f(one,s(f(one,s(s(one)))))))),
inference(step,[status(thm)],[t138,t8]) ).
cnf(t210,plain,
true = d(f(one,s(s(f(one,s(s(one))))))),
inference(step,[status(thm)],[t209,t9]) ).
cnf(t211,plain,
true = d(f(one,f(one,s(s(s(one)))))),
inference(step,[status(thm)],[t210,t9]) ).
cnf(t212,plain,
true = d(f(one,f(one,f(one,s(one))))),
inference(step,[status(thm)],[t211,t11]) ).
cnf(t21,plain,
f(s(X1),s(s(one))) = f(X1,f(X1,s(one))),
inference(cp,[status(thm)],[t12,t18]) ).
cnf(t111,plain,
f(s(X1),s(s(one))) = f(X1,f(X1,s(one))),
inference(orient,[status(thm)],[t21]) ).
cnf(t116,plain,
f(s(X1),s(s(s(one)))) = f(X1,f(X1,f(X1,s(one)))),
inference(cp,[status(thm)],[t12,t111]) ).
cnf(t206,plain,
f(s(X1),f(one,s(one))) = f(X1,f(X1,f(X1,s(one)))),
inference(step,[status(thm)],[t116,t11]) ).
cnf(t118,plain,
f(X1,f(X1,f(X1,s(one)))) = f(s(X1),f(one,s(one))),
inference(orient,[status(thm)],[t206]) ).
cnf(t213,plain,
true = d(f(s(one),f(one,s(one)))),
inference(step,[status(thm)],[t212,t118]) ).
cnf(t139,plain,
d(f(s(one),f(one,s(one)))) = true,
inference(orient,[status(thm)],[t213]) ).
cnf(f5,negated_conjecture,
~ d(f(s(s(one)),s(s(one)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
fof(f5_nnf,plain,
~ d(f(s(s(one)),s(s(one)))),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
~ d(f(s(s(one)),s(s(one)))),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
~ d(f(s(s(one)),s(s(one)))),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(goal_0,negated_conjecture,
d(f(s(s(one)),s(s(one)))) != true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(g0_0,plain,
d(f(s(one),f(one,s(one)))) != true,
inference(rw,[status(thm)],[goal_0,t174]) ).
cnf(g0_1,plain,
true != true,
inference(rw,[status(thm)],[g0_0,t139]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO038-1.003.003 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.38 % Computer : n008.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Fri Sep 25 02:48:25 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 18.18/2.75 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.18/2.75 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------