%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUN134-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 02:29:37 PM UTC 2026
% Result : Unsatisfiable 6.07s 1.35s
% Output : CNFRefutation 6.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 9
% Syntax : Number of clauses : 75 ( 75 unt; 0 nHn; 25 RR)
% Number of literals : 75 ( 74 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t8,axiom,
qtd0(X1,times(X2,X1)) = times(s(X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t37,plain,
qtd0(X1,times(X2,X1)) = times(s(X2),X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t5,axiom,
times(X1,X2) = times(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t16,plain,
times(X1,X2) = times(X2,X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t2,axiom,
times(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t14,plain,
times(X1,one) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t17,plain,
times(one,X1) = X1,
inference(cp,[status(thm)],[t16,t14]) ).
cnf(t68,plain,
times(one,X1) = X1,
inference(orient,[status(thm)],[t17]) ).
cnf(t69,plain,
times(s(one),X1) = qtd0(X1,X1),
inference(cp,[status(thm)],[t37,t68]) ).
cnf(t120,plain,
times(s(one),X1) = qtd0(X1,X1),
inference(orient,[status(thm)],[t69]) ).
cnf(t121,plain,
qtd0(X1,X1) = times(X1,s(one)),
inference(cp,[status(thm)],[t120,t16]) ).
cnf(t155,plain,
qtd0(X1,X1) = times(X1,s(one)),
inference(orient,[status(thm)],[t121]) ).
cnf(t10,axiom,
qtd0(qtd0(X1,X2),X3) = qtd0(X1,qtd0(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t47,plain,
qtd0(qtd0(X1,X2),X3) = qtd0(X1,qtd0(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(t6,axiom,
qtd0(s(X1),sum(X1)) = sum(s(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t4,axiom,
qtd0(X1,X2) = qtd0(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t43,plain,
qtd0(X1,X2) = qtd0(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t1361,plain,
qtd0(sum(X1),s(X1)) = sum(s(X1)),
inference(step,[status(thm)],[t6,t43]) ).
cnf(t62,plain,
qtd0(sum(X1),s(X1)) = sum(s(X1)),
inference(orient,[status(thm)],[t1361]) ).
cnf(t217,plain,
qtd0(sum(X1),s(X1)) = sum(s(X1)),
inference(rw,[status(thm)],[t62]) ).
cnf(t7,axiom,
s(qtd0(X1,X2)) = qtd0(s(X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t56,plain,
s(qtd0(X1,X2)) = qtd0(s(X1),X2),
inference(orient,[status(thm)],[t7]) ).
cnf(t61,plain,
qtd0(s(X1),X2) = s(qtd0(X2,X1)),
inference(cp,[status(thm)],[t56,t43]) ).
cnf(t39,plain,
times(s(X1),one) = qtd0(one,X1),
inference(cp,[status(thm)],[t37,t14]) ).
cnf(t1362,plain,
s(X1) = qtd0(one,X1),
inference(step,[status(thm)],[t39,t14]) ).
cnf(t77,plain,
qtd0(one,X1) = s(X1),
inference(orient,[status(thm)],[t1362]) ).
cnf(t79,plain,
s(X1) = qtd0(X1,one),
inference(cp,[status(thm)],[t77,t43]) ).
cnf(t85,plain,
qtd0(X1,one) = s(X1),
inference(orient,[status(thm)],[t79]) ).
cnf(t86,plain,
s(qtd0(X1,X2)) = qtd0(X1,qtd0(X2,one)),
inference(cp,[status(thm)],[t85,t47]) ).
cnf(t1369,plain,
qtd0(s(X1),X2) = qtd0(X1,qtd0(X2,one)),
inference(step,[status(thm)],[t86,t56]) ).
cnf(t1370,plain,
qtd0(s(X1),X2) = qtd0(X1,s(X2)),
inference(step,[status(thm)],[t1369,t85]) ).
cnf(t97,plain,
qtd0(s(X1),X2) = qtd0(X1,s(X2)),
inference(orient,[status(thm)],[t1370]) ).
cnf(t1385,plain,
qtd0(X1,s(X2)) = s(qtd0(X2,X1)),
inference(step,[status(thm)],[t61,t97]) ).
cnf(t1371,plain,
s(qtd0(X1,X2)) = qtd0(X1,s(X2)),
inference(step,[status(thm)],[t56,t97]) ).
cnf(t98,plain,
s(qtd0(X1,X2)) = qtd0(X1,s(X2)),
inference(orient,[status(thm)],[t1371]) ).
cnf(t1386,plain,
qtd0(X1,s(X2)) = qtd0(X2,s(X1)),
inference(step,[status(thm)],[t1385,t98]) ).
cnf(t207,plain,
qtd0(X1,s(X2)) = qtd0(X2,s(X1)),
inference(orient,[status(thm)],[t1386]) ).
cnf(t1387,plain,
qtd0(X1,s(sum(X1))) = sum(s(X1)),
inference(step,[status(thm)],[t217,t207]) ).
cnf(t218,plain,
qtd0(X1,s(sum(X1))) = sum(s(X1)),
inference(orient,[status(thm)],[t1387]) ).
cnf(t223,plain,
qtd0(X1,qtd0(s(sum(X1)),X2)) = qtd0(sum(s(X1)),X2),
inference(cp,[status(thm)],[t47,t218]) ).
cnf(t1396,plain,
qtd0(X1,qtd0(sum(X1),s(X2))) = qtd0(sum(s(X1)),X2),
inference(step,[status(thm)],[t223,t97]) ).
cnf(t590,plain,
qtd0(X1,qtd0(sum(X1),s(X2))) = qtd0(sum(s(X1)),X2),
inference(orient,[status(thm)],[t1396]) ).
cnf(t164,plain,
qtd0(X1,s(X1)) = s(times(X1,s(one))),
inference(cp,[status(thm)],[t98,t155]) ).
cnf(t327,plain,
qtd0(X1,s(X1)) = s(times(X1,s(one))),
inference(orient,[status(thm)],[t164]) ).
cnf(t9,axiom,
qtd0(sum(a),sum(a)) = times(a,s(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t42,plain,
qtd0(sum(a),sum(a)) = times(a,s(a)),
inference(orient,[status(thm)],[t9]) ).
cnf(t138,plain,
qtd0(sum(a),sum(a)) = times(a,s(a)),
inference(rw,[status(thm)],[t42]) ).
cnf(t1376,plain,
times(s(one),sum(a)) = times(a,s(a)),
inference(step,[status(thm)],[t138,t120]) ).
cnf(t1377,plain,
times(sum(a),s(one)) = times(a,s(a)),
inference(step,[status(thm)],[t1376,t16]) ).
cnf(t147,plain,
times(sum(a),s(one)) = times(a,s(a)),
inference(orient,[status(thm)],[t1377]) ).
cnf(t342,plain,
qtd0(sum(a),s(sum(a))) = s(times(a,s(a))),
inference(cp,[status(thm)],[t327,t147]) ).
cnf(t352,plain,
qtd0(sum(a),s(sum(a))) = s(times(a,s(a))),
inference(orient,[status(thm)],[t342]) ).
cnf(t596,plain,
qtd0(sum(s(a)),sum(a)) = qtd0(a,s(times(a,s(a)))),
inference(cp,[status(thm)],[t590,t352]) ).
cnf(t1397,plain,
qtd0(sum(a),sum(s(a))) = qtd0(a,s(times(a,s(a)))),
inference(step,[status(thm)],[t596,t43]) ).
cnf(t101,plain,
qtd0(X1,s(times(X2,s(X1)))) = times(s(X2),s(X1)),
inference(cp,[status(thm)],[t97,t37]) ).
cnf(t459,plain,
qtd0(X1,s(times(X2,s(X1)))) = times(s(X2),s(X1)),
inference(orient,[status(thm)],[t101]) ).
cnf(t1398,plain,
qtd0(sum(a),sum(s(a))) = times(s(a),s(a)),
inference(step,[status(thm)],[t1397,t459]) ).
cnf(t621,plain,
qtd0(sum(a),sum(s(a))) = times(s(a),s(a)),
inference(orient,[status(thm)],[t1398]) ).
cnf(t622,plain,
qtd0(sum(a),s(sum(s(a)))) = s(times(s(a),s(a))),
inference(cp,[status(thm)],[t98,t621]) ).
cnf(t1137,plain,
qtd0(sum(a),s(sum(s(a)))) = s(times(s(a),s(a))),
inference(orient,[status(thm)],[t622]) ).
cnf(t1141,plain,
qtd0(sum(s(a)),sum(s(a))) = qtd0(a,s(times(s(a),s(a)))),
inference(cp,[status(thm)],[t590,t1137]) ).
cnf(t1409,plain,
times(sum(s(a)),s(one)) = qtd0(a,s(times(s(a),s(a)))),
inference(step,[status(thm)],[t1141,t155]) ).
cnf(t1410,plain,
times(s(one),sum(s(a))) = qtd0(a,s(times(s(a),s(a)))),
inference(step,[status(thm)],[t1409,t16]) ).
cnf(t41,plain,
times(s(X1),X2) = qtd0(X2,times(X2,X1)),
inference(cp,[status(thm)],[t37,t16]) ).
cnf(t104,plain,
qtd0(X1,times(X1,X2)) = times(s(X2),X1),
inference(orient,[status(thm)],[t41]) ).
cnf(t105,plain,
times(s(X1),s(X2)) = qtd0(X2,s(times(s(X2),X1))),
inference(cp,[status(thm)],[t104,t97]) ).
cnf(t507,plain,
qtd0(X1,s(times(s(X1),X2))) = times(s(X2),s(X1)),
inference(orient,[status(thm)],[t105]) ).
cnf(t1411,plain,
times(s(one),sum(s(a))) = times(s(s(a)),s(a)),
inference(step,[status(thm)],[t1410,t507]) ).
cnf(t1412,plain,
times(s(one),sum(s(a))) = times(s(a),s(s(a))),
inference(step,[status(thm)],[t1411,t16]) ).
cnf(t1333,plain,
times(s(a),s(s(a))) = times(s(one),sum(s(a))),
inference(orient,[status(thm)],[t1412]) ).
cnf(goal_0,negated_conjecture,
qtd0(sum(s(a)),sum(s(a))) != times(s(a),s(s(a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
times(sum(s(a)),s(one)) != times(s(a),s(s(a))),
inference(rw,[status(thm)],[goal_0,t155]) ).
cnf(g0_1,plain,
times(s(one),sum(s(a))) != times(s(a),s(s(a))),
inference(rw,[status(thm)],[g0_0,t16]) ).
cnf(g0_2,plain,
times(s(one),sum(s(a))) != times(s(one),sum(s(a))),
inference(rw,[status(thm)],[g0_1,t1333]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN134-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 % Computer : n015.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Thu Sep 24 06:08:11 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.07/1.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.07/1.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------