%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN134-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 : Thu Sep 24 01:57:19 PM UTC 2026
% Result : Unsatisfiable 4.15s 0.95s
% Output : CNFRefutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 16
% Syntax : Number of formulae : 63 ( 63 unt; 6 def)
% Number of atoms : 63 ( 62 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 58 ( 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : '+'(X,Y) = '+'(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : '+'(X,'+'(Y,Z)) = '+'('+'(X,Y),Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : times(X,Y) = times(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : times(X,one) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y,Z] : times(X,'+'(Y,Z)) = '+'(times(X,Y),times(X,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : '+'(s(X),Y) = s('+'(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : times(s(X),Y) = '+'(Y,times(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [N] : sum(s(N)) = '+'(s(N),sum(N)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
'+'(sum(a),sum(a)) = times(a,s(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
'+'(sum(s(a)),sum(s(a))) != times(s(a),s(s(a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,plain,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f17,plain,
! [X0,X1,X2] : '+'(X0,'+'(X1,X2)) = '+'('+'(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f18,plain,
! [X0,X1] : times(X0,X1) = times(X1,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
! [X0] : times(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f23,plain,
! [X0,X1,X2] : times(X0,'+'(X1,X2)) = '+'(times(X0,X1),times(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f25,plain,
! [X0,X1] : '+'(s(X0),X1) = s('+'(X0,X1)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0,X1] : times(s(X0),X1) = '+'(X1,times(X0,X1)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
! [X0] : sum(s(X0)) = '+'(s(X0),sum(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f29,plain,
'+'(sum(a),sum(a)) = times(a,s(a)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f30,plain,
'+'(sum(s(a)),sum(s(a))) != times(s(a),s(s(a))),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f31,definition,
sF2_fnc = s(a),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f32,definition,
sF1_fnc = sum(sF2_fnc),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f33,definition,
sF3_fnc = sum(sF2_fnc),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f34,definition,
sF0_fnc = '+'(sF1_fnc,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f35,definition,
sF5_fnc = s(sF2_fnc),
introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition]) ).
fof(f36,definition,
sF4_fnc = times(sF2_fnc,sF5_fnc),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f37,plain,
sF0_fnc != sF4_fnc,
inference(definition_folding,[],[f30,f36,f35,f34,f33,f32,f31]) ).
fof(f38,plain,
! [X0] : sum(s(X0)) = s('+'(X0,sum(X0))),
inference(forward_demodulation,[status(thm)],[f25,f28]) ).
fof(f39,plain,
'+'(sum(a),sum(a)) = times(a,sF2_fnc),
inference(backward_demodulation,[status(thm)],[f31,f29]) ).
fof(f40,plain,
sF3_fnc = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f32,f33]) ).
fof(f41,plain,
sF0_fnc = '+'(sF1_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f40,f34]) ).
fof(f50,plain,
! [X0,X1] : '+'(X0,s(X1)) = s('+'(X1,X0)),
inference(paramodulation,[status(thm)],[f16,f25]) ).
fof(f107,plain,
! [X0] : '+'(X0,sF2_fnc) = s('+'(a,X0)),
inference(paramodulation,[status(thm)],[f31,f50]) ).
fof(f197,plain,
! [X0,X1,X2] : '+'(X0,'+'(X1,X2)) = '+'(X2,'+'(X0,X1)),
inference(paramodulation,[status(thm)],[f16,f17]) ).
fof(f333,plain,
sum(s(a)) = '+'(sum(a),sF2_fnc),
inference(paramodulation,[status(thm)],[f107,f38]) ).
fof(f347,plain,
! [X0,X1] : '+'(sum(s(X0)),X1) = s('+'('+'(X0,sum(X0)),X1)),
inference(paramodulation,[status(thm)],[f38,f25]) ).
fof(f348,plain,
sum(sF2_fnc) = '+'(sum(a),sF2_fnc),
inference(forward_demodulation,[status(thm)],[f31,f333]) ).
fof(f349,plain,
sF1_fnc = '+'(sum(a),sF2_fnc),
inference(forward_demodulation,[status(thm)],[f32,f348]) ).
fof(f350,plain,
sF1_fnc = '+'(sF2_fnc,sum(a)),
inference(forward_demodulation,[status(thm)],[f16,f349]) ).
fof(f377,plain,
! [X0,X1] : '+'(sum(s(X0)),X1) = s('+'(X0,'+'(sum(X0),X1))),
inference(forward_demodulation,[status(thm)],[f17,f347]) ).
fof(f411,plain,
! [X0] : times(s(X0),one) = '+'(one,X0),
inference(paramodulation,[status(thm)],[f22,f26]) ).
fof(f429,plain,
! [X0] : s(X0) = '+'(one,X0),
inference(forward_demodulation,[status(thm)],[f22,f411]) ).
fof(f473,plain,
! [X0,X1] : times(X0,'+'(one,X1)) = '+'(X0,times(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f23]) ).
fof(f497,plain,
! [X0,X1] : times(X0,s(X1)) = '+'(X0,times(X0,X1)),
inference(forward_demodulation,[status(thm)],[f429,f473]) ).
fof(f1013,plain,
! [X0,X1] : times(X0,s(X1)) = '+'(X0,times(X1,X0)),
inference(paramodulation,[status(thm)],[f18,f497]) ).
fof(f1473,plain,
! [X0,X1,X2] : '+'('+'(X0,X1),X2) = '+'(X1,'+'(X2,X0)),
inference(paramodulation,[status(thm)],[f16,f197]) ).
fof(f2314,plain,
! [X0,X1,X2] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X2,X1)),
inference(paramodulation,[status(thm)],[f16,f1473]) ).
fof(f3698,plain,
! [X0] : '+'(sF1_fnc,X0) = '+'(sF2_fnc,'+'(X0,sum(a))),
inference(paramodulation,[status(thm)],[f350,f2314]) ).
fof(f5000,plain,
'+'(sum(s(a)),sum(a)) = s('+'(a,times(a,sF2_fnc))),
inference(paramodulation,[status(thm)],[f39,f377]) ).
fof(f5056,plain,
'+'(sum(a),sum(s(a))) = s('+'(a,times(a,sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f16,f5000]) ).
fof(f5057,plain,
'+'(sum(a),sum(sF2_fnc)) = s('+'(a,times(a,sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f31,f5056]) ).
fof(f5058,plain,
'+'(sum(a),sF1_fnc) = s('+'(a,times(a,sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f32,f5057]) ).
fof(f5059,plain,
'+'(sF1_fnc,sum(a)) = s('+'(a,times(a,sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f16,f5058]) ).
fof(f5060,plain,
'+'(sF1_fnc,sum(a)) = '+'(times(a,sF2_fnc),sF2_fnc),
inference(forward_demodulation,[status(thm)],[f107,f5059]) ).
fof(f5061,plain,
'+'(sF1_fnc,sum(a)) = '+'(sF2_fnc,times(a,sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f16,f5060]) ).
fof(f5062,plain,
'+'(sF1_fnc,sum(a)) = times(sF2_fnc,s(a)),
inference(forward_demodulation,[status(thm)],[f1013,f5061]) ).
fof(f5063,plain,
'+'(sF1_fnc,sum(a)) = times(sF2_fnc,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f31,f5062]) ).
fof(f5437,plain,
'+'(sF1_fnc,sF1_fnc) = '+'(sF2_fnc,times(sF2_fnc,sF2_fnc)),
inference(paramodulation,[status(thm)],[f5063,f3698]) ).
fof(f5478,plain,
sF0_fnc = '+'(sF2_fnc,times(sF2_fnc,sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f41,f5437]) ).
fof(f5479,plain,
sF0_fnc = times(sF2_fnc,s(sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f1013,f5478]) ).
fof(f5480,plain,
sF4_fnc = sF0_fnc,
inference(backward_demodulation,[status(thm)],[f5481,f36]) ).
fof(f5481,plain,
sF0_fnc = times(sF2_fnc,sF5_fnc),
inference(forward_demodulation,[status(thm)],[f35,f5479]) ).
fof(f5522,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5480,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN134-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 03:33:37 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 4.15/0.95 % Refutation found
% 4.15/0.95 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.15/0.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.15/0.99 % Elapsed time: 0.597302 seconds
% 4.15/0.99 % CPU time: 4.411154 seconds
% 4.15/0.99 % Total memory used: 45.775 MB
% 4.15/0.99 % Net memory used: 44.490 MB
%------------------------------------------------------------------------------