%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO029-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 12:06:35 PM UTC 2026
% Result : Unsatisfiable 0.02s 0.34s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 52 ( 52 unt; 4 def)
% Number of atoms : 52 ( 51 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 90 ( 90 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : add(X,multiply(Y,multiply(X,Z))) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : add(add(multiply(X,Y),multiply(Y,Z)),Y) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] : multiply(X,add(Y,add(X,Z))) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] : multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : add(multiply(X,Y),multiply(X,inverse(Y))) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] : add(X,Y) = add(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] : multiply(X,Y) = multiply(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] : add(add(X,Y),Z) = add(X,add(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
add(b,inverse(b)) != add(a,inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,plain,
! [X0,X1,X2] : add(X0,multiply(X1,multiply(X0,X2))) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f13,plain,
! [X0,X1,X2] : add(add(multiply(X0,X1),multiply(X1,X2)),X1) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f15,plain,
! [X0,X1,X2] : multiply(X0,add(X1,add(X0,X2))) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f16,plain,
! [X0,X1,X2] : multiply(multiply(add(X0,X1),add(X1,X2)),X1) = X1,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f17,plain,
! [X0,X1] : add(multiply(X0,X1),multiply(X0,inverse(X1))) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f18,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f19,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f20,plain,
! [X0,X1,X2] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f21,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f22,plain,
add(b,inverse(b)) != add(a,inverse(a)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f23,definition,
sF1_fnc = inverse(b),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f24,definition,
sF0_fnc = add(b,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f25,definition,
sF3_fnc = inverse(a),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f26,definition,
sF2_fnc = add(a,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f27,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f22,f26,f25,f24,f23]) ).
fof(f42,plain,
! [X0] : add(multiply(X0,b),multiply(X0,sF1_fnc)) = X0,
inference(paramodulation,[status(thm)],[f23,f17]) ).
fof(f94,plain,
! [X0] : add(sF2_fnc,X0) = add(a,add(sF3_fnc,X0)),
inference(paramodulation,[status(thm)],[f26,f20]) ).
fof(f132,plain,
! [X0,X1] : add(multiply(X0,X1),multiply(inverse(X1),X0)) = X0,
inference(paramodulation,[status(thm)],[f19,f17]) ).
fof(f176,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f12,f15]) ).
fof(f179,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f15,f12]) ).
fof(f189,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = X0,
inference(paramodulation,[status(thm)],[f18,f176]) ).
fof(f206,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = X0,
inference(paramodulation,[status(thm)],[f19,f179]) ).
fof(f348,plain,
! [X0,X1,X2] : add(multiply(X0,X1),add(multiply(X1,X2),X1)) = X1,
inference(forward_demodulation,[status(thm)],[f20,f13]) ).
fof(f367,plain,
! [X0,X1,X2] : add(multiply(X0,X1),add(X1,multiply(X1,X2))) = X1,
inference(paramodulation,[status(thm)],[f18,f348]) ).
fof(f398,plain,
! [X0,X1] : add(multiply(X0,X1),X1) = X1,
inference(forward_demodulation,[status(thm)],[f206,f367]) ).
fof(f469,plain,
! [X0,X1,X2] : multiply(add(X0,X1),multiply(add(X1,X2),X1)) = X1,
inference(backward_demodulation,[status(thm)],[f21,f16]) ).
fof(f780,plain,
! [X0,X1,X2] : multiply(add(X0,X1),multiply(X1,add(X1,X2))) = X1,
inference(paramodulation,[status(thm)],[f19,f469]) ).
fof(f804,plain,
! [X0,X1] : add(X0,multiply(add(X0,X1),X0)) = multiply(add(X0,X1),X0),
inference(paramodulation,[status(thm)],[f469,f398]) ).
fof(f817,plain,
! [X0,X1] : multiply(add(X0,X1),X1) = X1,
inference(forward_demodulation,[status(thm)],[f189,f780]) ).
fof(f828,plain,
! [X0,X1] : X0 = multiply(add(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f179,f804]) ).
fof(f967,plain,
! [X0] : multiply(sF3_fnc,add(sF2_fnc,X0)) = sF3_fnc,
inference(paramodulation,[status(thm)],[f94,f15]) ).
fof(f999,plain,
! [X0,X1,X2] : multiply(add(X0,add(X1,X2)),X2) = X2,
inference(paramodulation,[status(thm)],[f20,f817]) ).
fof(f1056,plain,
! [X0] : a = multiply(add(sF2_fnc,X0),a),
inference(paramodulation,[status(thm)],[f94,f828]) ).
fof(f3320,plain,
! [X0] : add(a,multiply(inverse(a),add(sF2_fnc,X0))) = add(sF2_fnc,X0),
inference(paramodulation,[status(thm)],[f1056,f132]) ).
fof(f3336,plain,
! [X0] : add(a,multiply(sF3_fnc,add(sF2_fnc,X0))) = add(sF2_fnc,X0),
inference(forward_demodulation,[status(thm)],[f25,f3320]) ).
fof(f3337,plain,
! [X0] : add(a,sF3_fnc) = add(sF2_fnc,X0),
inference(forward_demodulation,[status(thm)],[f967,f3336]) ).
fof(f3338,plain,
! [X0] : sF2_fnc = add(sF2_fnc,X0),
inference(forward_demodulation,[status(thm)],[f26,f3337]) ).
fof(f3377,plain,
! [X0] : multiply(sF2_fnc,X0) = X0,
inference(paramodulation,[status(thm)],[f3338,f999]) ).
fof(f3456,plain,
add(multiply(sF2_fnc,b),sF1_fnc) = sF2_fnc,
inference(paramodulation,[status(thm)],[f3377,f42]) ).
fof(f3499,plain,
add(b,sF1_fnc) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f3377,f3456]) ).
fof(f3500,plain,
sF0_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f24,f3499]) ).
fof(f3501,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3500,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : BOO029-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Mon Sep 21 13:48:22 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.31 % Drodi V4.1.1
% 0.02/0.34 % Refutation found
% 0.02/0.34 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.02/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.02/0.35 % Elapsed time: 0.042515 seconds
% 0.02/0.35 % CPU time: 0.220921 seconds
% 0.02/0.35 % Total memory used: 11.592 MB
% 0.02/0.35 % Net memory used: 11.325 MB
%------------------------------------------------------------------------------