%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP702+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 12:35:10 PM UTC 2026
% Result : Theorem 0.14s 10.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 20 unt; 0 def)
% Number of atoms : 71 ( 70 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 80 ( 46 ~; 30 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 37 ( 29 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,A] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] : mult(A,unit) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : mult(unit,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B,A] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [B,A] : mult(A,mult(B,op_c)) = mult(mult(A,B),op_c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [B,A] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : op_d = ld(A,mult(op_c,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [X0,X1] :
( mult(X0,mult(op_d,X1)) = mult(mult(X0,op_d),X1)
& mult(X0,mult(X1,op_d)) = mult(mult(X0,X1),op_d)
& mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [X0,X1] :
( mult(X0,mult(op_d,X1)) = mult(mult(X0,op_d),X1)
& mult(X0,mult(X1,op_d)) = mult(mult(X0,X1),op_d)
& mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0] : mult(X0,unit) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f21,plain,
! [X0] : mult(unit,X0) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f23,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f24,plain,
! [X0,X1] : mult(X0,mult(X1,op_c)) = mult(mult(X0,X1),op_c),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f25,plain,
! [X0,X1] : mult(X0,mult(op_c,X1)) = mult(mult(X0,op_c),X1),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0] : op_d = ld(X0,mult(op_c,X0)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f29,plain,
? [X0,X1] :
( mult(X0,mult(op_d,X1)) != mult(mult(X0,op_d),X1)
| mult(X0,mult(X1,op_d)) != mult(mult(X0,X1),op_d)
| mult(op_d,mult(X0,X1)) != mult(mult(op_d,X0),X1) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f30,plain,
( ? [X0,X1] : mult(X0,mult(op_d,X1)) != mult(mult(X0,op_d),X1)
| ? [X0,X1] : mult(X0,mult(X1,op_d)) != mult(mult(X0,X1),op_d)
| ? [X0,X1] : mult(op_d,mult(X0,X1)) != mult(mult(op_d,X0),X1) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f31,plain,
( mult(sK4_skl,mult(op_d,sK5_skl)) != mult(mult(sK4_skl,op_d),sK5_skl)
| mult(sK2_skl,mult(sK3_skl,op_d)) != mult(mult(sK2_skl,sK3_skl),op_d)
| mult(op_d,mult(sK0_skl,sK1_skl)) != mult(mult(op_d,sK0_skl),sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl),skolemize(X0,sK2_skl),skolemize(X1,sK3_skl),skolemize(X0,sK4_skl),skolemize(X1,sK5_skl)],[f30]) ).
fof(f32,plain,
( mult(sK4_skl,mult(op_d,sK5_skl)) != mult(mult(sK4_skl,op_d),sK5_skl)
| mult(sK2_skl,mult(sK3_skl,op_d)) != mult(mult(sK2_skl,sK3_skl),op_d)
| mult(op_d,mult(sK0_skl,sK1_skl)) != mult(mult(op_d,sK0_skl),sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f35,plain,
! [X0] : ld(unit,X0) = X0,
inference(paramodulation,[status(thm)],[f21,f16]) ).
fof(f88,plain,
op_d = mult(op_c,unit),
inference(paramodulation,[status(thm)],[f35,f26]) ).
fof(f95,plain,
! [X0] : mult(X0,op_d) = mult(op_c,X0),
inference(paramodulation,[status(thm)],[f26,f16]) ).
fof(f97,plain,
( mult(sK4_skl,mult(op_d,sK5_skl)) != mult(mult(sK4_skl,op_c),sK5_skl)
| mult(sK2_skl,mult(sK3_skl,op_d)) != mult(mult(sK2_skl,sK3_skl),op_d)
| mult(op_d,mult(sK0_skl,sK1_skl)) != mult(mult(op_d,sK0_skl),sK1_skl) ),
inference(backward_demodulation,[status(thm)],[f98,f32]) ).
fof(f98,plain,
op_d = op_c,
inference(forward_demodulation,[status(thm)],[f20,f88]) ).
fof(f104,plain,
! [X0] : mult(X0,op_c) = mult(op_c,X0),
inference(forward_demodulation,[status(thm)],[f98,f95]) ).
fof(f106,plain,
( mult(sK4_skl,mult(op_d,sK5_skl)) != mult(mult(sK4_skl,op_c),sK5_skl)
| mult(sK2_skl,mult(sK3_skl,op_d)) != mult(mult(sK2_skl,sK3_skl),op_d)
| mult(op_c,mult(sK0_skl,sK1_skl)) != mult(mult(op_d,sK0_skl),sK1_skl) ),
inference(forward_demodulation,[status(thm)],[f98,f97]) ).
fof(f107,plain,
( mult(sK4_skl,mult(op_d,sK5_skl)) != mult(mult(sK4_skl,op_c),sK5_skl)
| mult(sK2_skl,mult(sK3_skl,op_d)) != mult(mult(sK2_skl,sK3_skl),op_d)
| mult(op_c,mult(sK0_skl,sK1_skl)) != mult(mult(op_c,sK0_skl),sK1_skl) ),
inference(forward_demodulation,[status(thm)],[f98,f106]) ).
fof(f108,plain,
( mult(sK4_skl,mult(op_d,sK5_skl)) != mult(mult(sK4_skl,op_c),sK5_skl)
| mult(sK2_skl,mult(sK3_skl,op_d)) != mult(mult(sK2_skl,sK3_skl),op_d)
| mult(op_c,mult(sK0_skl,sK1_skl)) != mult(op_c,mult(sK0_skl,sK1_skl)) ),
inference(forward_demodulation,[status(thm)],[f23,f107]) ).
fof(f109,plain,
( mult(sK4_skl,mult(op_d,sK5_skl)) != mult(mult(sK4_skl,op_c),sK5_skl)
| mult(sK2_skl,mult(sK3_skl,op_c)) != mult(mult(sK2_skl,sK3_skl),op_d)
| mult(op_c,mult(sK0_skl,sK1_skl)) != mult(op_c,mult(sK0_skl,sK1_skl)) ),
inference(forward_demodulation,[status(thm)],[f98,f108]) ).
fof(f110,plain,
( mult(sK4_skl,mult(op_d,sK5_skl)) != mult(mult(sK4_skl,op_c),sK5_skl)
| mult(sK2_skl,mult(sK3_skl,op_c)) != mult(mult(sK2_skl,sK3_skl),op_c)
| mult(op_c,mult(sK0_skl,sK1_skl)) != mult(op_c,mult(sK0_skl,sK1_skl)) ),
inference(forward_demodulation,[status(thm)],[f98,f109]) ).
fof(f111,plain,
( mult(sK4_skl,mult(op_d,sK5_skl)) != mult(mult(sK4_skl,op_c),sK5_skl)
| mult(sK2_skl,mult(sK3_skl,op_c)) != mult(sK2_skl,mult(sK3_skl,op_c))
| mult(op_c,mult(sK0_skl,sK1_skl)) != mult(op_c,mult(sK0_skl,sK1_skl)) ),
inference(forward_demodulation,[status(thm)],[f24,f110]) ).
fof(f112,plain,
( mult(sK4_skl,mult(op_c,sK5_skl)) != mult(mult(sK4_skl,op_c),sK5_skl)
| mult(sK2_skl,mult(sK3_skl,op_c)) != mult(sK2_skl,mult(sK3_skl,op_c))
| mult(op_c,mult(sK0_skl,sK1_skl)) != mult(op_c,mult(sK0_skl,sK1_skl)) ),
inference(forward_demodulation,[status(thm)],[f98,f111]) ).
fof(f113,plain,
( mult(sK4_skl,mult(sK5_skl,op_c)) != mult(mult(sK4_skl,op_c),sK5_skl)
| mult(sK2_skl,mult(sK3_skl,op_c)) != mult(sK2_skl,mult(sK3_skl,op_c))
| mult(op_c,mult(sK0_skl,sK1_skl)) != mult(op_c,mult(sK0_skl,sK1_skl)) ),
inference(forward_demodulation,[status(thm)],[f104,f112]) ).
fof(f114,plain,
( mult(sK4_skl,mult(sK5_skl,op_c)) != mult(sK4_skl,mult(op_c,sK5_skl))
| mult(sK2_skl,mult(sK3_skl,op_c)) != mult(sK2_skl,mult(sK3_skl,op_c))
| mult(op_c,mult(sK0_skl,sK1_skl)) != mult(op_c,mult(sK0_skl,sK1_skl)) ),
inference(forward_demodulation,[status(thm)],[f25,f113]) ).
fof(f115,plain,
( mult(sK4_skl,mult(sK5_skl,op_c)) != mult(sK4_skl,mult(sK5_skl,op_c))
| mult(sK2_skl,mult(sK3_skl,op_c)) != mult(sK2_skl,mult(sK3_skl,op_c))
| mult(op_c,mult(sK0_skl,sK1_skl)) != mult(op_c,mult(sK0_skl,sK1_skl)) ),
inference(forward_demodulation,[status(thm)],[f104,f114]) ).
fof(f116,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP702+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.38 % Computer : n005.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Sun Sep 20 20:34:14 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.39 % Drodi V4.1.1
% 0.14/10.41 % Refutation found
% 0.14/10.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/10.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/10.44 % Elapsed time: 0.047178 seconds
% 0.14/10.44 % CPU time: 0.158582 seconds
% 0.14/10.44 % Total memory used: 63.370 MB
% 0.14/10.44 % Net memory used: 62.980 MB
%------------------------------------------------------------------------------