%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP700+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 01:28:05 PM UTC 2026
% Result : Theorem 0.14s 10.87s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 68 ( 63 unt; 0 def)
% Number of atoms : 73 ( 72 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 3 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 104 ( 2 sgn 37 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,conjecture,
! [X0] :
? [X1] :
( mult(X0,X1) = unit
& mult(X1,X0) = unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f8_neg,negated_conjecture,
~ ! [X0] :
? [X1] :
( mult(X0,X1) = unit
& mult(X1,X0) = unit ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [X0] :
! [X1] :
( mult(X0,X1) != unit
| mult(X1,X0) != unit ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
! [X1] :
( mult(sk0,X1) != unit
| mult(X1,sk0) != unit ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f8_nnf]) ).
cnf(c8,plain,
( mult(sk0,X1) != unit
| mult(X1,sk0) != unit ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t7,plain,
ifeq(mult(X1,sk0),unit,ifeq(mult(sk0,X1),unit,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t52,plain,
ifeq(mult(X1,sk0),unit,ifeq(mult(sk0,X1),unit,false,true),true) = true,
inference(orient,[status(thm)],[t7]) ).
fof(f3,axiom,
! [B,A] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f3_nnf,plain,
! [B,A] : rd(mult(A,B),B) = A,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] : rd(mult(A,B),B) = A,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
rd(mult(X1,X0),X0) = X1,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t6,plain,
rd(mult(X1,X2),X2) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t17,plain,
rd(mult(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t6]) ).
fof(f1,axiom,
! [B,A] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
fof(f1_nnf,plain,
! [B,A] : ld(A,mult(A,B)) = B,
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : ld(A,mult(A,B)) = B,
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
ld(X1,mult(X1,X0)) = X0,
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t3,plain,
ld(X1,mult(X1,X2)) = X2,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t21,plain,
ld(X1,mult(X1,X2)) = X2,
inference(orient,[status(thm)],[t3]) ).
fof(f6,axiom,
! [C,B,A] : mult(mult(mult(A,B),A),mult(A,C)) = mult(A,mult(mult(mult(B,A),A),C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
fof(f6_nnf,plain,
! [C,B,A] : mult(mult(mult(A,B),A),mult(A,C)) = mult(A,mult(mult(mult(B,A),A),C)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] : mult(mult(mult(A,B),A),mult(A,C)) = mult(A,mult(mult(mult(B,A),A),C)),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
mult(mult(mult(X2,X1),X2),mult(X2,X0)) = mult(X2,mult(mult(mult(X1,X2),X2),X0)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t9,plain,
mult(mult(mult(X1,X2),X1),mult(X1,X3)) = mult(X1,mult(mult(mult(X2,X1),X1),X3)),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t25,plain,
mult(mult(mult(X1,X2),X1),mult(X1,X3)) = mult(X1,mult(mult(mult(X2,X1),X1),X3)),
inference(orient,[status(thm)],[t9]) ).
fof(f4,axiom,
! [A] : mult(A,unit) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f4_nnf,plain,
! [A] : mult(A,unit) = A,
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A] : mult(A,unit) = A,
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
mult(X0,unit) = X0,
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t0,plain,
mult(X1,unit) = X1,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t11,plain,
mult(X1,unit) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t30,plain,
mult(X1,mult(mult(mult(X2,X1),X1),unit)) = mult(mult(mult(X1,X2),X1),X1),
inference(cp,[status(thm)],[t25,t11]) ).
cnf(t336,plain,
mult(X1,mult(mult(X2,X1),X1)) = mult(mult(mult(X1,X2),X1),X1),
inference(step,[status(thm)],[t30,t11]) ).
cnf(t96,plain,
mult(mult(mult(X1,X2),X1),X1) = mult(X1,mult(mult(X2,X1),X1)),
inference(orient,[status(thm)],[t336]) ).
fof(f0,axiom,
! [B,A] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
fof(f0_nnf,plain,
! [B,A] : mult(A,ld(A,B)) = B,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] : mult(A,ld(A,B)) = B,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
mult(X1,ld(X1,X0)) = X0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t4,plain,
mult(X1,ld(X1,X2)) = X2,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t10,plain,
mult(X1,ld(X1,X2)) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t100,plain,
mult(X1,mult(mult(ld(X1,X2),X1),X1)) = mult(mult(X2,X1),X1),
inference(cp,[status(thm)],[t96,t10]) ).
cnf(t266,plain,
mult(X1,mult(mult(ld(X1,X2),X1),X1)) = mult(mult(X2,X1),X1),
inference(orient,[status(thm)],[t100]) ).
cnf(t275,plain,
mult(mult(ld(X1,X2),X1),X1) = ld(X1,mult(mult(X2,X1),X1)),
inference(cp,[status(thm)],[t21,t266]) ).
cnf(t284,plain,
ld(X1,mult(mult(X2,X1),X1)) = mult(mult(ld(X1,X2),X1),X1),
inference(orient,[status(thm)],[t275]) ).
fof(f5,axiom,
! [A] : mult(unit,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
fof(f5_nnf,plain,
! [A] : mult(unit,A) = A,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] : mult(unit,A) = A,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
mult(unit,X0) = X0,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t1,plain,
mult(unit,X1) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t12,plain,
mult(unit,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t297,plain,
mult(mult(ld(X1,unit),X1),X1) = ld(X1,mult(X1,X1)),
inference(cp,[status(thm)],[t284,t12]) ).
cnf(t343,plain,
mult(mult(ld(X1,unit),X1),X1) = X1,
inference(step,[status(thm)],[t297,t21]) ).
cnf(t301,plain,
mult(mult(ld(X1,unit),X1),X1) = X1,
inference(orient,[status(thm)],[t343]) ).
cnf(t307,plain,
mult(ld(X1,unit),X1) = rd(X1,X1),
inference(cp,[status(thm)],[t17,t301]) ).
cnf(t20,plain,
unit = rd(X1,X1),
inference(cp,[status(thm)],[t17,t12]) ).
cnf(t60,plain,
rd(X1,X1) = unit,
inference(orient,[status(thm)],[t20]) ).
cnf(t344,plain,
mult(ld(X1,unit),X1) = unit,
inference(step,[status(thm)],[t307,t60]) ).
cnf(t318,plain,
mult(ld(X1,unit),X1) = unit,
inference(orient,[status(thm)],[t344]) ).
cnf(t328,plain,
true = ifeq(unit,unit,ifeq(mult(sk0,ld(sk0,unit)),unit,false,true),true),
inference(cp,[status(thm)],[t52,t318]) ).
cnf(t2,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(t345,plain,
true = ifeq(mult(sk0,ld(sk0,unit)),unit,false,true),
inference(step,[status(thm)],[t328,t16]) ).
cnf(t346,plain,
true = ifeq(unit,unit,false,true),
inference(step,[status(thm)],[t345,t10]) ).
cnf(t347,plain,
true = false,
inference(step,[status(thm)],[t346,t16]) ).
cnf(t330,plain,
false = true,
inference(orient,[status(thm)],[t347]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t330]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP700+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/10.37 % Computer : n020.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Wed Sep 23 15:45:59 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/10.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/10.87 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------