%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP710+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 01:28:15 PM UTC 2026
% Result : Theorem 4.49s 6.29s
% Output : Proof 4.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 7
% Syntax : Number of formulae : 108 ( 103 unt; 0 def)
% Number of atoms : 113 ( 112 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 3 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-4 aty)
% Number of variables : 180 ( 22 sgn 33 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,conjecture,
( ! [X3,X4] :
? [X5] : mult(X5,X4) = X3
& ! [X0,X1] :
? [X2] : mult(X0,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f5_neg,negated_conjecture,
~ ( ! [X3,X4] :
? [X5] : mult(X5,X4) = X3
& ! [X0,X1] :
? [X2] : mult(X0,X2) = X1 ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f5_nnf,plain,
( ? [X3,X4] :
! [X5] : mult(X5,X4) != X3
| ? [X0,X1] :
! [X2] : mult(X0,X2) != X1 ),
inference(nnf_transformation,[status(thm)],[f5_neg]) ).
fof(f5_sk,plain,
! [X2,X5] :
( mult(X5,sk3) != sk2
| mult(sk0,X2) != sk1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f5_nnf]) ).
cnf(c5,plain,
( mult(X5,sk3) != sk2
| mult(sk0,X2) != sk1 ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t5,plain,
ifeq(mult(sk0,X1),sk1,ifeq(mult(X2,sk3),sk2,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t22,plain,
ifeq(mult(sk0,X1),sk1,ifeq(mult(X2,sk3),sk2,false,true),true) = true,
inference(orient,[status(thm)],[t5]) ).
fof(f2,axiom,
! [C,B,A] : mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(f2_nnf,plain,
! [C,B,A] : mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C] : mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
mult(X2,mult(X1,mult(X1,X0))) = mult(mult(mult(X2,X1),X1),X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t6,plain,
mult(mult(mult(X1,X2),X2),X3) = mult(X1,mult(X2,mult(X2,X3))),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t10,plain,
mult(mult(mult(X1,X2),X2),X3) = mult(X1,mult(X2,mult(X2,X3))),
inference(orient,[status(thm)],[t6]) ).
fof(f0,axiom,
! [A] : mult(A,unit) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f0_nnf,plain,
! [A] : mult(A,unit) = A,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A] : mult(A,unit) = A,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
mult(X0,unit) = X0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t0,plain,
mult(X1,unit) = X1,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t7,plain,
mult(X1,unit) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t11,plain,
mult(X1,mult(X2,mult(X2,unit))) = mult(mult(X1,X2),X2),
inference(cp,[status(thm)],[t10,t7]) ).
cnf(t785,plain,
mult(X1,mult(X2,X2)) = mult(mult(X1,X2),X2),
inference(step,[status(thm)],[t11,t7]) ).
cnf(t29,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(orient,[status(thm)],[t785]) ).
cnf(t786,plain,
mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))),
inference(step,[status(thm)],[t10,t29]) ).
cnf(t34,plain,
mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))),
inference(rw,[status(thm)],[t786]) ).
cnf(t45,plain,
mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))),
inference(orient,[status(thm)],[t34]) ).
fof(f1,axiom,
! [A] : mult(unit,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(f1_nnf,plain,
! [A] : mult(unit,A) = A,
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A] : mult(unit,A) = A,
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
mult(unit,X0) = X0,
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t1,plain,
mult(unit,X1) = X1,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t8,plain,
mult(unit,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t53,plain,
mult(unit,mult(X1,mult(X1,X2))) = mult(mult(X1,X1),X2),
inference(cp,[status(thm)],[t45,t8]) ).
cnf(t790,plain,
mult(X1,mult(X1,X2)) = mult(mult(X1,X1),X2),
inference(step,[status(thm)],[t53,t8]) ).
cnf(t60,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)),
inference(orient,[status(thm)],[t790]) ).
fof(f4,axiom,
! [A] : mult(i(A),A) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f4_nnf,plain,
! [A] : mult(i(A),A) = unit,
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A] : mult(i(A),A) = unit,
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
mult(i(X0),X0) = unit,
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t3,plain,
mult(i(X1),X1) = unit,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t19,plain,
mult(i(X1),X1) = unit,
inference(orient,[status(thm)],[t3]) ).
cnf(t52,plain,
mult(i(mult(X1,X1)),mult(X1,mult(X1,X2))) = mult(unit,X2),
inference(cp,[status(thm)],[t45,t19]) ).
cnf(t796,plain,
mult(i(mult(X1,X1)),mult(X1,mult(X1,X2))) = X2,
inference(step,[status(thm)],[t52,t8]) ).
cnf(t131,plain,
mult(i(mult(X1,X1)),mult(X1,mult(X1,X2))) = X2,
inference(orient,[status(thm)],[t796]) ).
fof(f3,axiom,
! [A] : mult(A,i(A)) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(f3_nnf,plain,
! [A] : mult(A,i(A)) = unit,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A] : mult(A,i(A)) = unit,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
mult(X0,i(X0)) = unit,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t2,plain,
mult(X1,i(X1)) = unit,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t15,plain,
mult(X1,i(X1)) = unit,
inference(orient,[status(thm)],[t2]) ).
cnf(t30,plain,
mult(X1,mult(i(X1),i(X1))) = mult(unit,i(X1)),
inference(cp,[status(thm)],[t29,t15]) ).
cnf(t788,plain,
mult(X1,mult(i(X1),i(X1))) = i(X1),
inference(step,[status(thm)],[t30,t8]) ).
cnf(t37,plain,
mult(X1,mult(i(X1),i(X1))) = i(X1),
inference(orient,[status(thm)],[t788]) ).
cnf(t137,plain,
mult(i(X1),i(X1)) = mult(i(mult(X1,X1)),mult(X1,i(X1))),
inference(cp,[status(thm)],[t131,t37]) ).
cnf(t797,plain,
mult(i(X1),i(X1)) = mult(i(mult(X1,X1)),unit),
inference(step,[status(thm)],[t137,t15]) ).
cnf(t798,plain,
mult(i(X1),i(X1)) = i(mult(X1,X1)),
inference(step,[status(thm)],[t797,t7]) ).
cnf(t152,plain,
mult(i(X1),i(X1)) = i(mult(X1,X1)),
inference(orient,[status(thm)],[t798]) ).
cnf(t155,plain,
mult(i(X1),mult(i(X1),X2)) = mult(i(mult(X1,X1)),X2),
inference(cp,[status(thm)],[t60,t152]) ).
cnf(t171,plain,
mult(i(X1),mult(i(X1),X2)) = mult(i(mult(X1,X1)),X2),
inference(orient,[status(thm)],[t155]) ).
cnf(t31,plain,
mult(i(X1),mult(X1,X1)) = mult(unit,X1),
inference(cp,[status(thm)],[t29,t19]) ).
cnf(t787,plain,
mult(i(X1),mult(X1,X1)) = X1,
inference(step,[status(thm)],[t31,t8]) ).
cnf(t35,plain,
mult(i(X1),mult(X1,X1)) = X1,
inference(orient,[status(thm)],[t787]) ).
cnf(t51,plain,
mult(i(X1),mult(X1,mult(X1,X2))) = mult(X1,X2),
inference(cp,[status(thm)],[t45,t35]) ).
cnf(t79,plain,
mult(i(X1),mult(X1,mult(X1,X2))) = mult(X1,X2),
inference(orient,[status(thm)],[t51]) ).
cnf(t173,plain,
mult(i(mult(X1,X1)),mult(X1,mult(X1,X2))) = mult(i(X1),mult(X1,X2)),
inference(cp,[status(thm)],[t171,t79]) ).
cnf(t800,plain,
X2 = mult(i(X1),mult(X1,X2)),
inference(step,[status(thm)],[t173,t131]) ).
cnf(t185,plain,
mult(i(X1),mult(X1,X2)) = X2,
inference(orient,[status(thm)],[t800]) ).
cnf(t86,plain,
mult(i(X1),mult(X1,X1)) = mult(i(i(X1)),mult(i(X1),X1)),
inference(cp,[status(thm)],[t79,t35]) ).
cnf(t791,plain,
X1 = mult(i(i(X1)),mult(i(X1),X1)),
inference(step,[status(thm)],[t86,t35]) ).
cnf(t792,plain,
X1 = mult(i(i(X1)),unit),
inference(step,[status(thm)],[t791,t19]) ).
cnf(t793,plain,
X1 = i(i(X1)),
inference(step,[status(thm)],[t792,t7]) ).
cnf(t89,plain,
i(i(X1)) = X1,
inference(orient,[status(thm)],[t793]) ).
cnf(t186,plain,
X1 = mult(X2,mult(i(X2),X1)),
inference(cp,[status(thm)],[t185,t89]) ).
cnf(t197,plain,
mult(X1,mult(i(X1),X2)) = X2,
inference(orient,[status(thm)],[t186]) ).
cnf(t203,plain,
true = ifeq(X1,sk1,ifeq(mult(X2,sk3),sk2,false,true),true),
inference(cp,[status(thm)],[t22,t197]) ).
cnf(t329,plain,
ifeq(X1,sk1,ifeq(mult(X2,sk3),sk2,false,true),true) = true,
inference(orient,[status(thm)],[t203]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t330,plain,
true = ifeq(mult(X1,sk3),sk2,false,true),
inference(cp,[status(thm)],[t329,t9]) ).
cnf(t337,plain,
ifeq(mult(X1,sk3),sk2,false,true) = true,
inference(orient,[status(thm)],[t330]) ).
cnf(t341,plain,
true = ifeq(mult(X1,mult(sk3,sk3)),sk2,false,true),
inference(cp,[status(thm)],[t337,t29]) ).
cnf(t387,plain,
ifeq(mult(X1,mult(sk3,sk3)),sk2,false,true) = true,
inference(orient,[status(thm)],[t341]) ).
cnf(t194,plain,
mult(i(mult(X1,X1)),mult(X1,X2)) = mult(i(X1),X2),
inference(cp,[status(thm)],[t171,t185]) ).
cnf(t221,plain,
mult(i(mult(X1,X1)),mult(X1,X2)) = mult(i(X1),X2),
inference(orient,[status(thm)],[t194]) ).
cnf(t48,plain,
mult(X1,mult(X2,mult(X2,i(mult(X1,mult(X2,X2)))))) = unit,
inference(cp,[status(thm)],[t45,t15]) ).
cnf(t355,plain,
mult(X1,mult(X2,mult(X2,i(mult(X1,mult(X2,X2)))))) = unit,
inference(orient,[status(thm)],[t48]) ).
cnf(t377,plain,
mult(X1,mult(X1,i(mult(X2,mult(X1,X1))))) = mult(i(X2),unit),
inference(cp,[status(thm)],[t185,t355]) ).
cnf(t807,plain,
mult(X1,mult(X1,i(mult(X2,mult(X1,X1))))) = i(X2),
inference(step,[status(thm)],[t377,t7]) ).
cnf(t394,plain,
mult(X1,mult(X1,i(mult(X2,mult(X1,X1))))) = i(X2),
inference(orient,[status(thm)],[t807]) ).
cnf(t416,plain,
mult(i(X1),mult(X1,i(mult(X2,mult(X1,X1))))) = mult(i(mult(X1,X1)),i(X2)),
inference(cp,[status(thm)],[t221,t394]) ).
cnf(t808,plain,
i(mult(X2,mult(X1,X1))) = mult(i(mult(X1,X1)),i(X2)),
inference(step,[status(thm)],[t416,t185]) ).
cnf(t422,plain,
mult(i(mult(X1,X1)),i(X2)) = i(mult(X2,mult(X1,X1))),
inference(orient,[status(thm)],[t808]) ).
cnf(t427,plain,
i(mult(i(X1),mult(X2,X2))) = mult(i(mult(X2,X2)),X1),
inference(cp,[status(thm)],[t422,t89]) ).
cnf(t469,plain,
i(mult(i(X1),mult(X2,X2))) = mult(i(mult(X2,X2)),X1),
inference(orient,[status(thm)],[t427]) ).
cnf(t478,plain,
mult(i(X1),mult(X2,X2)) = i(mult(i(mult(X2,X2)),X1)),
inference(cp,[status(thm)],[t89,t469]) ).
cnf(t523,plain,
i(mult(i(mult(X1,X1)),X2)) = mult(i(X2),mult(X1,X1)),
inference(orient,[status(thm)],[t478]) ).
cnf(t525,plain,
mult(i(mult(X1,X2)),mult(X1,X1)) = i(mult(i(X1),X2)),
inference(cp,[status(thm)],[t523,t221]) ).
cnf(t735,plain,
mult(i(mult(X1,X2)),mult(X1,X1)) = i(mult(i(X1),X2)),
inference(orient,[status(thm)],[t525]) ).
cnf(t762,plain,
true = ifeq(i(mult(i(sk3),X1)),sk2,false,true),
inference(cp,[status(thm)],[t387,t735]) ).
cnf(t770,plain,
ifeq(i(mult(i(sk3),X1)),sk2,false,true) = true,
inference(orient,[status(thm)],[t762]) ).
cnf(t771,plain,
true = ifeq(i(X1),sk2,false,true),
inference(cp,[status(thm)],[t770,t185]) ).
cnf(t775,plain,
ifeq(i(X1),sk2,false,true) = true,
inference(orient,[status(thm)],[t771]) ).
cnf(t780,plain,
true = ifeq(X1,sk2,false,true),
inference(cp,[status(thm)],[t775,t89]) ).
cnf(t781,plain,
ifeq(X1,sk2,false,true) = true,
inference(orient,[status(thm)],[t780]) ).
cnf(t782,plain,
true = false,
inference(cp,[status(thm)],[t781,t9]) ).
cnf(t783,plain,
false = true,
inference(orient,[status(thm)],[t782]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t783]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP710+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.56 % Computer : n005.cluster.edu
% 0.09/5.56 % Model : x86_64 x86_64
% 0.09/5.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.56 % Memory : 8046.5625MB
% 0.09/5.56 % OS : Linux 6.8.0-71-generic
% 0.09/5.56 % CPULimit : 300
% 0.09/5.56 % WCLimit : 300
% 0.09/5.56 % DateTime : Wed Sep 23 15:48:23 UTC 2026
% 0.09/5.57 % CPUTime :
% 0.09/5.57 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.49/6.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.49/6.29 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------