%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP097-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 01:25:10 PM UTC 2026
% Result : Unsatisfiable 6.23s 1.43s
% Output : Proof 6.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 67
% Number of leaves : 4
% Syntax : Number of formulae : 108 ( 104 unt; 0 def)
% Number of atoms : 120 ( 119 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 18 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-4 aty)
% Number of variables : 211 ( 2 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f2_nnf,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t3,plain,
ifeq(multiply(inverse(a1),a1),multiply(inverse(b1),b1),ifeq(multiply(multiply(inverse(b2),b2),a2),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t10,plain,
ifeq(multiply(inverse(a1),a1),multiply(inverse(b1),b1),ifeq(multiply(multiply(inverse(b2),b2),a2),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true),true),true) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(f0,axiom,
divide(X,inverse(divide(divide(Y,Z),divide(X,Z)))) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f0_nnf,plain,
! [X,Y,Z] : divide(X,inverse(divide(divide(Y,Z),divide(X,Z)))) = Y,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,Z] : divide(X,inverse(divide(divide(Y,Z),divide(X,Z)))) = Y,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
divide(X0,inverse(divide(divide(X1,X2),divide(X0,X2)))) = X1,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t2,plain,
divide(X1,inverse(divide(divide(X2,X3),divide(X1,X3)))) = X2,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t4,plain,
divide(X1,inverse(divide(divide(X2,X3),divide(X1,X3)))) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(f1,axiom,
multiply(X,Y) = divide(X,inverse(Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f1_nnf,plain,
! [X,Y] : multiply(X,Y) = divide(X,inverse(Y)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] : multiply(X,Y) = divide(X,inverse(Y)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
multiply(X0,X1) = divide(X0,inverse(X1)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t1,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t8,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t1]) ).
cnf(t554,plain,
multiply(X1,divide(divide(X2,X3),divide(X1,X3))) = X2,
inference(step,[status(thm)],[t4,t8]) ).
cnf(t9,plain,
multiply(X1,divide(divide(X2,X3),divide(X1,X3))) = X2,
inference(rw,[status(thm)],[t554]) ).
cnf(t11,plain,
multiply(X1,divide(divide(X2,X3),divide(X1,X3))) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t12,plain,
X1 = multiply(X2,divide(multiply(X1,X3),divide(X2,inverse(X3)))),
inference(cp,[status(thm)],[t11,t8]) ).
cnf(t555,plain,
X1 = multiply(X2,divide(multiply(X1,X3),multiply(X2,X3))),
inference(step,[status(thm)],[t12,t8]) ).
cnf(t14,plain,
multiply(X1,divide(multiply(X2,X3),multiply(X1,X3))) = X2,
inference(orient,[status(thm)],[t555]) ).
cnf(t15,plain,
X1 = multiply(X2,divide(X3,multiply(X2,divide(divide(X3,Y3),divide(X1,Y3))))),
inference(cp,[status(thm)],[t14,t11]) ).
cnf(t19,plain,
multiply(X1,divide(X2,multiply(X1,divide(divide(X2,X3),divide(Y3,X3))))) = Y3,
inference(orient,[status(thm)],[t15]) ).
cnf(t20,plain,
X1 = multiply(X1,divide(X2,X2)),
inference(cp,[status(thm)],[t19,t11]) ).
cnf(t25,plain,
multiply(X1,divide(X2,X2)) = X1,
inference(orient,[status(thm)],[t20]) ).
cnf(t27,plain,
X1 = multiply(X2,divide(X1,multiply(X2,divide(X3,X3)))),
inference(cp,[status(thm)],[t14,t25]) ).
cnf(t556,plain,
X1 = multiply(X2,divide(X1,X2)),
inference(step,[status(thm)],[t27,t25]) ).
cnf(t30,plain,
multiply(X1,divide(X2,X1)) = X2,
inference(orient,[status(thm)],[t556]) ).
cnf(t31,plain,
X1 = multiply(inverse(X2),multiply(X1,X2)),
inference(cp,[status(thm)],[t30,t8]) ).
cnf(t38,plain,
multiply(inverse(X1),multiply(X2,X1)) = X2,
inference(orient,[status(thm)],[t31]) ).
cnf(t42,plain,
X1 = multiply(inverse(divide(X2,X2)),X1),
inference(cp,[status(thm)],[t38,t25]) ).
cnf(t40,plain,
X1 = multiply(inverse(divide(X2,X1)),X2),
inference(cp,[status(thm)],[t38,t30]) ).
cnf(t52,plain,
multiply(inverse(divide(X1,X2)),X1) = X2,
inference(orient,[status(thm)],[t40]) ).
cnf(t57,plain,
inverse(divide(X1,X2)) = multiply(inverse(X1),X2),
inference(cp,[status(thm)],[t38,t52]) ).
cnf(t61,plain,
inverse(divide(X1,X2)) = multiply(inverse(X1),X2),
inference(orient,[status(thm)],[t57]) ).
cnf(t558,plain,
X1 = multiply(multiply(inverse(X2),X2),X1),
inference(step,[status(thm)],[t42,t61]) ).
cnf(t67,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(orient,[status(thm)],[t558]) ).
cnf(t559,plain,
ifeq(multiply(inverse(a1),a1),multiply(inverse(b1),b1),ifeq(a2,a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true),true),true) = true,
inference(step,[status(thm)],[t10,t67]) ).
cnf(t0,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t7,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t560,plain,
ifeq(multiply(inverse(a1),a1),multiply(inverse(b1),b1),ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true),true) = true,
inference(step,[status(thm)],[t559,t7]) ).
cnf(t80,plain,
ifeq(multiply(inverse(a1),a1),multiply(inverse(b1),b1),ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true),true) = true,
inference(rw,[status(thm)],[t560]) ).
cnf(t73,plain,
divide(multiply(X1,X2),multiply(multiply(inverse(X3),X3),X2)) = X1,
inference(cp,[status(thm)],[t67,t14]) ).
cnf(t561,plain,
divide(multiply(X1,X2),X2) = X1,
inference(step,[status(thm)],[t73,t67]) ).
cnf(t81,plain,
divide(multiply(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t561]) ).
cnf(t84,plain,
X1 = divide(X2,divide(X2,X1)),
inference(cp,[status(thm)],[t81,t30]) ).
cnf(t97,plain,
divide(X1,divide(X1,X2)) = X2,
inference(orient,[status(thm)],[t84]) ).
cnf(t101,plain,
X1 = multiply(divide(X1,X2),X2),
inference(cp,[status(thm)],[t30,t97]) ).
cnf(t129,plain,
multiply(divide(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t101]) ).
cnf(t133,plain,
divide(X1,X2) = multiply(inverse(X2),X1),
inference(cp,[status(thm)],[t38,t129]) ).
cnf(t137,plain,
multiply(inverse(X1),X2) = divide(X2,X1),
inference(orient,[status(thm)],[t133]) ).
cnf(t591,plain,
ifeq(divide(a1,a1),multiply(inverse(b1),b1),ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true),true) = true,
inference(step,[status(thm)],[t80,t137]) ).
cnf(t86,plain,
X1 = divide(X1,divide(X2,X2)),
inference(cp,[status(thm)],[t81,t25]) ).
cnf(t108,plain,
divide(X1,divide(X2,X2)) = X1,
inference(orient,[status(thm)],[t86]) ).
cnf(t110,plain,
divide(X1,X1) = divide(X2,X2),
inference(cp,[status(thm)],[t97,t108]) ).
cnf(t223,plain,
divide(X1,X1) = divide(X2,X2),
inference(orient,[status(thm)],[t110]) ).
cnf(t592,plain,
ifeq(divide(true,true),multiply(inverse(b1),b1),ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true),true) = true,
inference(step,[status(thm)],[t591,t223]) ).
cnf(t593,plain,
ifeq(divide(true,true),divide(b1,b1),ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true),true) = true,
inference(step,[status(thm)],[t592,t137]) ).
cnf(t594,plain,
ifeq(divide(true,true),divide(true,true),ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true),true) = true,
inference(step,[status(thm)],[t593,t223]) ).
cnf(t595,plain,
ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true) = true,
inference(step,[status(thm)],[t594,t7]) ).
cnf(t562,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(step,[status(thm)],[t61,t137]) ).
cnf(t138,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(orient,[status(thm)],[t562]) ).
cnf(t99,plain,
X1 = divide(multiply(X2,X1),X2),
inference(cp,[status(thm)],[t97,t81]) ).
cnf(t115,plain,
divide(multiply(X1,X2),X1) = X2,
inference(orient,[status(thm)],[t99]) ).
cnf(t122,plain,
divide(multiply(X1,X2),multiply(X3,X2)) = divide(X1,X3),
inference(cp,[status(thm)],[t115,t14]) ).
cnf(t302,plain,
divide(multiply(X1,X2),multiply(X3,X2)) = divide(X1,X3),
inference(orient,[status(thm)],[t122]) ).
cnf(t98,plain,
inverse(X1) = divide(X2,multiply(X2,X1)),
inference(cp,[status(thm)],[t97,t8]) ).
cnf(t157,plain,
divide(X1,multiply(X1,X2)) = inverse(X2),
inference(orient,[status(thm)],[t98]) ).
cnf(t165,plain,
divide(multiply(X1,X2),X1) = inverse(inverse(X2)),
inference(cp,[status(thm)],[t138,t157]) ).
cnf(t565,plain,
X2 = inverse(inverse(X2)),
inference(step,[status(thm)],[t165,t115]) ).
cnf(t172,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t565]) ).
cnf(t173,plain,
multiply(X1,inverse(X2)) = divide(X1,X2),
inference(cp,[status(thm)],[t8,t172]) ).
cnf(t175,plain,
multiply(X1,inverse(X2)) = divide(X1,X2),
inference(orient,[status(thm)],[t173]) ).
cnf(t305,plain,
divide(X1,X2) = divide(divide(X1,X3),multiply(X2,inverse(X3))),
inference(cp,[status(thm)],[t302,t175]) ).
cnf(t570,plain,
divide(X1,X2) = divide(divide(X1,X3),divide(X2,X3)),
inference(step,[status(thm)],[t305,t175]) ).
cnf(t144,plain,
divide(X1,divide(X2,X3)) = multiply(divide(X3,X2),X1),
inference(cp,[status(thm)],[t137,t138]) ).
cnf(t252,plain,
divide(X1,divide(X2,X3)) = multiply(divide(X3,X2),X1),
inference(orient,[status(thm)],[t144]) ).
cnf(t571,plain,
divide(X1,X2) = multiply(divide(X3,X2),divide(X1,X3)),
inference(step,[status(thm)],[t570,t252]) ).
cnf(t318,plain,
multiply(divide(X1,X2),divide(X3,X1)) = divide(X3,X2),
inference(orient,[status(thm)],[t571]) ).
cnf(t322,plain,
divide(X1,multiply(X2,X3)) = multiply(inverse(X3),divide(X1,X2)),
inference(cp,[status(thm)],[t318,t157]) ).
cnf(t572,plain,
divide(X1,multiply(X2,X3)) = divide(divide(X1,X2),X3),
inference(step,[status(thm)],[t322,t137]) ).
cnf(t342,plain,
divide(divide(X1,X2),X3) = divide(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t572]) ).
cnf(t360,plain,
divide(X1,divide(X2,X3)) = inverse(divide(X2,multiply(X3,X1))),
inference(cp,[status(thm)],[t138,t342]) ).
cnf(t574,plain,
multiply(divide(X3,X2),X1) = inverse(divide(X2,multiply(X3,X1))),
inference(step,[status(thm)],[t360,t252]) ).
cnf(t575,plain,
multiply(divide(X3,X2),X1) = divide(multiply(X3,X1),X2),
inference(step,[status(thm)],[t574,t138]) ).
cnf(t334,plain,
divide(multiply(X1,X2),X3) = multiply(divide(X2,X3),X1),
inference(cp,[status(thm)],[t318,t81]) ).
cnf(t362,plain,
divide(multiply(X1,X2),X3) = multiply(divide(X2,X3),X1),
inference(orient,[status(thm)],[t334]) ).
cnf(t576,plain,
multiply(divide(X3,X2),X1) = multiply(divide(X1,X2),X3),
inference(step,[status(thm)],[t575,t362]) ).
cnf(t382,plain,
multiply(divide(X1,X2),X3) = multiply(divide(X3,X2),X1),
inference(orient,[status(thm)],[t576]) ).
cnf(t92,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(cp,[status(thm)],[t30,t81]) ).
cnf(t217,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t92]) ).
cnf(t385,plain,
multiply(divide(X1,X2),X3) = multiply(X1,divide(X3,X2)),
inference(cp,[status(thm)],[t382,t217]) ).
cnf(t398,plain,
multiply(divide(X1,X2),X3) = multiply(X1,divide(X3,X2)),
inference(orient,[status(thm)],[t385]) ).
cnf(t408,plain,
multiply(X1,divide(X2,inverse(X3))) = multiply(multiply(X1,X3),X2),
inference(cp,[status(thm)],[t398,t8]) ).
cnf(t585,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X3),X2),
inference(step,[status(thm)],[t408,t8]) ).
cnf(t418,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X3,X2)),
inference(orient,[status(thm)],[t585]) ).
cnf(t596,plain,
ifeq(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true) = true,
inference(step,[status(thm)],[t595,t418]) ).
cnf(t597,plain,
ifeq(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(c3,b3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true) = true,
inference(step,[status(thm)],[t596,t217]) ).
cnf(t598,plain,
ifeq(multiply(a4,b4),multiply(b4,a4),false,true) = true,
inference(step,[status(thm)],[t597,t7]) ).
cnf(t599,plain,
ifeq(multiply(b4,a4),multiply(b4,a4),false,true) = true,
inference(step,[status(thm)],[t598,t217]) ).
cnf(t600,plain,
false = true,
inference(step,[status(thm)],[t599,t7]) ).
cnf(t553,plain,
false = true,
inference(orient,[status(thm)],[t600]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t553]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP097-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.57 % Computer : n001.cluster.edu
% 0.08/0.57 % Model : x86_64 x86_64
% 0.08/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.57 % Memory : 8046.5625MB
% 0.08/0.57 % OS : Linux 6.8.0-71-generic
% 0.08/0.57 % CPULimit : 300
% 0.08/0.57 % WCLimit : 300
% 0.08/0.57 % DateTime : Wed Sep 23 13:37:06 UTC 2026
% 0.08/0.58 % CPUTime :
% 0.08/0.58 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.23/1.43 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.23/1.43 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------