%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP017-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 01:24:56 PM UTC 2026
% Result : Unsatisfiable 6.88s 1.35s
% Output : Proof 6.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 11
% Syntax : Number of formulae : 121 ( 113 unt; 0 def)
% Number of atoms : 141 ( 90 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 26 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 194 ( 2 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,axiom,
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).
fof(f5_nnf,plain,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t10,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,X3,X4),X4) = X4,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t14,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,X3,X4),X4) = X4,
inference(orient,[status(thm)],[t10]) ).
cnf(f4,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1) ).
fof(f4_nnf,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t9,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t16,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t18,plain,
multiply(X1,X2) = ifeq(product(X1,X2,X3),true,ifeq(true,true,X3,multiply(X1,X2)),multiply(X1,X2)),
inference(cp,[status(thm)],[t14,t16]) ).
cnf(t6,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(t684,plain,
multiply(X1,X2) = ifeq(product(X1,X2,X3),true,X3,multiply(X1,X2)),
inference(step,[status(thm)],[t18,t13]) ).
cnf(t160,plain,
ifeq(product(X1,X2,X3),true,X3,multiply(X1,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t684]) ).
cnf(f6,axiom,
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
fof(f6_nnf,plain,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t12,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X2,X4,X5),true,ifeq(product(X3,X4,X6),true,product(X1,X5,X6),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t43,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X2,X4,X5),true,ifeq(product(X3,X4,X6),true,product(X1,X5,X6),true),true),true) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(f3,axiom,
product(X,inverse(X),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f3_nnf,plain,
! [X] : product(X,inverse(X),identity),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] : product(X,inverse(X),identity),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t7,plain,
product(X1,inverse(X1),identity) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t22,plain,
product(X1,inverse(X1),identity) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t45,plain,
true = ifeq(true,true,ifeq(product(inverse(X1),X2,X3),true,ifeq(product(identity,X2,X4),true,product(X1,X3,X4),true),true),true),
inference(cp,[status(thm)],[t43,t22]) ).
cnf(t703,plain,
true = ifeq(product(inverse(X1),X2,X3),true,ifeq(product(identity,X2,X4),true,product(X1,X3,X4),true),true),
inference(step,[status(thm)],[t45,t13]) ).
cnf(t406,plain,
ifeq(product(inverse(X1),X2,X3),true,ifeq(product(identity,X2,X4),true,product(X1,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t703]) ).
cnf(f0,axiom,
product(identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f0_nnf,plain,
! [X] : product(identity,X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : product(identity,X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
product(identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t5,plain,
product(identity,X1,X1) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t25,plain,
product(identity,X1,X1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t423,plain,
true = ifeq(product(inverse(X1),X2,X3),true,ifeq(true,true,product(X1,X3,X2),true),true),
inference(cp,[status(thm)],[t406,t25]) ).
cnf(t709,plain,
true = ifeq(product(inverse(X1),X2,X3),true,product(X1,X3,X2),true),
inference(step,[status(thm)],[t423,t13]) ).
cnf(t511,plain,
ifeq(product(inverse(X1),X2,X3),true,product(X1,X3,X2),true) = true,
inference(orient,[status(thm)],[t709]) ).
cnf(t512,plain,
true = ifeq(true,true,product(X1,multiply(inverse(X1),X2),X2),true),
inference(cp,[status(thm)],[t511,t16]) ).
cnf(t715,plain,
true = product(X1,multiply(inverse(X1),X2),X2),
inference(step,[status(thm)],[t512,t13]) ).
cnf(t562,plain,
product(X1,multiply(inverse(X1),X2),X2) = true,
inference(orient,[status(thm)],[t715]) ).
cnf(t44,plain,
true = ifeq(true,true,ifeq(product(X1,X2,X3),true,ifeq(product(multiply(X4,X1),X2,X5),true,product(X4,X3,X5),true),true),true),
inference(cp,[status(thm)],[t43,t16]) ).
cnf(t691,plain,
true = ifeq(product(X1,X2,X3),true,ifeq(product(multiply(X4,X1),X2,X5),true,product(X4,X3,X5),true),true),
inference(step,[status(thm)],[t44,t13]) ).
cnf(t215,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(multiply(X4,X1),X2,X5),true,product(X4,X3,X5),true),true) = true,
inference(orient,[status(thm)],[t691]) ).
cnf(f11,hypothesis,
product(c,a,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_a_is_identity) ).
fof(f11_nnf,plain,
product(c,a,identity),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
product(c,a,identity),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(t4,plain,
product(c,a,identity) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t37,plain,
product(c,a,identity) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t220,plain,
true = ifeq(true,true,ifeq(product(multiply(X1,c),a,X2),true,product(X1,identity,X2),true),true),
inference(cp,[status(thm)],[t215,t37]) ).
cnf(t698,plain,
true = ifeq(product(multiply(X1,c),a,X2),true,product(X1,identity,X2),true),
inference(step,[status(thm)],[t220,t13]) ).
cnf(t352,plain,
ifeq(product(multiply(X1,c),a,X2),true,product(X1,identity,X2),true) = true,
inference(orient,[status(thm)],[t698]) ).
cnf(t353,plain,
true = ifeq(true,true,product(X1,identity,multiply(multiply(X1,c),a)),true),
inference(cp,[status(thm)],[t352,t16]) ).
cnf(t699,plain,
true = product(X1,identity,multiply(multiply(X1,c),a)),
inference(step,[status(thm)],[t353,t13]) ).
cnf(t362,plain,
product(X1,identity,multiply(multiply(X1,c),a)) = true,
inference(orient,[status(thm)],[t699]) ).
cnf(f2,axiom,
product(inverse(X),X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f2_nnf,plain,
! [X] : product(inverse(X),X,identity),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : product(inverse(X),X,identity),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t8,plain,
product(inverse(X1),X1,identity) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t40,plain,
product(inverse(X1),X1,identity) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t41,plain,
X1 = ifeq(true,true,ifeq(product(inverse(X2),X2,X1),true,identity,X1),X1),
inference(cp,[status(thm)],[t14,t40]) ).
cnf(t680,plain,
X1 = ifeq(product(inverse(X2),X2,X1),true,identity,X1),
inference(step,[status(thm)],[t41,t13]) ).
cnf(t155,plain,
ifeq(product(inverse(X1),X1,X2),true,identity,X2) = X2,
inference(orient,[status(thm)],[t680]) ).
cnf(t156,plain,
multiply(inverse(X1),X1) = ifeq(true,true,identity,multiply(inverse(X1),X1)),
inference(cp,[status(thm)],[t155,t16]) ).
cnf(t681,plain,
multiply(inverse(X1),X1) = identity,
inference(step,[status(thm)],[t156,t13]) ).
cnf(t157,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t681]) ).
cnf(t363,plain,
true = product(inverse(c),identity,multiply(identity,a)),
inference(cp,[status(thm)],[t362,t157]) ).
cnf(t26,plain,
X1 = ifeq(true,true,ifeq(product(identity,X2,X1),true,X2,X1),X1),
inference(cp,[status(thm)],[t14,t25]) ).
cnf(t662,plain,
X1 = ifeq(product(identity,X2,X1),true,X2,X1),
inference(step,[status(thm)],[t26,t13]) ).
cnf(t129,plain,
ifeq(product(identity,X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t662]) ).
cnf(t130,plain,
multiply(identity,X1) = ifeq(true,true,X1,multiply(identity,X1)),
inference(cp,[status(thm)],[t129,t16]) ).
cnf(t663,plain,
multiply(identity,X1) = X1,
inference(step,[status(thm)],[t130,t13]) ).
cnf(t133,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t663]) ).
cnf(t700,plain,
true = product(inverse(c),identity,a),
inference(step,[status(thm)],[t363,t133]) ).
cnf(t385,plain,
product(inverse(c),identity,a) = true,
inference(orient,[status(thm)],[t700]) ).
cnf(t387,plain,
multiply(inverse(c),identity) = ifeq(true,true,a,multiply(inverse(c),identity)),
inference(cp,[status(thm)],[t160,t385]) ).
cnf(f1,axiom,
product(X,identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f1_nnf,plain,
! [X] : product(X,identity,X),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : product(X,identity,X),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
product(X0,identity,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t0,plain,
product(X1,identity,X1) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t19,plain,
product(X1,identity,X1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t20,plain,
X1 = ifeq(true,true,ifeq(product(X2,identity,X1),true,X2,X1),X1),
inference(cp,[status(thm)],[t14,t19]) ).
cnf(t658,plain,
X1 = ifeq(product(X2,identity,X1),true,X2,X1),
inference(step,[status(thm)],[t20,t13]) ).
cnf(t119,plain,
ifeq(product(X1,identity,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t658]) ).
cnf(t120,plain,
multiply(X1,identity) = ifeq(true,true,X1,multiply(X1,identity)),
inference(cp,[status(thm)],[t119,t16]) ).
cnf(t660,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t120,t13]) ).
cnf(t127,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t660]) ).
cnf(t701,plain,
inverse(c) = ifeq(true,true,a,multiply(inverse(c),identity)),
inference(step,[status(thm)],[t387,t127]) ).
cnf(t702,plain,
inverse(c) = a,
inference(step,[status(thm)],[t701,t13]) ).
cnf(t405,plain,
inverse(c) = a,
inference(orient,[status(thm)],[t702]) ).
cnf(t565,plain,
true = product(c,multiply(a,X1),X1),
inference(cp,[status(thm)],[t562,t405]) ).
cnf(t615,plain,
product(c,multiply(a,X1),X1) = true,
inference(orient,[status(thm)],[t565]) ).
cnf(f8,hypothesis,
product(a,b,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_identity) ).
fof(f8_nnf,plain,
product(a,b,identity),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
product(a,b,identity),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(t1,plain,
product(a,b,identity) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t28,plain,
product(a,b,identity) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t29,plain,
X1 = ifeq(true,true,ifeq(product(a,b,X1),true,identity,X1),X1),
inference(cp,[status(thm)],[t14,t28]) ).
cnf(t665,plain,
X1 = ifeq(product(a,b,X1),true,identity,X1),
inference(step,[status(thm)],[t29,t13]) ).
cnf(t135,plain,
ifeq(product(a,b,X1),true,identity,X1) = X1,
inference(orient,[status(thm)],[t665]) ).
cnf(t136,plain,
multiply(a,b) = ifeq(true,true,identity,multiply(a,b)),
inference(cp,[status(thm)],[t135,t16]) ).
cnf(t666,plain,
multiply(a,b) = identity,
inference(step,[status(thm)],[t136,t13]) ).
cnf(t137,plain,
multiply(a,b) = identity,
inference(orient,[status(thm)],[t666]) ).
cnf(t616,plain,
true = product(c,identity,b),
inference(cp,[status(thm)],[t615,t137]) ).
cnf(t635,plain,
product(c,identity,b) = true,
inference(orient,[status(thm)],[t616]) ).
cnf(t637,plain,
multiply(c,identity) = ifeq(true,true,b,multiply(c,identity)),
inference(cp,[status(thm)],[t160,t635]) ).
cnf(t717,plain,
c = ifeq(true,true,b,multiply(c,identity)),
inference(step,[status(thm)],[t637,t127]) ).
cnf(t718,plain,
c = b,
inference(step,[status(thm)],[t717,t13]) ).
cnf(t657,plain,
b = c,
inference(orient,[status(thm)],[t718]) ).
cnf(f12,negated_conjecture,
b != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_equals_c) ).
fof(f12_nnf,plain,
b != c,
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
b != c,
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
b != c,
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
c != b,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(g0_0,plain,
c != c,
inference(rw,[status(thm)],[goal_0,t657]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP017-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n006.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 13:14:34 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.88/1.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.88/1.35 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------