%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP079-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 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 01:30:41 PM UTC 2026
% Result : Unsatisfiable 2.83s 1.28s
% Output : CNFRefutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 66 ( 60 unt; 0 def)
% Number of atoms : 77 ( 76 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 24 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 84 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(double_divide(X1,X2),double_divide(identity,identity)),double_divide(X0,X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0] : inverse(X0) = double_divide(X0,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f4,axiom,
! [X0] : identity = double_divide(X0,inverse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f6,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != multiply(identity,a2)
| identity != multiply(inverse(a1),a1) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,plain,
( double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity)
| a2 != double_divide(double_divide(a2,identity),identity)
| identity != double_divide(double_divide(a1,double_divide(a1,identity)),identity) ),
inference(definition_unfolding,[],[f6,f2,f3,f2,f2,f2,f2,f2]) ).
fof(f8,plain,
! [X0] : identity = double_divide(X0,double_divide(X0,identity)),
inference(definition_unfolding,[],[f4,f3]) ).
tcf(c_54,negated_conjecture,
( ( double_divide(double_divide(a2,identity),identity) != a2 )
| ( double_divide(double_divide(a1,double_divide(a1,identity)),identity) != identity )
| ( double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(identity,X0),double_divide(double_divide(double_divide(X1,X2),double_divide(identity,identity)),double_divide(X0,X2))) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_56,plain,
! [X0: $i] : double_divide(X0,double_divide(X0,identity)) = identity,
inference(cnf_transformation,[],[f8]) ).
tcf(c_69,plain,
( ( double_divide(identity,identity) != identity )
| ( double_divide(double_divide(a2,identity),identity) != a2 )
| ( double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) ) ),
inference(demodulation,[status(thm)],[c_54,c_56]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(double_divide(X0,X1),double_divide(identity,identity)),double_divide(double_divide(identity,identity),X1))) = X0,
inference(superposition,[status(thm)],[c_56,c_55]) ).
tcf(c_109,plain,
! [X0: $i] : double_divide(double_divide(identity,double_divide(double_divide(X0,identity),double_divide(identity,identity))),identity) = X0,
inference(superposition,[status(thm)],[c_56,c_55]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,X0),double_divide(double_divide(double_divide(X1,double_divide(X0,identity)),double_divide(identity,identity)),identity)) = X1,
inference(superposition,[status(thm)],[c_56,c_55]) ).
tcf(c_125,plain,
! [X0: $i] : double_divide(double_divide(identity,double_divide(X0,double_divide(identity,identity))),identity) = double_divide(identity,double_divide(double_divide(X0,identity),double_divide(identity,identity))),
inference(superposition,[status(thm)],[c_109,c_109]) ).
tcf(c_127,plain,
! [X0: $i] : double_divide(identity,double_divide(double_divide(double_divide(X0,identity),identity),double_divide(identity,identity))) = X0,
inference(demodulation,[status(thm)],[c_109,c_125]) ).
tcf(c_215,plain,
! [X0: $i] : double_divide(double_divide(identity,X0),double_divide(double_divide(identity,double_divide(identity,identity)),identity)) = X0,
inference(superposition,[status(thm)],[c_56,c_113]) ).
tcf(c_248,plain,
! [X0: $i] : double_divide(double_divide(identity,X0),double_divide(identity,identity)) = X0,
inference(demodulation,[status(thm)],[c_215,c_56]) ).
tcf(c_250,plain,
double_divide(identity,identity) = identity,
inference(superposition,[status(thm)],[c_56,c_248]) ).
tcf(c_254,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,X0),double_divide(X1,double_divide(X0,X1))) = identity,
inference(superposition,[status(thm)],[c_248,c_55]) ).
tcf(c_261,plain,
! [X0: $i] : double_divide(double_divide(identity,X0),double_divide(double_divide(X0,identity),identity)) = identity,
inference(superposition,[status(thm)],[c_248,c_113]) ).
tcf(c_263,plain,
( ( double_divide(double_divide(a2,identity),identity) != a2 )
| ( double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_69,c_250]) ).
tcf(c_264,plain,
! [X0: $i] : double_divide(double_divide(identity,X0),identity) = X0,
inference(demodulation,[status(thm)],[c_248,c_250]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,X0),double_divide(double_divide(double_divide(X1,double_divide(X0,identity)),identity),identity)) = X1,
inference(demodulation,[status(thm)],[c_113,c_250]) ).
tcf(c_266,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(double_divide(X0,X1),identity),double_divide(identity,X1))) = X0,
inference(demodulation,[status(thm)],[c_108,c_250]) ).
tcf(c_267,plain,
! [X0: $i] : double_divide(identity,double_divide(double_divide(double_divide(X0,identity),identity),identity)) = X0,
inference(demodulation,[status(thm)],[c_127,c_250]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(identity,X0),double_divide(double_divide(double_divide(X1,X2),identity),double_divide(X0,X2))) = X1,
inference(demodulation,[status(thm)],[c_55,c_250]) ).
tcf(c_305,plain,
! [X0: $i] : double_divide(identity,double_divide(X0,double_divide(identity,X0))) = identity,
inference(superposition,[status(thm)],[c_250,c_254]) ).
tcf(c_330,plain,
! [X0: $i] : double_divide(X0,double_divide(identity,X0)) = double_divide(identity,identity),
inference(superposition,[status(thm)],[c_305,c_264]) ).
tcf(c_332,plain,
! [X0: $i] : double_divide(X0,double_divide(identity,X0)) = identity,
inference(light_normalisation,[status(thm)],[c_330,c_250]) ).
tcf(c_359,plain,
! [X0: $i] : double_divide(identity,double_divide(double_divide(X0,identity),identity)) = double_divide(identity,X0),
inference(superposition,[status(thm)],[c_264,c_267]) ).
tcf(c_369,plain,
! [X0: $i] : double_divide(identity,double_divide(X0,identity)) = X0,
inference(demodulation,[status(thm)],[c_267,c_359]) ).
tcf(c_409,plain,
! [X0: $i] : double_divide(double_divide(X0,identity),X0) = identity,
inference(superposition,[status(thm)],[c_369,c_332]) ).
tcf(c_597,plain,
! [X0: $i] : double_divide(identity,double_divide(double_divide(identity,identity),double_divide(identity,double_divide(X0,identity)))) = X0,
inference(superposition,[status(thm)],[c_56,c_266]) ).
tcf(c_617,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(X0,X1),identity),double_divide(identity,X1)) = double_divide(X0,identity),
inference(superposition,[status(thm)],[c_266,c_264]) ).
tcf(c_631,plain,
! [X0: $i] : double_divide(identity,double_divide(identity,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_597,c_250,c_369]) ).
tcf(c_729,plain,
! [X0: $i] : double_divide(double_divide(identity,double_divide(X0,identity)),double_divide(double_divide(identity,identity),identity)) = double_divide(identity,X0),
inference(superposition,[status(thm)],[c_261,c_265]) ).
tcf(c_733,plain,
! [X0: $i] : double_divide(double_divide(identity,X0),double_divide(double_divide(identity,identity),identity)) = double_divide(double_divide(X0,identity),identity),
inference(superposition,[status(thm)],[c_409,c_265]) ).
tcf(c_735,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(double_divide(double_divide(X1,X0),identity),identity)) = X1,
inference(superposition,[status(thm)],[c_264,c_265]) ).
tcf(c_745,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(double_divide(double_divide(X1,X0),identity),identity)) = X1,
inference(light_normalisation,[status(thm)],[c_735,c_631]) ).
tcf(c_746,plain,
! [X0: $i] : double_divide(double_divide(X0,identity),identity) = X0,
inference(light_normalisation,[status(thm)],[c_733,c_250,c_264]) ).
tcf(c_748,plain,
! [X0: $i] : double_divide(X0,identity) = double_divide(identity,X0),
inference(light_normalisation,[status(thm)],[c_729,c_250,c_369]) ).
tcf(c_751,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
inference(backward_subsumption_resolution,[status(thm)],[c_263,c_746]) ).
tcf(c_753,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,X0),double_divide(X1,double_divide(X0,identity))) = X1,
inference(demodulation,[status(thm)],[c_265,c_746]) ).
tcf(c_783,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(identity,X0),double_divide(double_divide(identity,double_divide(X1,X2)),double_divide(X0,X2))) = X1,
inference(demodulation,[status(thm)],[c_269,c_748]) ).
tcf(c_804,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,identity),double_divide(double_divide(identity,double_divide(X0,double_divide(X1,identity))),X1)) = X0,
inference(superposition,[status(thm)],[c_369,c_783]) ).
tcf(c_819,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(identity,double_divide(X0,double_divide(X1,identity))),X1)) = X0,
inference(light_normalisation,[status(thm)],[c_804,c_250]) ).
tcf(c_936,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),
inference(demodulation,[status(thm)],[c_751,c_748]) ).
tcf(c_985,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(demodulation,[status(thm)],[c_745,c_369,c_748]) ).
tcf(c_1003,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_985,c_985]) ).
tcf(c_1013,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(identity,double_divide(X0,X1)),double_divide(X2,X1)) = double_divide(X0,double_divide(identity,X2)),
inference(superposition,[status(thm)],[c_783,c_1003]) ).
tcf(c_1031,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,identity),X1) = double_divide(double_divide(identity,X0),X1),
inference(superposition,[status(thm)],[c_1003,c_753]) ).
tcf(c_1037,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X1,identity)) = double_divide(X0,double_divide(identity,X1)),
inference(superposition,[status(thm)],[c_753,c_1003]) ).
tcf(c_1129,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,identity),double_divide(identity,X1)) = double_divide(double_divide(identity,X0),double_divide(X1,identity)),
inference(superposition,[status(thm)],[c_1037,c_1031]) ).
tcf(c_1373,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,double_divide(X0,X1)),double_divide(X1,identity)) = double_divide(X0,identity),
inference(demodulation,[status(thm)],[c_617,c_1129]) ).
tcf(c_1402,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,double_divide(X0,double_divide(identity,X1))),X1) = double_divide(X0,identity),
inference(superposition,[status(thm)],[c_1003,c_1373]) ).
tcf(c_1455,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(identity,X0),X1)) = double_divide(double_divide(X1,identity),X0),
inference(superposition,[status(thm)],[c_1003,c_819]) ).
tcf(c_1491,plain,
double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))) != double_divide(double_divide(a3,identity),double_divide(c3,b3)),
inference(demodulation,[status(thm)],[c_936,c_1455]) ).
tcf(c_1647,plain,
double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))) != double_divide(double_divide(identity,a3),double_divide(c3,b3)),
inference(demodulation,[status(thm)],[c_1491,c_1031]) ).
tcf(c_1687,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(X0,double_divide(identity,X1))) = double_divide(X1,double_divide(X0,identity)),
inference(superposition,[status(thm)],[c_1402,c_985]) ).
tcf(c_1721,plain,
double_divide(double_divide(identity,a3),double_divide(c3,b3)) != double_divide(double_divide(b3,a3),double_divide(c3,identity)),
inference(demodulation,[status(thm)],[c_1647,c_1687]) ).
tcf(c_1873,plain,
double_divide(double_divide(identity,a3),double_divide(c3,b3)) != double_divide(double_divide(b3,a3),double_divide(identity,c3)),
inference(demodulation,[status(thm)],[c_1721,c_1037]) ).
tcf(c_4232,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,X1),double_divide(identity,X2)) = double_divide(double_divide(identity,X1),double_divide(X2,X0)),
inference(superposition,[status(thm)],[c_1003,c_1013]) ).
tcf(c_4358,plain,
double_divide(double_divide(identity,a3),double_divide(c3,b3)) != double_divide(double_divide(identity,a3),double_divide(c3,b3)),
inference(demodulation,[status(thm)],[c_1873,c_4232]) ).
tcf(c_4359,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_4358]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP079-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 13:34:34 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 2.83/1.28 % SZS status Started for theBenchmark.p
% 2.83/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.83/1.28
% 2.83/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.83/1.28
% 2.83/1.28 % ------ iProver source info
% 2.83/1.28
% 2.83/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.83/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.83/1.28 % git: non_committed_changes: false
% 2.83/1.28
% 2.83/1.28 % ------ Parsing...% successful
% 2.83/1.28
% 2.83/1.28
% 2.83/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.83/1.28
% 2.83/1.28 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.83/1.28
% 2.83/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.83/1.28
% 2.83/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.83/1.28 % ------ Proving...
% 2.83/1.28 % ------ Problem Properties
% 2.83/1.28
% 2.83/1.28 %
% 2.83/1.28 % clauses 3
% 2.83/1.28 % conjectures 0
% 2.83/1.28 % EPR 0
% 2.83/1.28 % Horn 3
% 2.83/1.28 % unary 2
% 2.83/1.28 % binary 0
% 2.83/1.28 % lits 5
% 2.83/1.28 % lits eq 5
% 2.83/1.28 % fd_pure 0
% 2.83/1.28 % fd_pseudo 0
% 2.83/1.28 % fd_cond 0
% 2.83/1.28 % fd_pseudo_cond 0
% 2.83/1.28 % AC symbols 0
% 2.83/1.28
% 2.83/1.28 % ------ Schedule dynamic 5 is on
% 2.83/1.28
% 2.83/1.28 % ------ no conjectures: strip conj schedule
% 2.83/1.28
% 2.83/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.83/1.28
% 2.83/1.28
% 2.83/1.28 % ------
% 2.83/1.28 % Current options:
% 2.83/1.28 % ------
% 2.83/1.28
% 2.83/1.28
% 2.83/1.28 %
% 2.83/1.28
% 2.83/1.28 % ------ Proving...
% 2.83/1.28 %
% 2.83/1.28
% 2.83/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.83/1.28
% 2.83/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.83/1.28
% 2.83/1.28
%------------------------------------------------------------------------------