%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP078-1 : 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 : 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 01:30:40 PM UTC 2026
% Result : Unsatisfiable 3.63s 1.29s
% Output : CNFRefutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 5
% Syntax : Number of formulae : 58 ( 51 unt; 0 def)
% Number of atoms : 70 ( 69 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 24 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 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 : 74 ( 0 sgn 74 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(double_divide(double_divide(X0,X1),identity),double_divide(X2,X1)))) = X2,
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(identity,double_divide(double_divide(double_divide(X0,X1),identity),double_divide(X2,X1)))) = X2,
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(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),X0),identity),double_divide(X1,X0)))) = X1,
inference(superposition,[status(thm)],[c_56,c_55]) ).
tcf(c_109,plain,
! [X0: $i] : double_divide(double_divide(identity,X0),double_divide(identity,identity)) = double_divide(double_divide(X0,identity),identity),
inference(superposition,[status(thm)],[c_56,c_55]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(double_divide(identity,identity),double_divide(X1,double_divide(X0,identity))))) = X1,
inference(superposition,[status(thm)],[c_56,c_55]) ).
tcf(c_122,plain,
double_divide(double_divide(double_divide(identity,identity),identity),identity) = identity,
inference(superposition,[status(thm)],[c_56,c_109]) ).
tcf(c_134,plain,
! [X0: $i] : double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(identity,double_divide(X0,identity)))) = X0,
inference(superposition,[status(thm)],[c_122,c_55]) ).
tcf(c_142,plain,
! [X0: $i] : double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X0,identity)))) = X0,
inference(demodulation,[status(thm)],[c_134,c_56]) ).
tcf(c_143,plain,
double_divide(identity,double_divide(identity,double_divide(identity,identity))) = double_divide(double_divide(identity,identity),identity),
inference(superposition,[status(thm)],[c_122,c_142]) ).
tcf(c_160,plain,
double_divide(double_divide(identity,identity),identity) = double_divide(identity,identity),
inference(demodulation,[status(thm)],[c_143,c_56]) ).
tcf(c_161,plain,
double_divide(double_divide(identity,identity),identity) = identity,
inference(demodulation,[status(thm)],[c_122,c_160]) ).
tcf(c_162,plain,
double_divide(identity,identity) = identity,
inference(demodulation,[status(thm)],[c_160,c_161]) ).
tcf(c_163,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_162]) ).
tcf(c_164,plain,
! [X0: $i] : double_divide(double_divide(X0,identity),identity) = double_divide(double_divide(identity,X0),identity),
inference(demodulation,[status(thm)],[c_109,c_162]) ).
tcf(c_178,plain,
( ( double_divide(double_divide(identity,a2),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_163,c_164]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(identity,X0),identity),double_divide(X1,X0)))) = X1,
inference(light_normalisation,[status(thm)],[c_108,c_162]) ).
tcf(c_188,plain,
! [X0: $i] : double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(X0,identity)),identity),identity))) = X0,
inference(superposition,[status(thm)],[c_56,c_181]) ).
tcf(c_230,plain,
! [X0: $i] : double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(X0,identity))),identity))) = X0,
inference(demodulation,[status(thm)],[c_188,c_164]) ).
tcf(c_238,plain,
! [X0: $i] : double_divide(identity,double_divide(identity,double_divide(X0,identity))) = double_divide(identity,X0),
inference(superposition,[status(thm)],[c_230,c_142]) ).
tcf(c_243,plain,
! [X0: $i] : double_divide(identity,double_divide(identity,X0)) = X0,
inference(demodulation,[status(thm)],[c_142,c_238]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(identity,double_divide(X1,double_divide(X0,identity))))) = X1,
inference(light_normalisation,[status(thm)],[c_111,c_162]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,X0),double_divide(X1,double_divide(X0,identity))) = X1,
inference(demodulation,[status(thm)],[c_250,c_243]) ).
tcf(c_253,plain,
! [X0: $i] : double_divide(double_divide(identity,X0),identity) = X0,
inference(superposition,[status(thm)],[c_56,c_251]) ).
tcf(c_255,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(identity,double_divide(double_divide(X1,identity),double_divide(X2,double_divide(X1,double_divide(X0,identity)))))) = X2,
inference(superposition,[status(thm)],[c_251,c_55]) ).
tcf(c_259,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(identity,double_divide(double_divide(X1,identity),double_divide(X2,double_divide(X1,double_divide(X0,identity)))))) = X2,
inference(light_normalisation,[status(thm)],[c_255,c_243]) ).
tcf(c_260,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_178,c_253]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(double_divide(double_divide(X0,identity),identity),X1))) = double_divide(identity,X1),
inference(superposition,[status(thm)],[c_253,c_55]) ).
tcf(c_270,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(X1,X0)) = X1,
inference(superposition,[status(thm)],[c_253,c_251]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(light_normalisation,[status(thm)],[c_270,c_243]) ).
tcf(c_314,plain,
! [X0: $i] : double_divide(X0,identity) = double_divide(identity,X0),
inference(superposition,[status(thm)],[c_243,c_253]) ).
tcf(c_340,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_260,c_314]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_273,c_273]) ).
tcf(c_397,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,identity),X1) = double_divide(double_divide(identity,X0),X1),
inference(superposition,[status(thm)],[c_350,c_251]) ).
tcf(c_399,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(X0,X1))) = double_divide(identity,X1),
inference(demodulation,[status(thm)],[c_269,c_273,c_397]) ).
tcf(c_402,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,identity),double_divide(identity,double_divide(X0,X1))) = double_divide(identity,X1),
inference(superposition,[status(thm)],[c_314,c_399]) ).
tcf(c_405,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(identity,double_divide(double_divide(identity,X0),X1))) = double_divide(identity,X1),
inference(superposition,[status(thm)],[c_243,c_399]) ).
tcf(c_1265,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,identity),double_divide(identity,X1)) = double_divide(identity,double_divide(X1,X0)),
inference(superposition,[status(thm)],[c_273,c_402]) ).
tcf(c_1314,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(X0,double_divide(identity,X1))) = double_divide(X1,double_divide(identity,X0)),
inference(superposition,[status(thm)],[c_273,c_405]) ).
tcf(c_1336,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(identity,X0),X1)) = double_divide(double_divide(identity,X1),X0),
inference(superposition,[status(thm)],[c_405,c_350]) ).
tcf(c_1362,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(double_divide(b3,a3),double_divide(identity,c3)),
inference(demodulation,[status(thm)],[c_340,c_1314]) ).
tcf(c_1369,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_1362,c_1336]) ).
tcf(c_1767,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(X0,identity),X1)) = double_divide(double_divide(X1,identity),X0),
inference(superposition,[status(thm)],[c_273,c_1265]) ).
tcf(c_2980,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(double_divide(identity,double_divide(X1,double_divide(X2,double_divide(X0,identity)))),X2)) = X1,
inference(demodulation,[status(thm)],[c_259,c_397,c_1767]) ).
tcf(c_3011,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,double_divide(X1,identity)),X2) = double_divide(X1,double_divide(double_divide(identity,X2),X0)),
inference(superposition,[status(thm)],[c_350,c_2980]) ).
tcf(c_4876,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(identity,X0),double_divide(double_divide(identity,X1),X2)) = double_divide(double_divide(X2,X0),X1),
inference(superposition,[status(thm)],[c_350,c_3011]) ).
tcf(c_6873,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_243,c_4876]) ).
tcf(c_6938,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_1369,c_6873]) ).
tcf(c_6939,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_6938]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP078-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 13:29:32 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 0.08/0.42
% 0.08/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.42
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 3.63/1.29 % SZS status Started for theBenchmark.p
% 3.63/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 3.63/1.29
% 3.63/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.63/1.29
% 3.63/1.29 % ------ iProver source info
% 3.63/1.29
% 3.63/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 3.63/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.63/1.29 % git: non_committed_changes: false
% 3.63/1.29
% 3.63/1.29 % ------ Parsing...% successful
% 3.63/1.29
% 3.63/1.29
% 3.63/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.63/1.29
% 3.63/1.29 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.63/1.29
% 3.63/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.63/1.29
% 3.63/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.63/1.29 % ------ Proving...
% 3.63/1.29 % ------ Problem Properties
% 3.63/1.29
% 3.63/1.29 %
% 3.63/1.29 % clauses 3
% 3.63/1.29 % conjectures 0
% 3.63/1.29 % EPR 0
% 3.63/1.29 % Horn 3
% 3.63/1.29 % unary 2
% 3.63/1.29 % binary 0
% 3.63/1.29 % lits 5
% 3.63/1.29 % lits eq 5
% 3.63/1.29 % fd_pure 0
% 3.63/1.29 % fd_pseudo 0
% 3.63/1.29 % fd_cond 0
% 3.63/1.29 % fd_pseudo_cond 0
% 3.63/1.29 % AC symbols 0
% 3.63/1.29
% 3.63/1.29 % ------ Schedule dynamic 5 is on
% 3.63/1.29
% 3.63/1.29 % ------ no conjectures: strip conj schedule
% 3.63/1.29
% 3.63/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.63/1.29
% 3.63/1.29
% 3.63/1.29 % ------
% 3.63/1.29 % Current options:
% 3.63/1.29 % ------
% 3.63/1.29
% 3.63/1.29
% 3.63/1.29 %
% 3.63/1.29
% 3.63/1.29 % ------ Proving...
% 3.63/1.29 %
% 3.63/1.29
% 3.63/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 3.63/1.29
% 3.63/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.63/1.29
% 3.63/1.29
%------------------------------------------------------------------------------