%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP108-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n003.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 01:30:55 PM UTC 2026
% Result : Unsatisfiable 3.80s 1.20s
% Output : CNFRefutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 3
% Syntax : Number of formulae : 50 ( 40 unt; 0 def)
% Number of atoms : 76 ( 75 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 64 ( 38 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 9 ( 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 94 ( 0 sgn 94 !; 0 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : inverse(double_divide(inverse(double_divide(X0,inverse(double_divide(X1,double_divide(X0,X2))))),X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,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/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f4,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != multiply(multiply(inverse(b2),b2),a2)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(reorient_equations,[],[f3]) ).
fof(f5,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
| a2 != inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2)))))
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(definition_unfolding,[],[f4,f2,f2,f2,f2,f2,f2,f2,f2,f2,f2]) ).
tcf(c_52,negated_conjecture,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) )
| ( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) )
| ( inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 ) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(inverse(double_divide(X0,inverse(double_divide(X1,double_divide(X0,X2))))),X2)) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(double_divide(X0,inverse(double_divide(X1,double_divide(X0,double_divide(X2,X3)))))) = inverse(double_divide(inverse(double_divide(X2,X1)),X3)),
inference(superposition,[status(thm)],[c_53,c_53]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(inverse(double_divide(inverse(double_divide(X0,X1)),X2)),double_divide(X0,X2))) = X1,
inference(superposition,[status(thm)],[c_112,c_53]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(X0,double_divide(inverse(double_divide(X1,X0)),double_divide(X1,X2)))) = X2,
inference(superposition,[status(thm)],[c_116,c_116]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(double_divide(inverse(double_divide(X0,X1)),double_divide(X2,X1))) = double_divide(inverse(double_divide(X3,X2)),double_divide(X3,X0)),
inference(superposition,[status(thm)],[c_126,c_116]) ).
tcf(c_570,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(X0,X1)),double_divide(X0,inverse(double_divide(X1,X2)))) = X2,
inference(superposition,[status(thm)],[c_144,c_116]) ).
tcf(c_587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(inverse(double_divide(inverse(double_divide(X0,X1)),double_divide(inverse(double_divide(X2,double_divide(X3,double_divide(X3,X0)))),X1)))) = X2,
inference(superposition,[status(thm)],[c_144,c_53]) ).
tcf(c_608,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(X0,inverse(double_divide(inverse(double_divide(X1,X2)),double_divide(X0,X2))))) = X1,
inference(superposition,[status(thm)],[c_144,c_126]) ).
tcf(c_1176,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(X0,inverse(inverse(double_divide(inverse(double_divide(X1,X2)),double_divide(X1,X2)))))) = X0,
inference(superposition,[status(thm)],[c_144,c_608]) ).
tcf(c_1582,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,inverse(inverse(double_divide(inverse(X1),X1))))) = X0,
inference(superposition,[status(thm)],[c_570,c_1176]) ).
tcf(c_1600,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(X0,inverse(double_divide(inverse(double_divide(X1,X2)),double_divide(X1,X2))))) = X0,
inference(superposition,[status(thm)],[c_144,c_1582]) ).
tcf(c_1902,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,inverse(double_divide(inverse(X1),X1)))) = X0,
inference(superposition,[status(thm)],[c_570,c_1600]) ).
tcf(c_1928,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(X0,double_divide(inverse(double_divide(X1,X2)),double_divide(X1,X2)))) = X0,
inference(superposition,[status(thm)],[c_144,c_1902]) ).
tcf(c_2265,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,double_divide(inverse(X1),X1))) = X0,
inference(superposition,[status(thm)],[c_570,c_1928]) ).
tcf(c_2304,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(inverse(double_divide(inverse(double_divide(X0,X1)),double_divide(X2,X1)))) = inverse(double_divide(inverse(X0),X2)),
inference(superposition,[status(thm)],[c_144,c_2265]) ).
tcf(c_2336,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(inverse(double_divide(X0,X1)),X2)) = inverse(double_divide(inverse(double_divide(X0,X2)),X1)),
inference(superposition,[status(thm)],[c_2265,c_112]) ).
tcf(c_2350,plain,
! [X0: $i,X1: $i] : inverse(double_divide(inverse(X0),inverse(double_divide(X1,X0)))) = X1,
inference(superposition,[status(thm)],[c_2265,c_608]) ).
tcf(c_2356,plain,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) )
| ( inverse(double_divide(inverse(double_divide(c3,a3)),b3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) )
| ( inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 ) ),
inference(demodulation,[status(thm)],[c_52,c_2336]) ).
tcf(c_3336,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(inverse(X0),inverse(double_divide(X1,double_divide(X2,double_divide(X2,X0)))))) = X1,
inference(demodulation,[status(thm)],[c_587,c_2304]) ).
tcf(c_3393,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,double_divide(X0,X1))) = inverse(X1),
inference(superposition,[status(thm)],[c_3336,c_1902]) ).
tcf(c_3659,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(inverse(double_divide(X0,X1)),X2)) = inverse(double_divide(X0,inverse(double_divide(X1,X2)))),
inference(superposition,[status(thm)],[c_570,c_3393]) ).
tcf(c_3679,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(X0,X1)),double_divide(X0,inverse(X2))) = double_divide(X1,X2),
inference(superposition,[status(thm)],[c_3393,c_570]) ).
tcf(c_3688,plain,
! [X0: $i,X1: $i] : inverse(double_divide(inverse(double_divide(X0,X1)),inverse(X1))) = X0,
inference(superposition,[status(thm)],[c_3393,c_608]) ).
tcf(c_3697,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_570,c_3679]) ).
tcf(c_4013,plain,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) )
| ( inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) )
| ( inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 ) ),
inference(demodulation,[status(thm)],[c_2356,c_3659]) ).
tcf(c_4018,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,inverse(double_divide(X1,inverse(X1))))) = X0,
inference(demodulation,[status(thm)],[c_3688,c_3659]) ).
tcf(c_4019,plain,
( ( a2 != a2 )
| ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) )
| ( inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) ) ),
inference(demodulation,[status(thm)],[c_4013,c_4018]) ).
tcf(c_4020,plain,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) )
| ( inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) ) ),
inference(equality_resolution_simp,[status(thm)],[c_4019]) ).
tcf(c_4049,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[c_4018,c_2350]) ).
tcf(c_4050,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,double_divide(X1,inverse(X1)))) = X0,
inference(superposition,[status(thm)],[c_4018,c_4018]) ).
tcf(c_4175,plain,
! [X0: $i,X1: $i] : double_divide(inverse(X0),inverse(double_divide(X1,X0))) = inverse(X1),
inference(superposition,[status(thm)],[c_2350,c_4049]) ).
tcf(c_4193,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X1,inverse(X1))) = inverse(X0),
inference(superposition,[status(thm)],[c_4050,c_4049]) ).
tcf(c_4207,plain,
! [X0: $i,X1: $i] : double_divide(X0,inverse(X0)) = double_divide(X1,inverse(X1)),
inference(superposition,[status(thm)],[c_4193,c_3697]) ).
tcf(c_4883,plain,
! [X0: $i,X1: $i] : double_divide(inverse(X0),inverse(X1)) = inverse(double_divide(X1,X0)),
inference(superposition,[status(thm)],[c_4175,c_3697]) ).
tcf(c_4891,plain,
! [X0: $i,X1: $i] : inverse(double_divide(double_divide(X0,X1),X1)) = inverse(X0),
inference(demodulation,[status(thm)],[c_4175,c_4883]) ).
tcf(c_5015,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,X1),X1) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_4891,c_4049]) ).
tcf(c_5023,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,X1),X1) = X0,
inference(light_normalisation,[status(thm)],[c_5015,c_4049]) ).
tcf(c_5093,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(superposition,[status(thm)],[c_3697,c_5023]) ).
tcf(c_5202,plain,
! [X0: $i,X1: $i] : double_divide(X0,X1) = double_divide(X1,X0),
inference(superposition,[status(thm)],[c_5093,c_3697]) ).
tcf(c_5207,plain,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) )
| ( inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != inverse(double_divide(c3,inverse(double_divide(a3,b3)))) ) ),
inference(demodulation,[status(thm)],[c_4020,c_5202]) ).
tcf(c_5212,plain,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ) ),
inference(equality_resolution_simp,[status(thm)],[c_5207]) ).
tcf(c_5218,plain,
inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))),
inference(ground_joinability,[status(thm)],[c_5212,c_5202]) ).
tcf(c_5219,plain,
! [X0: $i] : inverse(double_divide(X0,inverse(X0))) != inverse(double_divide(a1,inverse(a1))),
inference(superposition,[status(thm)],[c_4207,c_5218]) ).
tcf(c_5227,plain,
$false,
inference(equality_resolution,[status(thm)],[c_5219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP108-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 13:34:04 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 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...
% 3.80/1.20 % SZS status Started for theBenchmark.p
% 3.80/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 3.80/1.20
% 3.80/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.80/1.20
% 3.80/1.20 % ------ iProver source info
% 3.80/1.20
% 3.80/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 3.80/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.80/1.20 % git: non_committed_changes: false
% 3.80/1.20
% 3.80/1.20 % ------ Parsing...% successful
% 3.80/1.20
% 3.80/1.20
% 3.80/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.80/1.20
% 3.80/1.20 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.80/1.20
% 3.80/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.80/1.20
% 3.80/1.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.80/1.20 % ------ Proving...
% 3.80/1.20 % ------ Problem Properties
% 3.80/1.20
% 3.80/1.20 %
% 3.80/1.20 % clauses 2
% 3.80/1.20 % conjectures 1
% 3.80/1.20 % EPR 0
% 3.80/1.20 % Horn 2
% 3.80/1.20 % unary 1
% 3.80/1.20 % binary 0
% 3.80/1.20 % lits 5
% 3.80/1.20 % lits eq 5
% 3.80/1.20 % fd_pure 0
% 3.80/1.20 % fd_pseudo 0
% 3.80/1.20 % fd_cond 0
% 3.80/1.20 % fd_pseudo_cond 0
% 3.80/1.20 % AC symbols 0
% 3.80/1.20
% 3.80/1.20 % ------ Schedule dynamic 5 is on
% 3.80/1.20
% 3.80/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.80/1.20
% 3.80/1.20
% 3.80/1.20 % ------
% 3.80/1.20 % Current options:
% 3.80/1.20 % ------
% 3.80/1.20
% 3.80/1.20
% 3.80/1.20 %
% 3.80/1.20
% 3.80/1.20 % ------ Proving...
% 3.80/1.20 %
% 3.80/1.20
% 3.80/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 3.80/1.20
% 3.80/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.80/1.20
% 3.80/1.20
%------------------------------------------------------------------------------