%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.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 02:38:08 PM UTC 2026
% Result : Unsatisfiable 4.13s 1.30s
% Output : CNFRefutation 4.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 74 ( 62 unt; 1 def)
% Number of atoms : 202 ( 58 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 59 ( 32 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-1 aty)
% Number of variables : 91 ( 0 sgn 91 !; 0 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
fof(f2,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).
fof(f9,axiom,
! [X2,X0,X1] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity2) ).
fof(f19,axiom,
! [X2,X0,X1] :
( product(additive_inverse(X0),X1,additive_inverse(X2))
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_lemma2) ).
fof(f21,axiom,
sum(b,additive_inverse(c),bS_Ic),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_plus_inverse_c) ).
fof(f22,axiom,
product(a,b,aPb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
fof(f23,axiom,
product(a,c,aPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c) ).
fof(f24,axiom,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aPb_plus_IaPc) ).
fof(f25,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_times_bS_Ic_is_aPb_S__IaPc) ).
tcf(c_74,plain,
! [X0: $i] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_75,plain,
! [X0: $i] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_79,plain,
! [X0: $i] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[],[f6]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X2,X5,X4)
| ~ sum(X1,X5,X3)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(additive_inverse(X0),X1,additive_inverse(X2))
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_94,plain,
sum(b,additive_inverse(c),bS_Ic),
inference(cnf_transformation,[],[f21]) ).
tcf(c_95,plain,
product(a,b,aPb),
inference(cnf_transformation,[],[f22]) ).
tcf(c_96,plain,
product(a,c,aPc),
inference(cnf_transformation,[],[f23]) ).
tcf(c_97,plain,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
inference(cnf_transformation,[],[f24]) ).
tcf(c_98,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
inference(cnf_transformation,[],[f25]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(additive_inverse(X0),X1) = additive_inverse(X2) )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_92]) ).
tcf(c_115,plain,
add(b,additive_inverse(c)) = bS_Ic,
inference(well_definedness,[status(thm)],[c_94]) ).
tcf(c_116,plain,
multiply(a,b) = aPb,
inference(well_definedness,[status(thm)],[c_95]) ).
tcf(c_117,plain,
multiply(a,c) = aPc,
inference(well_definedness,[status(thm)],[c_96]) ).
tcf(c_118,plain,
add(aPb,additive_inverse(aPc)) = aPb_S_IaPc,
inference(well_definedness,[status(thm)],[c_97]) ).
tcf(c_119,plain,
multiply(a,bS_Ic) != aPb_S_IaPc,
inference(well_definedness,[status(thm)],[c_98]) ).
tcf(c_120,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_74]) ).
tcf(c_121,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(well_definedness,[status(thm)],[c_75]) ).
tcf(c_125,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(well_definedness,[status(thm)],[c_79]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( add(X2,X5) = X4 )
| ( add(X1,X5) != X3 )
| ( add(X0,X3) != X4 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_81]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( add(X1,X0) = X2 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_82]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X0,X5) = X6 )
| ( add(X2,X4) != X6 )
| ( add(X1,X3) != X5 )
| ( multiply(X0,X3) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_86]) ).
tcf(c_280,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(unflattening,[status(thm)],[c_130]) ).
tcf(c_283,plain,
! [X0: $i,X1: $i] : additive_inverse(multiply(X0,X1)) = multiply(additive_inverse(X0),X1),
inference(unflattening,[status(thm)],[c_111]) ).
tcf(c_291,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_128]) ).
tcf(c_295,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_138]) ).
tcf(c_346,definition,
iPr_def_10 = multiply(a,bS_Ic),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_347,plain,
iPr_def_10 != aPb_S_IaPc,
inference(demodulation,[status(thm)],[c_119,c_346]) ).
tcf(c_424,plain,
multiply(additive_inverse(a),b) = additive_inverse(aPb),
inference(superposition,[status(thm)],[c_116,c_283]) ).
tcf(c_425,plain,
multiply(additive_inverse(a),c) = additive_inverse(aPc),
inference(superposition,[status(thm)],[c_117,c_283]) ).
tcf(c_426,plain,
multiply(additive_inverse(a),bS_Ic) = additive_inverse(iPr_def_10),
inference(superposition,[status(thm)],[c_346,c_283]) ).
tcf(c_428,plain,
add(aPb,multiply(additive_inverse(a),c)) = aPb_S_IaPc,
inference(demodulation,[status(thm)],[c_118,c_425]) ).
tcf(c_441,plain,
add(aPc,multiply(additive_inverse(a),c)) = additive_identity,
inference(superposition,[status(thm)],[c_425,c_125]) ).
tcf(c_514,plain,
! [X0: $i] : add(b,add(additive_inverse(c),X0)) = add(bS_Ic,X0),
inference(superposition,[status(thm)],[c_115,c_291]) ).
tcf(c_517,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = add(additive_identity,X1),
inference(superposition,[status(thm)],[c_125,c_291]) ).
tcf(c_520,plain,
! [X0: $i] : add(aPc,add(multiply(additive_inverse(a),c),X0)) = add(additive_identity,X0),
inference(superposition,[status(thm)],[c_441,c_291]) ).
tcf(c_523,plain,
! [X0: $i] : add(aPc,add(multiply(additive_inverse(a),c),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_520,c_120]) ).
tcf(c_813,plain,
add(bS_Ic,additive_inverse(additive_inverse(c))) = add(b,additive_identity),
inference(superposition,[status(thm)],[c_125,c_514]) ).
tcf(c_820,plain,
add(bS_Ic,additive_inverse(additive_inverse(c))) = add(additive_identity,b),
inference(theory_normalisation,[status(thm)],[c_813,c_291,c_280]) ).
tcf(c_822,plain,
add(bS_Ic,additive_inverse(additive_inverse(c))) = b,
inference(demodulation,[status(thm)],[c_820,c_120]) ).
tcf(c_827,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_517,c_120]) ).
tcf(c_832,plain,
! [X0: $i] : additive_inverse(additive_inverse(X0)) = add(X0,additive_identity),
inference(superposition,[status(thm)],[c_125,c_827]) ).
tcf(c_833,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(superposition,[status(thm)],[c_280,c_827]) ).
tcf(c_850,plain,
! [X0: $i] : additive_inverse(additive_inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_832,c_121]) ).
tcf(c_855,plain,
add(bS_Ic,c) = b,
inference(demodulation,[status(thm)],[c_822,c_850]) ).
tcf(c_856,plain,
add(c,bS_Ic) = b,
inference(theory_normalisation,[status(thm)],[c_855,c_291,c_280]) ).
tcf(c_897,plain,
! [X0: $i] : add(multiply(X0,c),multiply(X0,bS_Ic)) = multiply(X0,b),
inference(superposition,[status(thm)],[c_856,c_295]) ).
tcf(c_909,plain,
! [X0: $i] : add(aPc,add(X0,multiply(additive_inverse(a),c))) = X0,
inference(superposition,[status(thm)],[c_425,c_833]) ).
tcf(c_1184,plain,
add(aPc,aPb_S_IaPc) = aPb,
inference(superposition,[status(thm)],[c_428,c_909]) ).
tcf(c_1198,plain,
! [X0: $i] : add(aPc,add(aPb_S_IaPc,X0)) = add(aPb,X0),
inference(superposition,[status(thm)],[c_1184,c_291]) ).
tcf(c_1212,plain,
! [X0: $i] : add(aPb,add(additive_inverse(aPb_S_IaPc),X0)) = add(aPc,X0),
inference(superposition,[status(thm)],[c_827,c_1198]) ).
tcf(c_1758,plain,
add(aPc,additive_inverse(aPb)) = additive_inverse(aPb_S_IaPc),
inference(superposition,[status(thm)],[c_1212,c_833]) ).
tcf(c_1760,plain,
add(aPc,multiply(additive_inverse(a),b)) = additive_inverse(aPb_S_IaPc),
inference(light_normalisation,[status(thm)],[c_1758,c_424]) ).
tcf(c_2494,plain,
add(aPc,multiply(additive_inverse(a),b)) = multiply(additive_inverse(a),bS_Ic),
inference(superposition,[status(thm)],[c_897,c_523]) ).
tcf(c_2500,plain,
add(aPc,multiply(additive_inverse(a),b)) = additive_inverse(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_2494,c_426]) ).
tcf(c_2509,plain,
additive_inverse(aPb_S_IaPc) = additive_inverse(iPr_def_10),
inference(demodulation,[status(thm)],[c_1760,c_2500]) ).
tcf(c_2567,plain,
add(aPb_S_IaPc,additive_inverse(iPr_def_10)) = additive_identity,
inference(superposition,[status(thm)],[c_2509,c_125]) ).
tcf(c_2640,plain,
add(iPr_def_10,additive_identity) = aPb_S_IaPc,
inference(superposition,[status(thm)],[c_2567,c_833]) ).
tcf(c_2656,plain,
add(iPr_def_10,additive_identity) != iPr_def_10,
inference(demodulation,[status(thm)],[c_347,c_2640]) ).
tcf(c_2657,plain,
$false,
inference(ground_joinability,[status(thm)],[c_2656,c_121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 07:42:54 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 4.13/1.30 % SZS status Started for theBenchmark.p
% 4.13/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 4.13/1.30
% 4.13/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.13/1.30
% 4.13/1.30 % ------ iProver source info
% 4.13/1.30
% 4.13/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.13/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.13/1.30 % git: non_committed_changes: false
% 4.13/1.30
% 4.13/1.30 % ------ Parsing...% successful
% 4.13/1.30
% 4.13/1.30
% 4.13/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.13/1.30
% 4.13/1.30 % ------ Preprocessing... sup_sim: 20 sf_s rm: 0 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.13/1.30
% 4.13/1.30 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 4.13/1.30 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.13/1.30
% 4.13/1.30 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.13/1.30 % ------ Proving...
% 4.13/1.30 % ------ Problem Properties
% 4.13/1.30
% 4.13/1.30 %
% 4.13/1.30 % clauses 17
% 4.13/1.30 % conjectures 0
% 4.13/1.30 % EPR 1
% 4.13/1.30 % Horn 17
% 4.13/1.30 % unary 17
% 4.13/1.30 % binary 0
% 4.13/1.30 % lits 17
% 4.13/1.30 % lits eq 17
% 4.13/1.30 % fd_pure 0
% 4.13/1.30 % fd_pseudo 0
% 4.13/1.30 % fd_cond 0
% 4.13/1.30 % fd_pseudo_cond 0
% 4.13/1.30 % AC symbols 1
% 4.13/1.30
% 4.13/1.30 % ------ Schedule UEQ
% 4.13/1.30
% 4.13/1.30 % ------ Option_UEQ Time Limit: 10.
% 4.13/1.30
% 4.13/1.30
% 4.13/1.30 % ------
% 4.13/1.30 % Current options:
% 4.13/1.30 % ------
% 4.13/1.30
% 4.13/1.30
% 4.13/1.30 %
% 4.13/1.30
% 4.13/1.30 % ------ Proving...
% 4.13/1.30 %
% 4.13/1.30
% 4.13/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 4.13/1.30
% 4.13/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.13/1.30
% 4.13/1.30
%------------------------------------------------------------------------------